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Wavelength to Frequency Calculator – Convert nm, m & Hz Instantly

Wave Physics Tool

Wavelength to Frequency Calculator

Convert wavelength to frequency and frequency to wavelength for any wave type — light, sound, and radio waves. Calculate in nm, µm, m, Hz, MHz, GHz and view photon energy for electromagnetic waves.

nm to Hz & Hz to nm Converter (Light Waves)

Dedicated converter for electromagnetic waves — always uses speed of light c = 299,792,458 m/s

Wavelength to Frequency & Frequency to Wavelength
Wave speed: 299,792,458 m/s
f = v ÷ ?
Finding frequency from wavelength
Meters to Hz & Hz to Meters Converter

For radio waves and sound waves where wavelengths are in meters

Wave speed: 299,792,458 m/s
MHz to nm Converter

For radio frequency engineers — converts MHz to wavelength in nanometers

Wavelength to Frequency Formula

The relationship between wavelength and frequency is governed by the wave equation, one of the fundamental formulas in physics. Understanding this formula allows you to convert wavelength to frequency and frequency to wavelength for any type of wave — light, sound, radio waves, or any other electromagnetic or mechanical wave.

f = v ÷ ?
Finding frequency from wavelength
where f = frequency (Hz), v = wave speed (m/s), ? = wavelength (m)
? = v ÷ f
Finding wavelength from frequency
where ? = wavelength (m), v = wave speed (m/s), f = frequency (Hz)

For light specifically:

f = c ÷ ?
where c = 299,792,458 m/s (speed of light in vacuum)

For sound in air:

f = 343 ÷ ?
(at 20°C / 68°F at sea level)

Variable Definitions

  • f = frequency measured in Hertz (Hz), which is cycles per second
  • ? (lambda) = wavelength measured in meters (m), the distance between wave peaks
  • v = wave speed (m/s) — depends on the medium the wave travels through
  • c = speed of light in vacuum = 2.998 × 108 m/s (exact value: 299,792,458 m/s)

Key insight: Wavelength and frequency are inversely proportional. As wavelength increases, frequency decreases proportionally, and vice versa. The wave speed remains constant for a given medium.

Worked Examples

Example 1: Red Light (? = 700 nm)

Given: ? = 700 nm, medium = light in vacuum

  1. Convert wavelength to meters: 700 nm = 700 × 10-9 m = 7.00 × 10-7 m
  2. Wave speed c = 299,792,458 m/s
  3. Apply formula: f = c ÷ ? = 299,792,458 ÷ (7.00 × 10-7)
  4. Calculate: f = 4.28 × 1014 Hz
  5. Convert to THz: f = 428 THz

Answer: 4.28 × 1014 Hz = 428 THz (red light)

Example 2: Radio Wave (? = 2 m)

Given: ? = 2 m, medium = light in air

  1. Wavelength already in meters: ? = 2 m
  2. Wave speed c = 299,792,458 m/s
  3. Apply formula: f = c ÷ ? = 299,792,458 ÷ 2
  4. Calculate: f = 149,896,229 Hz
  5. Convert to MHz: f = 149.9 MHz

Answer: 1.499 × 108 Hz = 149.9 MHz (radio wave)

How to Convert Wavelength to Frequency

Follow these four steps to convert any wavelength to its corresponding frequency. This method works for all wave types — electromagnetic waves (light, radio, X-rays) and mechanical waves (sound, water waves).

Step-by-Step Guide

  1. Step 1: Identify the wavelength and convert to metres
    • If in nanometers (nm): multiply by 10-9
    • If in micrometers (µm): multiply by 10-6
    • If in millimeters (mm): multiply by 10-3
    • If in centimeters (cm): multiply by 0.01
    • If in kilometers (km): multiply by 1000
  2. Step 2: Identify the wave speed for your medium
    • Light in vacuum: c = 3 × 108 m/s (exact: 299,792,458 m/s)
    • Light in air: ~299,705,000 m/s
    • Light in water: ~225,000,000 m/s
    • Sound in air (20°C): 343 m/s
    • Sound in water: 1,482 m/s
  3. Step 3: Divide wave speed by wavelength
    • Use the formula: f = v ÷ ?
    • Make sure wavelength is in meters
  4. Step 4: Label answer in Hz and convert to appropriate unit
    • 1 kHz = 1,000 Hz
    • 1 MHz = 1,000,000 Hz = 106 Hz
    • 1 GHz = 1,000,000,000 Hz = 109 Hz
    • 1 THz = 1012 Hz

Example 1: Green Light ? = 532 nm ? f in THz

  1. Convert to meters: 532 nm = 532 × 10-9 m = 5.32 × 10-7 m
  2. Wave speed for light: c = 299,792,458 m/s
  3. Divide: f = 299,792,458 ÷ 5.32×10-7
  4. Calculate: f = 5.637 × 1014 Hz = 563.7 THz

Answer: 563.7 THz (green laser light)

Example 2: Sound Wave ? = 0.5 m in Air ? f in Hz

  1. Wavelength already in meters: ? = 0.5 m
  2. Wave speed for sound in air: v = 343 m/s
  3. Divide: f = 343 ÷ 0.5
  4. Calculate: f = 686 Hz

Answer: 686 Hz (audible sound, approximately the note E5)

Example 3: FM Radio Station f = 98.5 MHz ? ? in Metres

This time we're converting frequency to wavelength using ? = v ÷ f

  1. Convert frequency to Hz: 98.5 MHz = 98,500,000 Hz
  2. Wave speed for light: c = 299,792,458 m/s
  3. Divide: ? = 299,792,458 ÷ 98,500,000
  4. Calculate: ? = 3.044 m

Answer: 3.044 meters (typical FM radio wavelength)

Hz to nm — Hertz to Nanometers Converter

The Hz to nm conversion is specifically for light and other electromagnetic waves. Nanometers (nm) are the standard unit for measuring visible light wavelengths, while Hertz (Hz) measures frequency. This conversion uses the speed of light as the constant linking the two.

?(nm) = (c ÷ f) × 109
where c = 299,792,458 m/s (speed of light in vacuum)

The formula works in two steps:

  1. Calculate wavelength in meters: ?(m) = c ÷ f
  2. Convert meters to nanometers: multiply by 109

Worked Examples: Hz to nm

Example 1: f = 5×1014 Hz ? ? in nm

  1. Speed of light: c = 299,792,458 m/s
  2. Calculate wavelength in meters: ? = 299,792,458 ÷ 5×1014
  3. ? = 5.996 × 10-7 m
  4. Convert to nanometers: ? = 5.996 × 10-7 × 109
  5. ? = 599.6 nm

Answer: 599.6 nm (orange-yellow light)

Example 2: f = 2.45 GHz (Microwave) ? ? in mm and nm

  1. Convert to Hz: 2.45 GHz = 2.45 × 109 Hz
  2. Calculate: ? = 299,792,458 ÷ 2.45×109 = 0.1224 m
  3. Convert to mm: ? = 122.4 mm
  4. Convert to nm: ? = 122,400,000 nm

Answer: 122.4 mm = 122,400,000 nm (microwave oven frequency)

Example 3: f = 100 MHz (FM Radio) ? ? in m and nm

  1. Convert to Hz: 100 MHz = 100,000,000 Hz = 108 Hz
  2. Calculate: ? = 299,792,458 ÷ 108 = 2.998 m
  3. Convert to nm: ? = 2.998 × 109 nm

Answer: 2.998 m = 2,998,000,000 nm (FM radio wave)

Frequency to Wavelength Quick Reference

Meters to Hz — Wavelength to Frequency Conversion

For radio waves and sound waves, wavelengths are typically measured in meters (m), not nanometers. The meters to Hz conversion uses the same fundamental formula but with wavelengths on a much larger scale.

f(Hz) = v ÷ ?(m)
For light: v = c = 299,792,458 m/s
For sound in air: v = 343 m/s

Worked Examples: Meters to Hz

Example 1: ? = 3 m, Light ? f in MHz

  1. Wavelength: ? = 3 m
  2. Wave speed: c = 299,792,458 m/s
  3. Calculate: f = 299,792,458 ÷ 3
  4. f = 99,930,819 Hz
  5. Convert to MHz: f = 99.93 MHz

Answer: 99.93 MHz (FM radio band)

Example 2: ? = 1.715 m, Sound in Air ? f in Hz

  1. Wavelength: ? = 1.715 m
  2. Wave speed: v = 343 m/s (sound in air at 20°C)
  3. Calculate: f = 343 ÷ 1.715
  4. f = 200 Hz

Answer: 200 Hz (low bass tone)

Example 3: ? = 0.122 m (12.2 cm), Light ? f in GHz

  1. Wavelength: ? = 0.122 m
  2. Wave speed: c = 299,792,458 m/s
  3. Calculate: f = 299,792,458 ÷ 0.122
  4. f = 2.457 × 109 Hz
  5. Convert to GHz: f = 2.457 GHz

Answer: 2.457 GHz (microwave oven frequency)

Radio Wavelength Reference Table

FrequencyWavelengthRegion
WavelengthFrequencyApplication
3,000 m100 kHzLong wave radio
300 m1 MHzAM radio
3 m100 MHzFM radio
30 cm1 GHzMicrowave / Mobile
3 cm10 GHzRadar
3 mm100 GHzMillimeter wave

Electromagnetic Spectrum — Wavelength and Frequency Chart

The electromagnetic spectrum encompasses all types of electromagnetic radiation, from gamma rays with wavelengths smaller than atoms to radio waves with wavelengths measured in kilometers. Each region has characteristic wavelength and frequency ranges.

Gamma
<0.01nm
>3×10¹?Hz
X-Ray
0.01-10nm
3×10¹6-10¹?Hz
UV
10-380nm
0.8-3×10¹5Hz
Visible
380-700nm
4.3-7.9×10¹4Hz
IR
700nm-1mm
3×10¹¹-4×10¹4Hz
Microwave
1mm-1m
3×108-10¹¹Hz
Radio
>1m
<3×108Hz

Complete Electromagnetic Spectrum Table

RegionWavelength RangeFrequency RangeExamples
Gamma rays< 0.01 nm> 3×1019 HzNuclear reactions
X-rays0.01–10 nm3×1017–3×1019 HzMedical imaging
Ultraviolet10–380 nm7.9×1014–3×1016 HzSunburn, sterilization
Visible — Violet380–450 nm6.7–7.9×1014 HzHuman vision
Visible — Blue450–495 nm6.1–6.7×1014 HzSky color
Visible — Green495–570 nm5.3–6.1×1014 HzPlants, traffic lights
Visible — Yellow570–590 nm5.1–5.3×1014 HzSunlight peak
Visible — Orange590–620 nm4.8–5.1×1014 HzFire
Visible — Red620–700 nm4.3–4.8×1014 HzTraffic lights
Infrared700 nm–1 mm3×1011–4.3×1014 HzHeat, remote controls
Microwave1 mm–1 m3×108–3×1011 HzWiFi, microwave ovens
Radio> 1 m< 3×108 HzBroadcasting, mobile

Wavelength to Angular Frequency

Angular frequency (?, omega) measures how fast something oscillates in radians per second rather than cycles per second. It's commonly used in physics and engineering because it simplifies many wave equations.

? = 2pf
Angular frequency (rad/s) = 2p × frequency (Hz)
? = 2pv/?
Calculate angular frequency directly from wavelength

For light specifically:

? = 2pc/?
where c = speed of light = 299,792,458 m/s

Worked Example: ? = 500 nm

  1. Convert wavelength to meters: ? = 500 nm = 500 × 10-9 m = 5 × 10-7 m
  2. Calculate frequency: f = c/? = 299,792,458 ÷ 5×10-7 = 5.996 × 1014 Hz
  3. Calculate angular frequency: ? = 2pf = 2p × 5.996×1014
  4. ? = 3.768 × 1015 rad/s

Answer: ? = 3.768 × 1015 rad/s

Wave Number (k)

The wave number k is related to angular frequency and tells you how many radians of phase change occur per meter of distance.

k = 2p/? = ?/v
Wave number (rad/m) — spatial frequency of the wave

Example: ? = 500 nm

  1. Wavelength: ? = 500 × 10-9 m
  2. Calculate: k = 2p/? = 2p ÷ 500×10-9
  3. k = 1.257 × 107 rad/m

Answer: k = 1.257 × 107 rad/m

Worked Examples

Here are detailed solutions to common wavelength and frequency problems. Each shows every step of the calculation.

1. How to find frequency from wavelength for light

Problem: A laser has a wavelength of 632.8 nm. What is its frequency?

Solution:

  1. Given: ? = 632.8 nm, medium = light in air (use c)
  2. Convert to meters: ? = 632.8 × 10-9 m = 6.328 × 10-7 m
  3. Speed of light: c = 299,792,458 m/s
  4. Formula: f = c/?
  5. Calculate: f = 299,792,458 ÷ 6.328×10-7
  6. f = 4.738 × 1014 Hz = 473.8 THz

Answer: 473.8 THz (red helium-neon laser)

2. How to convert nm to Hz step by step

Problem: Convert 400 nm to Hz

Solution:

  1. Wavelength: ? = 400 nm
  2. Convert to meters: ? = 400 × 10-9 m = 4 × 10-7 m
  3. This is electromagnetic radiation, so use c = 299,792,458 m/s
  4. Formula: f = c/?
  5. Substitute: f = 299,792,458 ÷ 4×10-7
  6. Calculate: f = 7.495 × 1014 Hz = 749.5 THz

Answer: 7.495 × 1014 Hz (violet light at edge of visible spectrum)

3. How to convert Hz to nm step by step

Problem: Convert 6 × 1014 Hz to nm

Solution:

  1. Frequency: f = 6 × 1014 Hz
  2. Speed of light: c = 299,792,458 m/s ˜ 3 × 108 m/s
  3. Formula: ? = c/f
  4. Calculate: ? = 299,792,458 ÷ 6×1014
  5. ? = 4.997 × 10-7 m
  6. Convert to nm: ? = 4.997 × 10-7 × 109 = 499.7 nm

Answer: 499.7 nm (cyan-green light)

4. How to convert meters to Hz for radio waves

Problem: An FM radio antenna is 1.5 meters long (quarter-wave). What frequency does it receive?

Solution:

  1. Quarter-wave antenna means ?/4 = 1.5 m, so ? = 6 m
  2. Speed: c = 299,792,458 m/s
  3. Formula: f = c/?
  4. Calculate: f = 299,792,458 ÷ 6 = 49,965,410 Hz
  5. Convert to MHz: f = 49.97 MHz

Answer: 49.97 MHz (low end of FM radio band)

5. How to find wavelength from frequency in MHz

Problem: What is the wavelength of a 2.4 GHz WiFi signal?

Solution:

  1. Frequency: f = 2.4 GHz = 2,400 MHz = 2.4 × 109 Hz
  2. Speed: c = 299,792,458 m/s
  3. Formula: ? = c/f
  4. Calculate: ? = 299,792,458 ÷ 2.4×109
  5. ? = 0.1249 m = 12.49 cm

Answer: 12.49 cm (WiFi wavelength — this is why WiFi antennas are ~6 cm for half-wave)

6. How to convert 550 nm to frequency in THz

Problem: Green light has wavelength 550 nm. Express frequency in THz.

Solution:

  1. Wavelength: ? = 550 nm = 550 × 10-9 m = 5.5 × 10-7 m
  2. Speed of light: c = 299,792,458 m/s
  3. Calculate frequency: f = 299,792,458 ÷ 5.5×10-7
  4. f = 5.451 × 1014 Hz
  5. Convert to THz: f = 545.1 THz

Answer: 545.1 THz (peak sensitivity of human eye)

7. How to find frequency of red light (700 nm)

Problem: Calculate the frequency of red light at the long wavelength edge of the visible spectrum (700 nm).

Solution:

  1. Wavelength: ? = 700 nm = 7 × 10-7 m
  2. Formula: f = c/? where c = 299,792,458 m/s
  3. Calculate: f = 299,792,458 ÷ 7×10-7
  4. f = 4.283 × 1014 Hz = 428.3 THz
  5. Photon energy: E = hf = 6.626×10-34 × 4.283×1014 = 2.84×10-19 J = 1.77 eV

Answer: 428.3 THz, photon energy 1.77 eV (deep red light)

8. How to calculate wavelength of FM radio at 98.5 MHz

Problem: A radio station broadcasts at 98.5 MHz. What is the wavelength?

Solution:

  1. Frequency: f = 98.5 MHz = 98,500,000 Hz
  2. Speed: c = 299,792,458 m/s
  3. Formula: ? = c/f
  4. Calculate: ? = 299,792,458 ÷ 98,500,000
  5. ? = 3.044 m

Answer: 3.044 meters (typical FM radio wavelength)

9. How to convert wavelength to angular frequency

Problem: Light has wavelength 589 nm (sodium D-line). Find angular frequency ?.

Solution:

  1. Wavelength: ? = 589 nm = 5.89 × 10-7 m
  2. First find regular frequency: f = c/? = 299,792,458 ÷ 5.89×10-7
  3. f = 5.090 × 1014 Hz
  4. Angular frequency: ? = 2pf = 2p × 5.090×1014
  5. ? = 3.198 × 1015 rad/s

Answer: ? = 3.198 × 1015 rad/s (sodium yellow light)

10. What is the frequency of green light at 532 nm?

Problem: A green laser pointer emits light at 532 nm. Calculate the frequency and photon energy.

Solution:

  1. Wavelength: ? = 532 nm = 5.32 × 10-7 m
  2. Calculate frequency: f = c/? = 299,792,458 ÷ 5.32×10-7
  3. f = 5.637 × 1014 Hz = 563.7 THz
  4. Photon energy in joules: E = hf = 6.626×10-34 × 5.637×1014
  5. E = 3.735 × 10-19 J
  6. Convert to eV: E = 3.735×10-19 ÷ 1.602×10-19 = 2.33 eV

Answer: 563.7 THz, photon energy 2.33 eV (green laser light — Nd:YAG frequency-doubled)

Frequently Asked Questions

How do you convert wavelength to frequency?
To convert wavelength to frequency, use the formula f = v/? where f is frequency (Hz), v is wave speed (m/s), and ? is wavelength (m). For light, use v = c = 299,792,458 m/s. First convert your wavelength to meters (if in nm, multiply by 10??), then divide the wave speed by the wavelength. The result is frequency in Hz.
What is the formula for wavelength to frequency?
The wavelength to frequency formula is f = v ÷ ? (frequency equals wave speed divided by wavelength). For electromagnetic waves (light), this becomes f = c ÷ ? where c = 299,792,458 m/s. Make sure wavelength is in meters and the result will be in Hertz (Hz).
How do you convert nm to Hz?
To convert nanometers (nm) to Hertz (Hz): (1) multiply nm by 10?? to get meters, (2) divide the speed of light (299,792,458 m/s) by wavelength in meters. Formula: f = 299,792,458 ÷ (nm × 10??). Example: 550 nm ? f = 299,792,458 ÷ (550×10??) = 5.45 × 10¹4 Hz = 545 THz.
How do you convert Hz to nm?
To convert Hertz to nanometers: (1) divide the speed of light (299,792,458 m/s) by frequency in Hz to get wavelength in meters, (2) multiply by 10? to convert to nanometers. Formula: ?(nm) = (299,792,458 ÷ f) × 10?. Example: 5×10¹4 Hz ? ? = (299,792,458 ÷ 5×10¹4) × 10? = 599.6 nm.
What is the frequency of visible light?
Visible light has frequencies ranging from approximately 430 THz (red light, 700 nm) to 750 THz (violet light, 400 nm). The peak sensitivity of the human eye is around 540 THz (555 nm, yellow-green). The full range is 4.3×10¹4 Hz to 7.5×10¹4 Hz.
How do you convert meters to Hz?
To convert wavelength in meters to frequency in Hz, divide the wave speed by wavelength: f = v/?. For light: f = 299,792,458/?. For sound in air at 20°C: f = 343/?. Example: ? = 3 m (light) ? f = 299,792,458 ÷ 3 = 99.93 MHz. Always ensure wavelength is in meters and use the correct wave speed for your medium.
What is the wavelength of 100 MHz?
The wavelength of 100 MHz is 2.998 meters. Calculation: convert 100 MHz to Hz (100,000,000 Hz), then use ? = c/f = 299,792,458 ÷ 100,000,000 = 2.998 m. This is in the FM radio broadcast band (87.5–108 MHz). A half-wave dipole antenna for this frequency would be about 1.5 meters long.
How do you find angular frequency from wavelength?
To find angular frequency (?) from wavelength: first find regular frequency using f = v/?, then multiply by 2p: ? = 2pf. You can also use the direct formula ? = 2pv/?. For light: ? = 2pc/? where c = 299,792,458 m/s. The result is in radians per second (rad/s). Angular frequency is used in wave equations and oscillator physics.
What is the relationship between wavelength and frequency?
Wavelength and frequency are inversely proportional — as one increases, the other decreases. They're related by the equation v = f? (wave speed = frequency × wavelength). Since wave speed is constant in a given medium, if wavelength doubles, frequency halves, and vice versa. Short wavelengths mean high frequencies (gamma rays); long wavelengths mean low frequencies (radio waves).
How do you convert MHz to nm?
To convert MHz to nm: (1) convert MHz to Hz by multiplying by 106, (2) calculate wavelength in meters using ? = 299,792,458/f, (3) convert meters to nanometers by multiplying by 10?. Example: 100 MHz ? 100×106 Hz ? ? = 299,792,458 ÷ 100,000,000 = 2.998 m ? 2.998 × 10? nm. Note: MHz frequencies typically give wavelengths in meters, not nanometers.

Related Calculators

Key Formulas
f = v ÷ ?Wavelength ? Frequency
? = v ÷ fFrequency ? Wavelength
c = 3×108 m/sSpeed of light
v = 343 m/sSound in air (20°C)
E = hfPhoton energy
? = 2pfAngular frequency
Visible Light Spectrum
Color? (nm)f (THz)
Violet380-450670-790
Blue450-495610-670
Green495-570530-610
Yellow570-590510-530
Orange590-620480-510
Red620-700430-480
Unit Conversions
1 nm10?? m
1 µm10?6 m
1 mm10?³ m
1 Å10?¹° m
1 kHz10³ Hz
1 MHz106 Hz
1 GHz10? Hz
1 THz10¹² Hz
Quick Tips
  • Higher frequency = shorter wavelength
  • Visible light: 400-700 nm
  • FM radio: ~3 m wavelength
  • WiFi 2.4GHz: ~12.5 cm
  • Speed of light is constant in vacuum

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