Wavelength & Frequency Calculator
Convert between wavelength, frequency, and photon energy for light and any wave, using the wave equation and Planck's relation.
Como usar esta calculadora
- 1Choose whether you know the frequency or the wavelength.
- 2Enter the value and pick its unit — nanometres for light, MHz for radio, and so on.
- 3Leave the speed as the speed of light for electromagnetic waves, or set it to 343 m/s for sound in air.
Como funciona
The wave equation and Planck's relation
speed = frequency × wavelength (v = f λ) wavelength = speed ÷ frequency frequency = speed ÷ wavelength photon energy E = h × f (h = 6.626 × 10⁻³⁴ J·s) for light, speed = c = 299,792,458 m/s
Every wave obeys one simple relationship: its speed equals its frequency times its wavelength. Since the speed is fixed for a given medium, frequency and wavelength are two sides of the same coin — raise one and the other falls. For light, Planck's relation adds a second layer: each wave also carries energy in discrete photons, and that energy is proportional to the frequency, which is why high-frequency ultraviolet and X-rays are far more energetic and damaging than low-frequency radio.
Exemplo resolvido
Green light has a wavelength of about 550 nm (5.5 × 10⁻⁷ m). Its frequency is c ÷ λ = 2.998×10⁸ ÷ 5.5×10⁻⁷ ≈ 5.45 × 10¹⁴ Hz, and each photon carries h × f ≈ 3.6 × 10⁻¹⁹ J, or about 2.25 electronvolts.
Wavelength & Frequency Calculator: o guia completo
Two descriptions of the same wave
Frequency counts how many wave crests pass a point each second; wavelength measures the distance between crests. They are not independent — for a wave travelling at a fixed speed, they are locked together by v = fλ. A radio station described as '100 MHz' and 'a 3-metre wavelength' is describing the very same wave two ways, and multiplying them always returns the wave's speed.
This is why the same electromagnetic spectrum is labelled by wavelength at one end and frequency at the other, purely out of convenience. Radio engineers talk in megahertz because the wavelengths are metres long; opticians talk in nanometres because the frequencies are hundreds of terahertz. Both are correct, and this calculator converts freely between them.
The electromagnetic spectrum is all one thing
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays are not different phenomena — they are the same electromagnetic wave at different frequencies. What separates a radio broadcast from a lethal gamma ray is only the frequency, spanning some twenty orders of magnitude, and every one of them travels at exactly the speed of light in a vacuum.
Visible light occupies a tiny slice of this range, roughly 400 nm (violet) to 700 nm (red). The colours we see are simply the frequencies our eyes evolved to detect, a narrow window in an enormous spectrum. Bees see into the ultraviolet, snakes sense infrared, and our instruments reach the rest — but it is all the same underlying wave.
Why high frequency means high energy
Planck's relation, E = hf, says a wave's energy per photon rises with its frequency. This is the reason the spectrum is dangerous at one end and harmless at the other. Radio waves and microwaves are low frequency and low energy — they cannot break chemical bonds. Ultraviolet, X-rays, and gamma rays are high frequency and high energy, energetic enough to damage DNA, which is why they cause sunburn and are used, carefully, to kill cancer cells.
It also explains why a dim ultraviolet lamp can harm your skin while a powerful radio transmitter cannot. Total power is spread across many photons; what matters for breaking bonds is the energy of each individual photon, and that is set purely by frequency. A single UV photon carries more punch than millions of radio photons combined.
Perguntas frequentes
How do I convert frequency to wavelength?
Divide the wave's speed by the frequency: wavelength = speed ÷ frequency. For light, use the speed of light (299,792,458 m/s). A 100 MHz radio wave has a wavelength of about 3 metres.
Why are frequency and wavelength inversely related?
Because their product is the wave's speed, which is fixed for a given medium. If the speed cannot change, then raising the frequency must lower the wavelength by the same factor, and vice versa. They are two ways of describing one wave.
What is a photon's energy?
The energy carried by a single quantum of light, given by Planck's relation E = h × f, where h is Planck's constant. Higher-frequency light has higher-energy photons — which is why ultraviolet and X-rays are ionising and dangerous while radio waves are not.
Does this work for sound as well as light?
Yes, the wave equation v = fλ applies to any wave. Just set the wave speed appropriately — 343 m/s for sound in air at 20 °C instead of the speed of light. The photon-energy outputs are specific to electromagnetic waves and are hidden for other speeds.