The Wavelength Calculator solves v = fλ for wavelength, frequency or wave speed when any two of the three are known. Pick a medium to load a standard wave speed, or enter a custom speed; for light, the tool also names the electromagnetic band and, in the visible range, the colour.
Wavelength is the distance between consecutive corresponding points on a wave, such as crest to crest. Frequency is how many cycles pass per second. Their product is the wave speed in the medium.
Calculate wavelength from frequency and wave speed
Wavelength equals wave speed divided by frequency. Higher frequency at the same speed packs the wave into a shorter λ. The calculator applies λ = v/f once those two inputs are present and reports λ in metres (or a selected length unit).
| Symbol | Quantity | SI unit |
|---|---|---|
| λ | wavelength | metres (m) |
| f | frequency | hertz (Hz) |
| v | wave speed | metres per second (m/s) |
v = f λ
λ = v / f
f = v / λEnter any two quantities; the third follows. Frequency cannot be zero when solving for wavelength. Scientific notation in the 3.45e9 form is accepted, which matters for light frequencies in the 10¹⁴ Hz range.
Wave speed is a property of the wave type and the medium, not of the source frequency alone. Changing f changes λ when v is fixed by the medium.
Choose a medium for the wave speed
Medium presets load published speeds so a problem stated as "sound in air" or "light in water" needs no manual lookup. Light in vacuum is exactly c = 299,792,458 m/s. Sound in air depends on temperature; the 20 °C preset uses 343 m/s.
| Medium | Speed (m/s) | Note |
|---|---|---|
| Light in vacuum | 299,792,458 | Defining constant c |
| Light in air | 299,702,547 | Refractive index ≈ 1.0003 |
| Light in water | 225,000,000 | Refractive index ≈ 1.333 |
| Light in glass | 200,000,000 | Index ≈ 1.5; varies by glass |
| Sound in air at 20 °C | 343 | Rises about 0.6 m/s per °C |
| Sound in air at 0 °C | 331.3 | |
| Sound in water at 20 °C | 1,482 | |
| Sound in steel | 5,960 | Longitudinal wave |
Select a row to fill v, or type a custom speed. Glass and water optical speeds are approximate; specialty glasses differ. Sound speed in air should be adjusted if the problem states a temperature far from 20 °C.
Calculate frequency or wave speed
The same relation rearranges for frequency or speed. Given λ and v, frequency is f = v/λ. Given f and λ, speed is v = fλ. The calculator does not ask which rearrangement you want; filling any two fields is enough.
f = v / λ
v = f λA radio station at 100 MHz with radio waves travelling at c has:
λ = c / f = 299,792,458 / 1×10⁸ ≈ 3.00 m
A guitar string problem that gives frequency and string wave speed returns the wavelength of the vibrating string, which relates to the string length for standing-wave modes.
Find the wavelength of a 440 Hz note in air
Concert pitch A at 440 Hz is a standard reference tone. In air at 20 °C the speed of sound is 343 m/s from the medium table, so dividing speed by frequency gives the wavelength of that note in open air to four decimal places in metres.
1. List what is known. f = 440 Hz, v = 343 m/s (sound in air at 20 °C).
2. Apply λ = v/f. λ = 343 / 440
3. Solve. λ ≈ 0.7795 m
That is roughly 78 cm from compression to compression in open air. At 0 °C, v = 331.3 m/s and the same frequency gives λ = 331.3 / 440 ≈ 0.753 m. Temperature shifts the wavelength because it shifts the speed.
The calculator loads 343 m/s from the air-at-20 °C preset and divides by the frequency entered.
Identify the electromagnetic band
Radio, microwave, infrared, visible, ultraviolet, X-ray and gamma-ray bands partition the electromagnetic spectrum by wavelength. Entering λ lets the calculator name the electromagnetic band that contains that wavelength, using the published range edges stored in the shared physics reference file.
| Band | Wavelength range |
|---|---|
| Radio | 0.1 m to 100,000 m |
| Microwave | 0.001 m to 0.1 m |
| Infrared | 7×10⁻⁷ m to 0.001 m |
| Visible | 3.8×10⁻⁷ m to 7×10⁻⁷ m |
| Ultraviolet | 1×10⁻⁸ m to 3.8×10⁻⁷ m |
| X-ray | 1×10⁻¹¹ m to 1×10⁻⁸ m |
| Gamma ray | 1×10⁻¹⁶ m to 1×10⁻¹¹ m |
Boundaries are conventional and vary slightly between sources. A wavelength of 550 nm (5.5×10⁻⁷ m) falls in the Visible band. A 1 cm wave is Microwave. A 1 km wave is Radio.
Band labels appear for electromagnetic problems when λ is known. Mechanical waves such as sound in air are not assigned an EM band.
Identify the colour of visible light
Inside the narrow visible window from about 380 nm to 750 nm, teaching tables split wavelength into violet through red. Those colour names are conventional partitions for coursework, not a full model of human colour vision under every lighting condition.
| Colour | Wavelength (nm) |
|---|---|
| Violet | 380-450 |
| Blue | 450-495 |
| Green | 495-570 |
| Yellow | 570-590 |
| Orange | 590-620 |
| Red | 620-750 |
A wavelength of 550 nm is classified as Green and sits in the Visible band. Enter 550 nm (or 5.5×10⁻⁷ m) to see that classification. Human colour perception also depends on intensity and on the observer; the table is a standard teaching partition, not a vision-science model.
Calculate photon energy
A photon's energy equals Planck's constant times frequency: E = hf. With λ known, frequency is f = c/λ in vacuum, so E = hc/λ. The calculator can report energy in joules and in electron volts using the reference constants.
E = h f
E = h c / λ (in vacuum)Constants from the reference file:
- h = 6.62607015×10⁻³⁴ J·s
- c = 299,792,458 m/s
- e = 1.602176634×10⁻¹⁹ C (for E in eV: divide joules by e)
For λ = 550 nm:
f = c/λ ≈ 5.451×10¹⁴ Hz
E = hf ≈ 3.612×10⁻¹⁹ J ≈ 2.25 eV
Photon energy rises as wavelength falls. Ultraviolet and X-ray photons carry far more energy per photon than infrared or radio. A factor-of-two drop in λ doubles f and doubles E when the wave travels at c. That is why ionising radiation sits at short wavelengths: each photon can deliver enough energy to free electrons from atoms.
For sound problems the photon-energy path does not apply. Sound is not an electromagnetic wave, and Planck's relation is not used for pressure waves in air. Keep E = hf for light and other EM radiation only.
Frequently asked questions
How do I calculate wavelength from frequency?
Divide wave speed by frequency: λ = v/f. For a 440 Hz tone in air at 20 °C, v = 343 m/s and λ ≈ 0.7795 m. Select a medium preset or enter v yourself.
Does wave speed depend on frequency?
In non-dispersive media the speed is set by the medium and is independent of frequency; changing f then changes λ so that v = fλ stays constant. In dispersive media speed varies with frequency; use the speed that applies at the frequency of interest.
What is the wavelength of visible light?
Visible wavelengths run about 380 nm to 750 nm. Violet sits at the short end; red at the long end. Green light near 550 nm is in the middle of that window.
How do I find frequency from wavelength?
Use f = v/λ. For light in vacuum, v = c. For sound, use the appropriate air, water or steel speed from the medium table.
What band is 550 nm?
550 nm is Visible light and falls in the Green colour range (495-570 nm). The calculator reports both the EM band and the colour for wavelengths inside the visible window.
Why does sound wavelength change with temperature?
Because the speed of sound in air rises with temperature, about 0.6 m/s per °C. At fixed frequency, λ = v/f grows as v grows. The 20 °C preset uses 343 m/s; the 0 °C preset uses 331.3 m/s.
What is photon energy?
Photon energy is E = hf, the product of Planck's constant and frequency. Shorter wavelengths mean higher frequencies and higher energy per photon. Results can be shown in joules or electron volts.
Can I solve for wave speed?
Yes. Enter frequency and wavelength; v = fλ. That is useful when λ is measured from a standing-wave pattern and f is known from a driver or a tone.
Why is light slower in glass than in vacuum?
The refractive index of the glass is greater than one, so the phase speed of light in the material is c/n. The table lists about 2.00×10⁸ m/s for a typical index near 1.5. Different glass types have different indices; use a measured n when the problem supplies one.
Do sound waves have an electromagnetic band?
No. Sound is a mechanical pressure wave in a material medium. Band and colour labels apply to electromagnetic waves only. For sound, choose an air, water or steel speed preset and solve v = fλ without an EM classification.
Summary
The Wavelength Calculator solves v = fλ for any one variable from the other two, with medium presets for light and sound speeds including 343 m/s in air at 20 °C. A 440 Hz note in that air has λ ≈ 0.7795 m.
Electromagnetic wavelengths are labelled by band, and visible wavelengths by colour, so 550 nm reads as Green and Visible. Photon energy E = hf is available from the same frequency using Planck's constant from the shared reference file.