This wavelength calculator solves the wave equation v = f × λ in any direction: find wavelength from frequency and wave speed, frequency from wavelength, or the speed of a wave — for sound, light, radio and water waves.
The Wave Equation
Every wave — sound, light, radio, water, seismic — obeys one relation: speed = frequency × wavelength (v = fλ). Frequency counts how many wave crests pass per second; wavelength is the distance between crests; their product is how fast the pattern travels. Fix the speed (as a medium does) and frequency and wavelength trade off inversely: high pitch means short waves. This calculator is part of our Physics Calculators collection; for ordinary motion, see the Speed Calculator.
Worked Examples (Verified)
- Concert A (440 Hz) in air: λ = 343 ÷ 440 = 0.78 m — the tuning note’s waves are about guitar-length.
- Green light (~5 × 10¹⁴ Hz): λ = 3 × 10⁸ ÷ 5 × 10¹⁴ = 6 × 10⁻⁷ m = 600 nm — the whole visible spectrum spans just 380–750 nm.
- FM radio at 100 MHz: λ = 3 m — why car antennas are roughly quarter-wave sticks of ~75 cm.
- Bass note at 55 Hz: λ = 6.2 m in air — longer than most rooms, which is why bass leaks through walls and can’t be localized.
Wave Speeds Worth Knowing
| Wave | Speed |
|---|---|
| Sound in air (20 °C) | 343 m/s |
| Sound in water | 1,480 m/s |
| Sound in steel | ≈5,960 m/s |
| Light / radio in vacuum | 299,792,458 m/s (exact, by definition) |
The medium sets the speed; the source sets the frequency; the wavelength is whatever the equation then requires. Crossing into a new medium (light entering glass, sound entering water) changes speed and wavelength together while frequency stays fixed — the root mechanism of refraction and lenses.
Related Tools
- Speed Calculator — distance and time for ordinary motion
- Physics Calculators — the full collection
Frequently Asked Questions
How do I calculate wavelength?
Divide wave speed by frequency: λ = v ÷ f. Concert A: 343 ÷ 440 ≈ 0.78 m.
What is the wavelength of visible light?
Roughly 380 nm (violet) to 750 nm (red). Green sits near the middle at ~530–560 nm.
Does frequency change when a wave enters a new medium?
No — frequency is set by the source and stays constant; speed and wavelength change together. That is why light keeps its color entering water but bends.
What is the relationship between frequency and wavelength?
Inverse at a given speed: double the frequency, half the wavelength. High-frequency waves are short; low-frequency waves are long.
How long is a Wi-Fi wave?
At 2.4 GHz, about 12.5 cm; at 5 GHz, about 6 cm — sizes that explain a lot about antenna design and why signals leak through doorways but not walls’ rebar grids.
Is this wavelength calculator free?
Yes — free, instant, no sign-up.