Frequency and Wavelength Calculator — c = fλ
Calculate frequency, wavelength, or wave speed using c = fλ. Covers EM spectrum, sound waves, visible light, and practical radio/optical engineering examples.
Every wave — light, radio, sound, microwave — has a frequency and a wavelength, and they're tied together through the wave's speed. Higher frequency always means shorter wavelength for the same medium. This relationship is why radio stations use frequencies in MHz while gamma rays have wavelengths in picometers: they're both waves, just at wildly different scales.
The CalcHub frequency and wavelength calculator lets you convert between frequency, wavelength, and wave speed for any type of wave.
The Formula
c = f × λOr equivalently:
- f = c / λ
- λ = c / f
Where:
- c = wave speed (m/s) — use 3×10⁸ m/s for light in a vacuum
- f = frequency (Hz)
- λ = wavelength (m)
For sound in air at 20°C, use c ≈ 343 m/s. For light in water, c ≈ 2.26×10⁸ m/s.
The Electromagnetic Spectrum
| Band | Frequency | Wavelength |
|---|---|---|
| AM radio | 540–1700 kHz | 176–556 m |
| FM radio | 88–108 MHz | 2.78–3.41 m |
| WiFi (2.4 GHz) | 2.4 GHz | 12.5 cm |
| Visible light | 430–750 THz | 400–700 nm |
| X-rays | 30 PHz – 30 EHz | 0.01–10 nm |
Worked Example
A radio station broadcasts at 98.5 MHz. What is the wavelength of its signal?
λ = c / f = (3 × 10⁸) / (98.5 × 10⁶) = 3.045 m
That's why radio antennas are meter-scale. Optimal antenna length is often λ/4 ≈ 76 cm for a quarter-wave monopole.
For sound: a 440 Hz concert A note at room temperature has wavelength:
λ = 343 / 440 ≈ 0.78 m (78 cm)
Why do higher frequencies have more energy?
For photons (light, EM radiation), energy E = hf where h is Planck's constant. Higher frequency = higher photon energy. This is why UV causes sunburn but visible light doesn't — UV photons carry enough energy to damage DNA. Wavelength and frequency are inversely related, so short-wavelength radiation is high-energy.
Does wavelength change when light enters a different medium?
Yes — and interestingly, the frequency stays constant but the wavelength changes. Light slows down in glass or water, and since f = c/λ, when c decreases with constant f, λ must decrease too. This is what causes refraction.
What's the period of a wave and how does it relate to frequency?
Period T = 1/f. If a wave oscillates 100 times per second (100 Hz), each cycle takes 1/100 = 0.01 seconds. Period and frequency are simply reciprocals of each other.