Example 1
Tuning fork 440 Hz, v = 343 m/s -> λ ≈ 0.78 m.
Wavelength calculator
Enter wave speed and frequency. The calculator divides v by f and you get the distance between crests. A 440 Hz tuning fork at 343 m/s has λ ≈ 0.78 m, about an arm’s length. When you know λ and f and want v, open v = λ·f.
The inverse of this sum: v = λ·f. Photon energy from f: E = h·f. Doppler: f′ from source motion.
Result
Speed v (m/s) and Frequency f (Hz). The result shows up here.
How it works
You stand next to a speaker or an antenna and hear or measure one frequency. The wave also has a speed v in the medium. Wavelength is v divided by f: λ = v/f. That is the distance between successive crests, compressions, or field maxima. In one period T = 1/f the wave advances by one λ, so v = λ/T is the same formula from the other side.
Take a tuning fork from the cupboard. f = 440 Hz, classroom air about 343 m/s. λ = 343/440 ≈ 0.780 m, rounded on the page to 0.78 m. A 1000 Hz tone at the same v drops to 0.343 m. A 50 Hz bass note stretches to 6.86 m: a 20 cm speaker is likely to radiate that poorly, because the cone is much shorter than λ.
The same ratio works for radio and light. FM at 100 MHz with v = 3e8 m/s gives λ = 3 m, hence a dipole around 1.5 m. Wi-Fi at 2.4 GHz is 12.5 cm. Yellow light at f = 5e14 Hz drops to 600 nm. Sound in water is faster, about 1480 m/s, so 1000 Hz already has λ = 1.48 m, not 34 cm.
Frequency and speed have to be positive. At f = 0 you would divide by zero. Period T = 1/f sits beside the result, because it is the same information in seconds: at 440 Hz, T ≈ 0.00227 s. Speed and length follow the metric/US switch. Hertz stays in hertz. When λ falls into the visible range, the result also writes nanometers.
On the form, type v, then f. Air 343 and 440 give 0.78 m. You can type 3e8 and 1e8: you get exactly 3 m. A comma and a period both parse. The chart of λ versus f at fixed v falls as 1/f: higher pitch, shorter wave.
When you know λ and f and want the medium speed, open v = λ·f. When the source is moving, Doppler gives the frequency you hear, then you come back here with f′. A photon from that f is E = h·f, not a length.
How to use
- Type the wave speed in the medium. Classroom air is usually 343 m/s, water about 1480 m/s, light in vacuum 3e8.
- Type frequency in hertz. A tuning fork is 440, an FM station may be 1e8, an LED is around 5e14.
- Compute. 343 and 440 give λ ≈ 0.78 m. Beside it sits T = 1/440 ≈ 0.00227 s, the time of one crest.
- Change the medium if this is not air: 1480 and 1000 give 1.48 m in water, not 0.34 m.
- When you know λ and f and want v, open v = λ·f. When the source moves, do Doppler first, then come back here with f′.
Formula
λ = v / f
T = 1 / f. f > 0, v > 0.
Letters in λ = v/f
Crest spacing is λ = v/f. A 440 Hz tuning fork in 343 m/s air has λ ≈ 0.78 m, about an arm length.
- λ
- Wavelength in meters. 343/440 ≈ 0.78 m: that is the gap between compressions at this fork.
- v
- Wave speed in the medium, in m/s. Classroom air is near 343; water would differ, but here you divide that v by f.
- f
- Frequency in hertz. 440 Hz at 343 m/s sets λ; when you already know λ and f, v lives on the v = λ·f card.
- T
- Period T = 1/f. At 440 Hz, T ≈ 2.27 ms: in that time the wave advances one λ ≈ 0.78 m.
Real-life examples
Example 2
v = 343 m/s, f = 1000 Hz -> λ ≈ 0.34 m.
Example 3
v = 331 m/s, f = 262 Hz -> λ ≈ 1.26 m.
Example 4
v = 3e8 m/s, f = 1e8 Hz -> λ = 3 m (dipole).
Example 5
v = 3e8 m/s, f = 2.4e9 Hz -> λ = 12.5 cm.
Example 6
v = 3e8 m/s, f = 5e14 Hz -> λ ≈ 600 nm.
Example 7
v = 1480 m/s, f = 1000 Hz -> λ = 1.48 m.
Example 8
v = 343 m/s, f = 40000 Hz -> λ ≈ 8.6 mm.
Example 9
v = 3e8 m/s, f = 8.8e7 Hz -> λ ≈ 3.4 m.
Example 10
v = 343 m/s, f = 20 Hz -> λ ≈ 17 m.
Ways to use this calculator
- You check whether a 20 cm speaker can radiate 50 Hz bass (λ ≈ 6.86 m in air).
- You size a dipole: 100 MHz at c is λ = 3 m, each arm about λ/4.
- From a fork frequency and room v you compare a measured λ against the formula.
Frequently asked questions
What λ at 440 Hz and v = 343 m/s?
λ = 343/440 ≈ 0.780 m, about 0.78 m on the page. At 1000 Hz that is 0.343 m.
What v do I type for sound in a room?
In air, about 343 m/s at 20 °C. In water, about 1480 m/s. For light in vacuum, 3e8 m/s.
Why is λ = v/f?
In time T = 1/f the wave advances by one λ, so v = λ/T. Substitute T and you get λ = v/f.
What if I type f = 0?
You would divide by zero. Frequency must be positive, or there is no period and no wavelength.
Does the same formula work for light?
Yes. In vacuum v = c, so λ = c/f. 5e14 Hz gives 600 nm. In glass v is smaller, so λ is shorter at the same f.
When do I compute v instead of λ?
When you know λ and f and want the medium speed. That is the v = λ·f page. Here the unknown is λ.
Why is period T beside the result?
T = 1/f. At 440 Hz that is about 0.00227 s. In that time the wave takes one step of length λ.
What λ at 2.4 GHz and v = 3e8 m/s?
2.4e9 Hz. λ = 3e8 / 2.4e9 = 0.125 m, or 12.5 cm, typical Wi-Fi.
When will I see nanometers?
When λ falls to about 1e-7 m, as with visible light. Radio stays in meters or centimeters.
Do phase or amplitude enter the formula?
No. λ, v and f describe the travel of the wave. Phase is a snapshot shift; amplitude is loudness, not length.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.