Wavelength calculator
A wavelength calculator finds the length of one wave from its speed and frequency, using the wave equation: wavelength = speed ÷ frequency, or λ = v/f. Our Wave Speed Calculator finds the wavelength, the frequency or the speed from the other two, for sound, light or any wave, and for light it tells you which part of the electromagnetic spectrum you are in.
Choose Wavelength to find λ, or Frequency to go the other way, for a frequency to wavelength calculator or the reverse. It opens on a sound wave at 440 Hz.
Wave Speed Calculator
Link wave speed, frequency and wavelength
How to use the wavelength calculator
- Choose what to find: Wavelength, Frequency or Speed. A second group works with the period instead.
- Choose units. Wavelength can be anything from nanometres to kilometres, and frequency from hertz to terahertz.
- Type the wave speed, or pick one: sound in air, water or steel, or light in a vacuum, water or glass.
- Type the frequency (or the wavelength) and read the answer, with the formula and the numbers put in.
- Check the extra readings: the period, angular frequency and wave number, and, for waves at the speed of light, the electromagnetic region.
A snapshot of the wave is drawn with one wavelength marked. For practice, Practice and help sets wave equation questions with worked solutions.
The wavelength formula
Frequency and period are linked by f = 1/T, so you can also write v = λ/T. For a fixed speed, doubling the frequency halves the wavelength. All electromagnetic waves travel at the speed of light in a vacuum, c = 299,792,458 m/s, often rounded to 3.00 × 10⁸ m/s. Our wave speed equation guide covers the formula itself in depth.
Worked examples you can check in the calculator
Example 1: the wavelength of a sound
A note of 440 Hz travels through air at 343 m/s. What is its wavelength?
Choose Wavelength, pick Sound in air and type 440 Hz. The calculator gives 0.78 m, with a period of about 2.27 ms.
Example 2: a radio wave
An FM radio station broadcasts at 100 MHz. Radio waves travel at the speed of light:
Pick Light in a vacuum, set the frequency unit to MHz and type 100. The calculator gives 2.998 m and names the region as radio waves.
Example 3: green light
Light with a frequency of 540 THz has a wavelength of 2.998 × 10⁸ ÷ 5.40 × 10¹⁴ = 5.55 × 10⁻⁷ m, which is 555 nm. The calculator shows this and says it is visible, green. Set the wavelength unit to nm to read it directly.
Example 4: from the period
Water waves 2.5 m apart arrive every 4 s. The frequency is 1/4 = 0.25 Hz, so the speed is v = λ/T = 2.5 ÷ 4 = 0.625 m/s. Use the period group in the calculator, which takes the period directly.
Try the wave equation in the course, then press Mark:
Find a wavelength or frequency from c = f lambda, with the unit shown beside the answer.
Press Mark to have your answer marked in the Light & Energy course.
Wavelengths across the electromagnetic spectrum
The calculator names the region for any wave travelling at the speed of light, using these wavelength boundaries:
| Region | Wavelength | Example |
|---|---|---|
| Radio waves | Over 1 m | FM radio, about 3 m |
| Microwaves | 1 mm to 1 m | Wi-Fi and microwave ovens |
| Infrared | 750 nm to 1 mm | Heat from warm objects |
| Visible light | About 380 nm to 750 nm | Violet at the short end, red at the long end |
| Ultraviolet | 10 nm to 380 nm | Sunburn |
| X-rays | 0.01 nm to 10 nm | Medical imaging |
| Gamma rays | Under 0.01 nm | Radioactive decay |
The boundaries between regions are not sharp, and textbooks round them differently. NASA's electromagnetic spectrum pages describe each region.
Wavelength to energy
The energy of one photon of light is E = hf = hc/λ, where h = 6.626 × 10⁻³⁴ J s is the Planck constant. For the green light in Example 3:
That is about 2.23 electronvolts. The Wave Speed Calculator does not give photon energy, so work it out from its wavelength or frequency like this. For the wavelength of a moving particle, see our de Broglie wavelength guide.
Common mistakes
- Mixing units. MHz is 10⁶ Hz and nm is 10⁻⁹ m. Convert, or set the units in the calculator.
- Dividing the wrong way. Wavelength = speed ÷ frequency, not frequency ÷ speed.
- Using the speed of sound for light, or the other way round. Sound in air is about 343 m/s; light is about 3 × 10⁸ m/s.
- Thinking frequency changes when a wave enters a new material. The frequency stays the same; the speed and wavelength change.
- Confusing period and frequency. Period means seconds per wave, while frequency means waves per second, in hertz.
Practise waves in a short timed paper
The wave equation comes up in High School Physics and AP Physics 1 practice, and in GCSE Physics Higher in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. The Light and Energy course starts from what a wave is and builds up to photons.
Common questions
How do you calculate wavelength?
How do you convert wavelength to frequency?
What is the wavelength of visible light?
Does wavelength change in a different material?
How do you find the energy of light from its wavelength?
What is the speed of light used by the calculator?
Revision cards
Say the answer first, then flip the card to check it.
Where to go next
- Solve it
Wave Speed Calculator
Link wave speed, frequency and wavelength
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Light & Energy
Waves, photons and the electromagnetic spectrum explained
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Physics · Waves and lightWave speed equation: v = fλ with worked examplesThe wave speed equation v = fλ, the frequency equation f = 1/T, units and rearranging, worked examples for sound, water and light waves, and practice.