Convert frequency to wavelength for light, sound, and radio waves using λ = v/f. Supports EM waves, sound in air with temperature correction, and custom media.
The relationship between frequency and wavelength is foundational to all wave physics. Whether you are working with electromagnetic radiation, sound waves, seismic waves, or ocean waves, the same core equation applies: wavelength equals wave speed divided by frequency (λ = v/f).
This calculator handles the three most common scenarios: electromagnetic waves traveling at the speed of light, sound waves in air with temperature-dependent speed, and waves in custom media where you specify the propagation speed. It computes wavelength, period, angular frequency, and wave number — all the quantities needed for wave analysis.
The tool also generates a full harmonic series and a comparison table showing what wavelength your frequency would produce in different media. This makes it ideal for acoustics engineers, antenna designers, physicists, and musicians who need to relate frequency to physical dimensions. Preset buttons for common frequencies — FM radio, WiFi bands, musical notes, and ultrasound — let you explore instantly.
Frequency-to-wavelength conversion requires knowing the propagation speed, which varies dramatically between media. Light travels at 299,792,458 m/s while sound in air is only about 343 m/s — a million-fold difference. This calculator handles the correct speed for each medium, includes temperature correction for sound, and presents results in appropriate SI prefixes so you never confuse nanometers with millimeters.
Wavelength from frequency: λ = v / f For EM waves: v = c = 299,792,458 m/s For sound in air: v = 331.3 + 0.606 × T (°C) Period: T = 1 / f Angular frequency: ω = 2πf Wave number: k = 2π / λ Where: λ = wavelength (m) f = frequency (Hz) v = wave speed (m/s)
Result: 0.7795 m (77.95 cm)
At 20°C, the speed of sound is 331.3 + 0.606 × 20 = 343.4 m/s. For concert A (440 Hz): λ = 343.4 / 440 = 0.7805 m, about 78 cm. This is why organ pipes for this note are roughly that length.
Wavelength determines how waves interact with objects. Sound waves with wavelengths comparable to doorway widths (about 1 meter, corresponding to 343 Hz) diffract easily around corners — which is why you can hear someone speaking in the next room. Higher-frequency sounds with shorter wavelengths travel more directionally. The same principle applies to radio waves: AM radio (medium wave, ~300 m wavelength) diffracts around buildings and hills, while microwave signals (centimeter wavelengths) require line-of-sight.
In radio frequency engineering, antenna dimensions are directly tied to wavelength. A quarter-wave monopole antenna for FM radio at 100 MHz needs to be about 75 cm long (λ/4 = 3m/4). For 5 GHz WiFi, a quarter-wave element is only 1.5 cm. This calculator helps RF engineers quickly determine physical dimensions for any target frequency.
String and pipe instruments produce sound at frequencies determined by their physical dimensions. A guitar string vibrating at 440 Hz (A4) has a wavelength of about 78 cm in air. Open organ pipes are approximately half a wavelength long at their fundamental frequency. Understanding the frequency-wavelength relationship is essential for instrument design, room acoustics, and audio engineering.
Divide the wave speed by the frequency: λ = v/f. For light, v = 3 × 10⁸ m/s. For sound in air at 20°C, v ≈ 343 m/s. The result is wavelength in meters.
Because wave speed varies by medium. Sound travels at 343 m/s in air but 1,480 m/s in water. The same frequency produces a wavelength about 4.3× longer in water than in air.
λ = 3 × 10⁸ / 2.4 × 10⁹ = 0.125 m or 12.5 cm. This is why WiFi antennas are typically a few centimeters long (quarter-wave or half-wave designs).
Higher temperature increases the speed of sound, which increases wavelength for the same frequency. At 0°C, sound speed is 331 m/s; at 30°C it is about 349 m/s — a 5.4% increase.
Harmonics are integer multiples of a fundamental frequency. The 2nd harmonic is twice the fundamental frequency with half the wavelength. Harmonics are central to music, acoustics, and resonance analysis.
Angular frequency ω = 2πf measures oscillation rate in radians per second. It appears naturally in sine-wave equations, phasor analysis, and any context where phase angles matter — especially in AC circuit analysis and signal processing.