How do you convert wavelength to frequency?

Divide the wave speed by the wavelength. For light in vacuum, f = c ÷ λ: a 600 nm wave is 299,792,458 ÷ 6 × 10⁻⁷ = 5 × 10¹⁴ Hz, or 500 THz. For sound in air, use 343 m/s: a 1 m wave is 343 Hz. Enter the wavelength with its unit and the page divides for you.

What is the relationship between wavelength and frequency?

Their product is the wave's speed: v = fλ. At a fixed speed they are inversely proportional — double the frequency and the wavelength halves. That is why high-pitched sounds and blue light have short wavelengths and low pitches and red light long ones.

What wavelength is 500 THz, and what colour?

599.6 nm in vacuum — orange. Visible light runs roughly from 380 nm (violet, about 790 THz) to 750 nm (red, 400 THz); green sits around 495–570 nm, which is 525–605 THz.

How do I calculate the wavelength of a sound?

Divide the speed of sound by the frequency. In air at 20 °C, 343 m/s ÷ 440 Hz = 0.78 m for concert A; 343 ÷ 20,000 Hz = 1.7 cm at the top of hearing; 343 ÷ 20 Hz = 17 m at the bottom. Choose 'Sound in air' and enter the frequency in Hz.

What is the energy of a photon at a given frequency?

E = hf, with h = 6.626 × 10⁻³⁴ J·s. Visible photons carry 1.7–3.3 eV (red to violet); X-rays thousands of eV. The page shows E in joules and eV whenever the medium is light in vacuum.

Wavelength to Frequency Calculator (Light, Sound, Any Wave)

Wavelength from frequency or frequency from wavelength for light, sound in air or water, or any wave speed, with SI prefixes and photon energy.

Inputs

Calculate

Frequency

0100,000,000,000,000,000,000

Frequency unit

Wavelength

01,000,000,000,000

Wavelength unit

Wave and medium

Wave speed (for Other)(m/s)

0.001 m/s1,000,000,000,000 m/s

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Wavelength

5.9958e-7 m

Working: λ = v ÷ f = 299,792,458 m/s ÷ 5.0000e+14 Hz = 5.9958e-7 m
Wavelength: 599.6 nm (5.9958e-7 m)
Frequency: 500.0 THz (5.0000e+14 Hz)
Period: 2.0000e-15 s
Wave speed: Light in vacuum (c = 299,792,458 m/s)
Where it sits: visible — orange
Photon energy (E = hf): 3.3130e-19 J = 2.068 eV

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What each Wavelength to Frequency input means

Calculate: Find the wavelength from a frequency, or the frequency from a wavelength.
Frequency: The frequency, for wavelength mode — 440 for concert A in Hz, 2.4 for Wi-Fi in GHz, 500 for orange light in THz.
Frequency unit: Hz, kHz, MHz, GHz or THz. Each step is a factor of 1,000.
Wavelength: The wavelength, for frequency mode — 600 for orange light in nm, 12.2 for a microwave oven in cm.
Wavelength unit: Metres down to nanometres (nm); µm is a micrometre, a millionth of a metre.
Wave and medium: What the wave travels through: light in vacuum (exactly 299,792,458 m/s), sound in air at 20 °C (343 m/s) or in water (1,480 m/s), or a custom speed.
Wave speed (for Other): For the custom option, the wave's speed in m/s — light in glass, sound in steel, a wave on a string.

Wavelength to Frequency formula

v = f × λ · λ = v ÷ f · f = v ÷ λ · period T = 1 ÷ f · for light: photon energy E = h × f

v = f\lambda \qquad E = h f

For any wave, speed equals frequency times wavelength: in one second, f wavelengths go past, each λ long, so the wave has travelled fλ. Fix the speed and the two are inverses — high frequency means short wavelength. For light in vacuum the speed is c, exactly 299,792,458 m/s, so 500 THz light has a wavelength of c ÷ 5 × 10¹⁴ = 600 nm, orange; for sound in air at 20 °C the speed is about 343 m/s, so concert A at 440 Hz is a 78 cm wave. The page takes frequencies in Hz to THz and wavelengths in metres to nanometres, converts to SI, shows the division, and reports the period as well. For light it adds the photon energy E = hf in joules and electron-volts, and names the band — radio, microwave, infrared, the visible colours, ultraviolet, X-ray — the wavelength falls in.

Wavelength to Frequency worked example

Light at 500 THz in vacuum: λ = c ÷ f = 299,792,458 ÷ 5 × 10¹⁴ = 5.996 × 10⁻⁷ m, which is 599.6 nm — orange light, near the red end of yellow. Its period is 2 × 10⁻¹⁵ s and each photon carries E = hf = 6.626 × 10⁻³⁴ × 5 × 10¹⁴ = 3.31 × 10⁻¹⁹ J, or 2.07 eV. Green light is shorter, around 530 nm, which is 566 THz.

Where the Wavelength to Frequency calculator can give the wrong answer

The speed depends on the medium. Light slows in glass (about c ÷ 1.5) and water (c ÷ 1.33), so its wavelength shortens there while the frequency stays the same; sound is about 343 m/s in air at 20 °C, 1,480 m/s in water and around 5,000 m/s in steel. Choose the medium, or type the speed.
The sound-in-air figure is for 20 °C; it rises about 0.6 m/s per degree, so a cold-day calculation is a little off with the default.
Photon energy and the colour band are only shown for light in vacuum. A sound wave has no photons, and a radio wave's band label assumes vacuum wavelength.
Colour boundaries are approximate — sources put violet/blue and orange/red at slightly different nanometre values, and the eye's response is continuous. The label is a guide, not a spectrometer.
Very large and very small numbers are shown in scientific notation with four significant figures; the friendlier units line (nm, THz, cm) is rounded to four figures as well.

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Wavelength to Frequency FAQ

: Divide the wave speed by the wavelength. For light in vacuum, f = c ÷ λ: a 600 nm wave is 299,792,458 ÷ 6 × 10⁻⁷ = 5 × 10¹⁴ Hz, or 500 THz. For sound in air, use 343 m/s: a 1 m wave is 343 Hz. Enter the wavelength with its unit and the page divides for you.
: Their product is the wave's speed: v = fλ. At a fixed speed they are inversely proportional — double the frequency and the wavelength halves. That is why high-pitched sounds and blue light have short wavelengths and low pitches and red light long ones.
: 599.6 nm in vacuum — orange. Visible light runs roughly from 380 nm (violet, about 790 THz) to 750 nm (red, 400 THz); green sits around 495–570 nm, which is 525–605 THz.
: Divide the speed of sound by the frequency. In air at 20 °C, 343 m/s ÷ 440 Hz = 0.78 m for concert A; 343 ÷ 20,000 Hz = 1.7 cm at the top of hearing; 343 ÷ 20 Hz = 17 m at the bottom. Choose 'Sound in air' and enter the frequency in Hz.
: E = hf, with h = 6.626 × 10⁻³⁴ J·s. Visible photons carry 1.7–3.3 eV (red to violet); X-rays thousands of eV. The page shows E in joules and eV whenever the medium is light in vacuum.