Wavelength and frequency calculator
Wavelength and frequency, either way round. The constant in the middle is the most exact number in physics, and it is exact for a reason worth knowing. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
A number that cannot be wrong
The speed of light is 299,792,458 metres per second exactly. Not measured to that precision — exactly, with no uncertainty at all, and no possibility of a future experiment revising it.
That is because since 1983 the metre has been defined as the distance light travels in 1/299,792,458 of a second. The speed of light stopped being something we measure and became something we measure with. Improving the experiment now improves our knowledge of how long a metre is, not of how fast light goes.
It is one of very few numbers in science where asking "how accurate is it?" is a category error.
What 3×108 costs
Rounding it is a 0.0692% error, which sounds harmless and mostly is. Where it stops being harmless is anywhere the wavelength is compared against a physical length:
| Exact | Using 3×108 | Out by | |
|---|---|---|---|
| FM radio, 100 MHz | 2.997925 m | 3 m | 2.08 mm |
| Wi-Fi, 2.4 GHz | 124.914 mm | 125 mm | 0.09 mm |
| 5 GHz channel | 59.958 mm | 60 mm | 0.04 mm |
An antenna cut to a quarter wavelength from the rounded number is half a millimetre long at FM, which is inside the tolerance you could cut it to anyway. The rounding is fine. Knowing that it is a rounding, and of what, is the part worth having.
It works for sound too
The relationship v = fλ is not about light. It is about waves. Set the speed to 343 m/s and it tells you about sound instead — which is why a 20 Hz note, the bottom of human hearing, has a wavelength of about seventeen metres and is very difficult to put in a room.