Show the Working

One thousand two hundred and thirty-seven tools, no nonsense

Each one does a single job, shows its working, and needs no account. All but two run entirely in your browser, with nothing uploaded. The exceptions are the VIN decoder and the stolen-bike check, and each says so at the top of its own page — a vehicle's identity and a bicycle's history are not things that can be worked out from the number alone. Both ask a public register and neither passes through this site.

Matrix determinant and inverse Determinant, inverse and condition number by elimination rather than cofactors — and the reason no threshold on a determinant can tell a singular matrix from a small one, since scaling the entries by k multiplies it by kⁿ while the condition number does not move. Probability of two events P(A and B), P(A or B) and at least one in n tries — each as the range it genuinely lies in, because two probabilities do not determine the third and at 0.1 and 0.1 that range is ten times the answer every other calculator prints. Fuel cost and economy What a journey costs, with your economy in all four units — because the imperial and US gallons are 20.09% apart, and because miles per gallon is a reciprocal, so the same +5 mpg saves eighteen times as much fuel at 10 mpg as at 50. Horsepower and torque Power from torque and rpm in all three units called horsepower, which differ by 1.387% — and why every torque and power curve ever plotted crosses at 5252 rpm, which is a fact about 33,000 ÷ 2π rather than about any engine. Wilks and IPF GL points Both versions of Wilks side by side, because they disagree by up to a quarter and reverse the order of a third of tied lifters — and the IPF's own coefficients, marked with the date their stated validity expired. BMR and daily calories All three published equations with the error bar the researchers published — because the equations differ by about 70 kcal for one person and a single equation's own 95% range is 426 kcal wide. The argument everybody has is a sixth of the problem. Body fat from a tape measure The US Navy equation, with the band that decides which category you land in — and beside it the other formula published under the same name, which across 1.35 million swept measurements never comes within nineteen points of it for a woman. Heart rate zones Both of the methods called “heart rate zones”, and the distance between them — which is exactly your resting rate times how far below maximum you are working. They agree only at 100%, which is why nobody notices. All 588 file converters Grouped by what you are starting from. Every one runs in your browser — the file never leaves your device, so there is nothing to upload and nothing to queue for. All 445 unit conversions Grouped by what they measure. Each gives the exact factor, says whether the conversion is exact by definition, and shows what the rounded version everybody carries in their head actually costs. Any serial number One box. Type a serial and it runs the number past every dating scheme on this site at once, showing all of them it fits — because a television and a tractor can share a numbering scheme, and nothing in the number says which you are holding. Exact fits are kept apart from partial ones. Recipes 2064 recipes, each one written for this site rather than adapted from anybody else's. Dishes that are easily confused are written together, so each page says what it is that the others are not. Browse by protein or by country. Every page says plainly whether it is vegetarian and what stops it being so, because fish sauce is in almost everything. Baby names Every US name 1880–2025, with the real counts

Algebra and number theory

Combinations and permutations All four answers to “how many ways”, exactly — because n! overflows long before the answer does Exponents and roots Powers and roots, including the cube root of −8 — where JavaScript says NaN, Python says 1+1.73i and the real answer is −2. Three defensible answers, and your calculator picked one silently. Factorial calculator Every digit of n!, however many there are — because 23! is the first a double gets wrong and 171! is the first it cannot hold at all Highest common factor and LCM HCF and LCM of any number of values, with Euclid's method written out step by step Logarithm calculator Any base, using the dedicated function — because the change-of-base identity everyone uses gives 2.9999999999999996 for the logarithm of a thousand Number sequences Arithmetic and geometric sequences with the nth term and the sum, the closed form checked against the running total — and an honest stop at the term where the arithmetic leaves the numbers a computer can hold. Prime factorisation Prime factors, powers and the divisor count — the one calculation here with nothing to disown Quadratic solver ax² + bx + c = 0 without losing a root — the formula everybody learns returns zero for one of them Root calculator Square, cube and any nth root, including the odd roots of negative numbers that pow-based calculators return as an error

Arithmetic and averages

Geometric mean The average for things that multiply, computed through logs — because multiplying two hundred values together and rooting the product returns Infinity Long division Long division with every step, and the recurring block found exactly by watching the remainders rather than the digits Percent error Percent error with both denominators shown, because dividing by the measured value instead of the accepted one is common, gives a different answer, and is almost never labelled. Percentage difference How far apart two numbers are when neither came first, shown beside the percentage change people often mean instead. They agree on almost nothing Proportion calculator Solve a : b = c : x with the cross-multiplication written out, and without the overflow the usual order of operations causes Rounding calculator Half up or banker's rounding, showing the exact value in the machine that decided the answer Scientific notation To and from standard form, and then the exact value your machine is really holding — every digit of it Significant figures Figures rather than places, with the trailing-zero ambiguity reported rather than guessed at Weighted average A weighted mean of anything, with the weights normalised — because multiplying and adding without dividing is right only when they happen to total 1

Around the house

How old is my appliance? GE publish a full decoder and it gives up to six different years for the same letter. Shows all of them, along with the two years GE's own chart lists twice. Camera and lens dating Of 311 camera and lens makers, not one publishes a serial-to-year table — not Leica, not Nikon, not Canon. Leica tell you where the number is and not what it means. Zenit built the tool and it is broken. Dew point Dew point from temperature and humidity with the Magnus coefficients named, so the working can be reproduced — and why it predicts how a day will feel when relative humidity cannot. Firearm serial dating No decoder, deliberately. What the makers publish is described and linked rather than computed, because none of it is in a form anyone should compute from. What does the hallmark on my silver mean? 925, 750 and the pictures beside them, from the Hallmarking Act 1973 — including why the figure struck is not always the fineness, and why a missing date letter means nothing at all. Heat index The full National Weather Service procedure, including the simpler formula it uses below 80 °F and the two adjustments most implementations drop — and the fact that the whole thing assumes you are in the shade. How old is my air conditioner? Trane's published decoder dates a unit to the day — finer than anything else here. Rheem's gives month and year. Both read from the makers' own documents, including a typo of Rheem's that the page points out. Tool date codes Snap-on's is the code everyone searches for and Snap-on publish nothing about it. Milwaukee publish theirs in full — including seven battery formats, two of which read the same four digits in opposite orders. Watch dating Not one of 326 watch makers publishes a serial-to-year table. Several sell you the answer instead — what each offers, what it costs, and why the free charts elsewhere are not copied here. Wind chill Wind chill on the formula that replaced the famous one in 2001 — and a refusal outside the narrow range it is defined for. The old index was never a temperature at all: it measured how fast water froze in a bottle.

Binary and bases

Binary calculator Add, subtract, multiply and divide in any base, exactly, at any size — and what integer division does with the remainder Bitwise calculator AND, OR, XOR and both shifts above 32 bits, where JavaScript’s own operators silently stop being correct Number base converter Any base from 2 to 36, on numbers past 253 that a converter going through a JavaScript number would have already rounded Two's complement The bits actually stored for a signed number, and why the range holds one more negative than positive

Building and DIY

Aggregate The volume exactly — and why no standard will tell you what it weighs Ramp gradient 1:12 is only the limit for a two-metre flight — at ten metres it is 1:20 Roof pitch Degrees, rise-in-twelve, one-in-n or per cent — a bare “6” means 26.57° or 9.46° Staircases Every rise and going Part K permits for your floor height — with 2R+G kept separate, because it is a footnote

Chemistry

Atomic mass The standard atomic weight of any element with its uncertainty — including the fourteen that have no single value, and why lead is a range Concentration g/L, mg/L, % w/v, % w/w and ppm from one mass and one volume, with the density assumption inside ppm stated rather than hidden Density Mass over volume in any units, with what floats — and why 1.000 g/cm³ for water is true at one temperature and nowhere else Dilution C₁V₁ = C₂V₂ solved for whichever you leave blank, with the solvent to add — and why the easiest formula in chemistry teaches the worst habit Molar mass Molar mass from a formula, with the multiplication shown and the uncertainty that decides how many decimal places are real: Li₂CO₃ is 73.9, not 73.8880 Molarity Moles per litre from a mass and a volume — and which volume the formula actually means, which no arithmetic can check for you Mole calculator Mass, moles and molecules, any one to the other two, with the molar mass worked out in front of you rather than asserted pH pH from the charge balance, not the textbook shortcut — which says a very dilute acid is alkaline, and puts neutral at 7 when it is 6.995 at 25°C and 6.13 at boiling

Codes and markings

Date codes on everyday things Zippo stamp the month and year on the bottom of every lighter, and Browning use a letter cipher. Both decoded from the makers' own published keys. What does the E mark mean? The mark on a helmet, child seat, tyre or headlamp says which country granted its approval — not where it was made, and not when. There are two marks and almost everyone calls both of them the E mark. What do the numbers on an egg mean? A farming method digit, a country code and a producer number — and not a date, which is what nearly everyone takes it for. Including why Greece is EL and Croatia is missing entirely. What year is my engine? The EPA family name The twelve characters on a US emissions label start with a model year code — which for mowers, chainsaws, generators, outboards and snowmobiles is the only date anybody outside the factory can read. What does an FCC ID mean? Every wireless device has one: a grantee code then a product code. The regulation that creates it never says how long the first part is — so this page explains what it does settle, and refuses to guess. Is my gas cylinder out of date? The stamp on a propane bottle says when it was last requalified and which test was used — but not when it expires, because that depends on a specification stamped elsewhere. Includes the symbol 49 CFR 180.213 defines twice. What do the numbers on a hazard placard mean? Four digits on an orange plate, looked up in the Hazardous Materials Table — 2,480 entries reproduced whole, because a work of the US government carries no copyright. This one actually decodes. What do the numbers on a medicine box mean? The serial beside the 2D barcode is required by law to be generated at random, so it holds no date and no batch — and in Great Britain the regulation behind it has been revoked. What do the markings on a pallet mean? A country code, a producer number and a treatment abbreviation, read from 7 CFR 319.40-3 — including why a code this page cannot decode is not a bad code. What do the numbers on my tyre mean? 205/55 R16 91V decoded from the regulation that defines it — what it carries, how fast it is rated, and why the speed table is not in alphabetical order. How old are your tyres? Four digits on the sidewall give the week and year a tyre was made, and this reads them straight from 49 CFR 574.5 — a regulation that, unusually, defines its own week. It is not the week anyone else uses. What does an NDC number mean? A labeler, a product and a package code — and five permitted shapes, three of them ten digits long, so without the hyphens the number cannot be split at all.

Colour

Blend two colours Two colours mixed, shown both ways: averaging the hex values and mixing the actual light. Black and white come out 60 levels apart Colour converter Hex, RGB, HSL, HSV and CMYK, with the sum that produced them — and why HSL and HSV disagree Colour schemes Complementary, triad, tetrad and the rest — each colour rated for contrast, because a triad of red hides one you cannot read at 1.37:1 Contrast checker WCAG contrast against AA and AAA, showing the linearisation every other checker hides Invert a colour Inverting is not taking the complement, and the two agree for half a per cent of colours — both shown side by side Lighten and darken Lighten, darken, saturate or rotate the hue, with the light shown beside the lightness — the same +10 raises blue by 42.5% and yellow by 0.26%

Cooking

Air fryer conversion Five published rules for converting an oven recipe, and no two agree. The manufacturer's own manual says ten degrees; the figure everybody repeats is twenty, and the one UK body that publishes it contradicts itself in its own chart. Baker's percentage Every ingredient against the flour weight, which is what the convention actually means — and both readings of “hydration”, because the same dough is 70% and 41% depending which denominator you use, and recipes use both. Baking tin size What a different tin does to a recipe — area, not width, which is why one inch is a quarter more Boiling point at altitude What water boils at where you are, checked against the IAPWS steam tables — and the height above which an egg white will never firm up however long you boil it, because the temperature it needs is simply never reached. Butter converter Sticks, cups, tablespoons and grams, with the USDA weight each one came from Coffee ratio How much coffee for how much water at the SCA Golden Cup standard — which is 55 g per litre, or 1:18.18. The “1:18” everybody quotes is about 1% stronger than the standard it claims to be. Cooking converter Cups, spoons and millilitres — all five cups and all three tablespoons, saying which it used Cups to grams Volume to weight, with the density named and the USDA record it came from Grams to cups Weight to volume, and how far the answer moves depending on how you fill the cup Oven temperature °C, °F, gas mark and fan — including the mark two published charts disagree about Recipe scaling Scale a recipe, and see what does NOT scale: time, tin size and eggs

Dates and time

Add or subtract from a date Days, weeks, months or years on or off a date — and whether the answer comes back if you undo it Day of the year The ordinal date, the quarter, and the astronomical Julian Day beside it, because those two get confused Leap years The three-clause rule, and which clause decided it — 1900 was not one and 2000 was Time zones A time in one zone shown in another, with each one's clock changes found by walking the year Unix timestamps Timestamps to dates and back, with the twenty-seven leap seconds it omits by design Week number The ISO week number and the year it belongs to — which is not always the year the date is in

Electricity

LED resistor The series resistor for an LED, rounded UP to a value you can buy — because the nearest one lets too much current through Ohm's law Any two of voltage, current, resistance and power give the other two, with the E24 part you could actually buy Resistor colour code Bands to a value and back, IEC 60062:2016 — and miscounting them is a factor of ten thousand Series and parallel Series and parallel for resistors, capacitors and inductors — capacitors are the other way round Voltage divider What two resistors give you, and what happens the moment you connect something to the output Wire gauge AWG to millimetres from the two diameters that define the scale — and what a gauge does not tell you

Gases and heat

Boyle's law Pressure and volume at constant temperature — the one gas law whose units cannot catch you out, which is why it teaches nobody to check the others Charles's law Volume and temperature, with what the same sum gives in Celsius: two litres where the answer is 1.068, and a division by zero at 0°C Ideal gas law PV = nRT in any units, with the gas constant that matches them — because the wrong R turns 22.414 litres into 2,271 Specific heat Q = mcΔT solved four ways, and why water’s 4184 J/(kg K) is a definition wearing a measurement’s clothes Speed of sound The speed of sound from √(γRT/M), with the familiar 331.3 + 0.606t beside it — a fit that touches the real curve twice and only across the weather

Health and fitness

Alcohol units A unit is ten millilitres of pure ethanol, so a large glass of wine is three and a quarter of them BMI calculator Kilograms, stones or pounds — plus the lower thresholds NICE recommends for some ethnic backgrounds, which most calculators ignore. Calorie calculator Daily calories from the Mifflin-St Jeor equation, with the arithmetic shown and a floor it will not recommend going below. Due date Naegele's rule is two rules that disagree by up to three days — and 4% of babies arrive on the day Max heart rate Fox, Tanaka, Gulati and Nes side by side, with what each one actually rests on. The famous “220 minus age” was never a study — and it agrees exactly with the properly derived formulas at 25 and at 40, which is why nobody notices. One-rep max All seven published formulas at once — Epley, Brzycki, Lander, Lombardi, Mayhew, O’Conner and Wathen — with each author’s own repetition limit shown against every row. They disagree by 12% at twelve reps, and two of them return negative numbers if you push them far enough. Race time predictor Riegel's formula, and your own fade rate fitted from two races you have actually run — because two runners with the same 5 km time can be forty-five minutes apart over a marathon, and Riegel gives them both the same answer. Running pace calculator Distance, time and pace: fill in any two and the third follows, in per-kilometre and per-mile at once. Includes the real race distances — 42.195, not 42 — and even splits. Waist to height Keep your waist under half your height — NICE's 2022 rule, and where to put the tape

Money

Discounts Stack as many discounts as you like — they do not add up, and 20% then 10% is 28% Interest rates Nominal to AER and back at any compounding frequency, and what APR actually includes Loan & mortgage calculator The payment on a loan or mortgage from three numbers, with the formula printed using your own figures and the first payment split into interest and capital. Overpayments and fees are there if you want them. Percentage calculator Type two numbers and get every percentage relationship between them at once — percent of, percent change, percent off, percent added — each with its arithmetic beside it. No choosing a form first. Salary converter Pay converted between hourly, daily, weekly, monthly and yearly all at once, with the hours-and-weeks assumptions printed on every reading — because those assumptions are the whole of the conversion. Compound interest & savings calculator What savings grow to, from three numbers. Shows the AER behind your quoted rate, how much of the total is interest rather than money you put in, and the year the interest starts outpacing your deposits. SIP calculator What a monthly investment grows to, with an annual step-up and an inflation-adjusted figure showing what it will actually buy. VAT Add VAT or take it off — and taking it off is a division, not a subtraction

Musical instruments and gear

Amplifier dating Most amps have no usable serial, but nearly all carry a date code on the pots and transformers. Reads it, shows every year it could be — and is clear that it dates the part, not the amplifier. Band instrument dating Ludwig, Gemeinhardt and Conn-Selmer publish 818 rows between them. Those tables contradict themselves in places, and the page shows where rather than quietly tidying it up. Guitar serial dating Ninety-one makers, from published sources — showing every year a serial could be, because plenty of them cover more than one. Of 253 makers looked at, a little under half cannot be dated from the number by anybody. NAM file inspector What is actually inside a Neural Amp Modeler capture — including the sample rate it expects, which most of them do not state. NAM to NAMB Convert a .nam capture to the compact binary format, in your browser Pedal dating Most pedal makers publish nothing, but the chips inside carry the week they were made. Reads that code, shows every year it could be — and is honest that the list of makers is thin, because seven of the best-known have no Wikipedia entry at all. Piano dating Kawai and Grotrian publish their serial ranges; almost nobody else does. Shows every year a number could be — Kawai's own tables overlap, so some numbers genuinely have more than one answer. Synth and keyboard dating Not one of 72 keyboard makers publishes a serial table. The chips inside do carry dates, so this reads those — and is clear that it gives you the earliest the instrument can be, not when it was built.

Numbers and dates

Mean, median, mode & standard deviation Paste a list of numbers and get every average and spread at once. Shows BOTH the sample and population standard deviation rather than making you choose, and says which one you want. Date & age calculator The gap between two dates in years, months and days, plus total days, working days and the next anniversary — and it tells you which convention it used for months, because a month is not a fixed length. Fraction calculator Type 1/2 + 3/4 in one box and get the answer with the common denominator shown, as a fraction, a mixed number, a decimal and a percentage. Turns decimals back into fractions too, and says how close they really are. Weighted grade calculator Paste your marks and their weights and get the weighted average with the working shown — plus what you would need on whatever is left, and a plain answer when a target is no longer reachable. Hours between two times Hours worked between two times, with breaks off and night shifts handled. Gives the answer both as hours and minutes and as decimal hours, because writing 7h 30m as 7.30 loses twelve minutes every time. Right-angled triangle calculator Fill in any two of the sides, the hypotenuse and an angle, and the rest follows — with Pythagoras and the trigonometry written out using your own numbers. No dropdown asking which two you know. Subnet calculator One box takes 192.168.1.10/24 and gives the network, broadcast, mask, wildcard, usable range and host count — with the binary shown so you can see where the mask cuts, and why 256 addresses give 254 hosts. Unit converter One value and its unit, and every other unit appears at once. Says which gallon and which ton it means, and which conversions are exact by definition rather than approximate.

Oil and gas

Annular velocity How fast mud comes up the gap between the pipe and the hole — and what the pipe not being centred does to it API gravity API, specific gravity and density — with the round specific gravities the 31.1 and 22.3 bands are really made of Hydrostatic pressure Mud weight times true vertical depth, with 0.052 shown to be exactly one part in a thousand high Oil and gas units Barrels, Mcf and boe — where M means a thousand, not a million, and a standard cubic foot is three different things

Paper and print

Aspect ratio The exact ratio, the standard shape it is nearest, and how much of the picture cropping would throw away DPI and print size Pixels to a print size and back — an image has no physical size until something prints it Paper sizes Every ISO and North American size, derived from the standard's own rule — and A0 is not a square metre

Physics

Half-life Half-life, mean lifetime and decay constant are three names for one thing, and swapping two of them is a 44% error that looks entirely reasonable Kinetic energy Half the mass times the speed squared, which squares the unit error too: 108 km/h unconverted is out by 12.96, not 3.6 Potential energy Mass times gravity times height, with 9.80665 named as the definition it is — and the 0.53% spread of the real thing Radioactive decay Activity in becquerels and curies, with what the units mean — one of them is a round number somebody chose, not a measurement of radium Terminal velocity Where gravity and drag balance — and why the drag coefficient is not a constant but a function of the answer you are looking for Wavelength and frequency Wavelength and frequency either way round, using the speed of light exactly — a number that cannot be wrong, because the metre is defined from it

Randomness

Coin flip A fair flip, the longest run, and the exact chance of a run that long — six heads in a hundred is more likely than not Dice roller Any dice, drawn without the modulo bias that makes a naive d20 8% unfair, with the exact distribution of the total Gaussian numbers Normally distributed numbers, and the hard ceiling at 8.57 sigma that Box-Muller cannot get past Pick one at random Pick one at random, with weights, in a single draw — so 0.5 and 2.5 work as well as whole numbers Random colour Random sRGB colours with the luminance and the contrast — and which of black or white text to put on them Random date A date drawn uniformly across the days, not by picking a month and a day, which makes 28 February four times too likely Random name A name drawn uniformly from all 24,204 with a page here — not by picking a letter first, which makes an X name 19 times too likely Random strings Random strings with the entropy worked out honestly, including what “one of each class” costs you Shuffle a list A genuinely uniform shuffle — and the counting argument showing the usual one-liner cannot be one

Shapes and geometry

Circle calculator Radius, diameter, circumference or area — give any one and get the other three, with the arithmetic and what π costs you Distance between two points Distance, midpoint and slope, computed without the overflow that makes the usual formula return Infinity for far-apart points Rectangle calculator Area, perimeter and diagonal in mixed units — and why converting an area with a length factor is out by a factor of three Triangle area Area from three sides — using the rearrangement that survives a thin triangle, where the textbook formula is 14% wrong Trigonometry Sine, cosine and tangent with the exact answer beside the computed one, because sin(30°) works out at 0.49999999999999994 Volume calculator Cube, box, sphere, cylinder and cone, each showing the formula it used and the numbers put into it

Text and generators

Base64 Base64 with both alphabets shown, because the standard one ends in characters that mean something else in a URL — and a string encoded with one and decoded with the other often comes back wrong without complaining. Fancy text generator Fifteen Unicode styles that survive being pasted into bios and messages, with an honest note on what they cost you. Password generator Made in your browser from the operating system's cryptographic randomness and never sent anywhere — with the entropy worked out in bits rather than a colour, and three crack times instead of one made-up one. Random number generator Any range, with or without duplicates. Uses cryptographic randomness and corrects for modulo bias. Roman numerals Numbers to Roman numerals and back, with only the six legal subtractions — IC for 99 looks perfectly reasonable and was never written. Reads IIII, and says why clock faces use it. URL encoding Percent-encoding shown three ways at once, because a space is %20 in a path and + in form data — and the string a+b decodes to two different things depending on where in a URL it sat. Username generator Twelve suggestions at a time in five styles, with length limits and separators that match what platforms actually accept. Word counter Words, characters, sentences and reading time — and a count that excludes citations and quotations, which is what word limits usually mean.

Text and lists

Case converter Nine cases including the programming ones — and why ß gets longer going up Count characters Characters, code points, UTF-16 units and bytes, counted separately — a family emoji is one character and eighteen bytes Find and replace Plain text and patterns kept apart, so a search for 3.50 means three point five nought Number to words In words, British or American — and what a billion meant before 1974 Remove duplicate lines The first of each kept, and you decide whether capitals and spaces count Remove empty lines Blank lines out, counting separately the ones that are truly empty and the ones holding only spaces — identical on screen, different to everything else Remove line breaks Wrapped text back into paragraphs, with a choice of what fills the gap, because joining with nothing welds brown to fox Repeat text A string repeated, with a separator and a stated limit rather than a tab that freezes Reverse text Backwards text that keeps its flags and accents — reversing 🇬🇧 the usual way gives you Bulgaria Sort lines Dictionary, code point or natural order — two of them are right and they disagree Tabs and spaces Tabs expanded to the next STOP rather than a fixed count — which is why every other converter pulls tab-separated columns out of line Trim whitespace Spaces off the ends, and a count of the lines ending in a zero width space, the one kind of space nothing will trim for you Words per minute Typing speed, where a “word” is five characters and never was a word

Vehicles and machines

Is this bike stolen? The one question here that gets asked with money in your hand. Searches Bike Index's free register of 300,000-plus bicycles — and is blunt that no match means nothing at all, because a mistyped character looks exactly the same. How old is my boat? Every US boat carries a 12-character hull number and the Coast Guard say in law what each character means. The build year is one digit and ambiguous ten ways; the model year, three characters later, is not — and fixes it. Heavy plant and farm machinery Of 337 makers of tractors, excavators and forklifts, exactly one publishes a serial decoder — and its terms forbid reproducing it. There is no tool on this page, and the page says why rather than inventing one. How old is my motorcycle? From 1981 the VIN answers it — but the rule that resolves a car's 30-year year-code ambiguity does not cover motorcycles, and before 1981 Harley-Davidson say their own records are limited or non-existent. What do the numbers on a train mean? The twelve figures on a railway vehicle give the type and the country of registration — and the last one is arithmetic on the other eleven, so this is the one tool here that can prove a number impossible. What does an aircraft tail number mean? Nothing about the aircraft — and 14 CFR 47.15 says so positively rather than by omission. What it does give is a complete format, so a bad mark can be told exactly which rule it breaks. What year is my number plate? A UK registration since 2001 carries where it was first registered and when the number was issued. From DVLA’s own leaflet — including why there has never been an 01 plate, and why the car can be older than its plate but never newer. VIN decoder What a vehicle is and which factory built it, from the US government's own database — with the check-digit arithmetic shown so you can see whether the number is genuine.

Statistics

Anscombe's quartet Four datasets that share a mean, a variance, a correlation and a regression line and look nothing alike. Drawn here, with every statistic computed from the published numbers rather than repeated. Confidence intervals Intervals for a mean and a proportion, using t rather than 1.96 and Wilson rather than Wald — the textbook interval gives a lower bound of −3.15% for 2 out of 20, which is not a proportion. Correlation Pearson and Spearman together, because they answer different questions — one asks how straight the relationship is, the other only whether it goes one way. Tied ranks are averaged, which is where implementations quietly disagree. Critical values z, t and chi-square critical values at any alpha, with the surrounding table — and why t is always larger than 1.96, by how much, and why chi-square has only one tail. Linear regression Slope, intercept, R² and the standard error — and every residual listed, because the leftovers are the evidence for whether a straight line was the right shape at all. Mean, median, mode All three averages at once, with the mode saying plainly when there is not one rather than handing back the first value or the whole dataset. Outliers Tukey’s 1.5 × IQR fences, and the same rule under all nine quartile definitions — on some datasets they disagree about whether a value is an outlier at all. P-values p from a t, z or chi-square statistic, with both tails always shown and no badge saying “significant” — because 0.049 and 0.051 are not different findings. Percentiles The value at a percentile and the percentile of a value, which are different questions sharing a word, under all nine published definitions. Quartiles and IQR Q1, Q3 and the interquartile range — and all nine published definitions of a quartile side by side, because they disagree on half of all datasets and no other calculator says which it used. Sample size How many people to survey for the precision you want — and why the answer is 385 whether the population is fifty thousand or fifty million, which is the genuinely surprising part of sampling. Standard deviation Both denominators given and labelled, and the textbook shortcut formula checked against the right answer every time — on some data it is out by hundreds of per cent. T-test One and two sample t-tests that lead with the difference between your groups rather than with p, use Welch by default, and put Cohen's d beside every result. Z scores How many standard deviations from the mean, and the percentile that implies — with a straight account of when that percentile means nothing, and tail probabilities computed without subtracting.

What this site does differently

There are hundreds of tool sites. Most are the same calculator with a different logo, so it is worth saying plainly what is different here.

What you type is not stored

Every tool listed above except the VIN decoder and the stolen-bike check is plain HTML and JavaScript running on your own machine. There is no server doing the calculation, which means there is nothing to log. Your text, your weight, your draw results — none of it is transmitted, and reloading the page loses it.

The two exceptions send one thing each — a VIN, or a bicycle serial — straight from your browser to a public register, and nowhere else. This site never sees either, because the request does not pass through it. Both pages say so above the box rather than below it.

Each tool's own page says this again in its own words, because it is a property of that tool rather than a slogan about the site. Anything added later that genuinely needs a server will say so on its own page, and will not be quietly covered by a promise made here.

The honest test: turn off your wi-fi after the page loads. Everything still works — except those two, which will tell you they could not reach the register rather than pretending to know the answer.