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Sources & Methodology
Speed of light from NIST CODATA exact value. Sound speed from NIST. EM spectrum bands from ITU Radio Regulations.
NIST CODATA — Speed of Light in Vacuum
Exact defined value c = 299,792,458 m/s (exact by SI definition since 1983), used for all electromagnetic wavelength and frequency calculations in this calculator.
ITU Radio Regulations — Frequency Band Allocations
International Telecommunication Union frequency allocation table used to identify the radio band and typical application for any calculated electromagnetic wavelength and frequency in this calculator.
Methodology: λ = v/f. f = v/λ. v = λ×f. Speed of light in vacuum c = 299,792,458 m/s (exact). Speed of light in medium: v = c/n (n = refractive index). Sound in air at 20°C = 343 m/s (NIST). Period T = 1/f. Angular frequency ω = 2πf. Wavenumber k = 2π/λ. Half-wave dipole = 150/f(MHz) metres. Quarter-wave monopole = 75/f(MHz) metres.
⏱ Last reviewed: April 2026
How to Calculate Wavelength — Formula, Spectrum & Antenna Sizing
Wavelength is the distance between successive identical points on a wave. Together with frequency it fully describes the wave’s oscillatory behaviour. The fundamental relationship λ = v/f applies to every wave type — from long-wave radio to gamma rays — with only the wave speed differing by medium and wave type.
The Wavelength Formula
λ = v / f f = v / λ v = λ × f
λ = wavelength (m) • v = wave speed (m/s) • f = frequency (Hz)
FM radio 100 MHz: λ = 299792458 / 10⁸ = 2.998 m
WiFi 2.4 GHz: λ = 299792458 / 2.4×10⁹ = 12.49 cm
Sound A4 440 Hz in air: λ = 343 / 440 = 0.780 m
Green light 550 nm: f = 299792458 / 550×10⁻⁹ = 545 THz
FM radio 100 MHz: λ = 299792458 / 10⁸ = 2.998 m
WiFi 2.4 GHz: λ = 299792458 / 2.4×10⁹ = 12.49 cm
Sound A4 440 Hz in air: λ = 343 / 440 = 0.780 m
Green light 550 nm: f = 299792458 / 550×10⁻⁹ = 545 THz
Electromagnetic Spectrum Quick Reference
| Band | Frequency | Wavelength | Typical Use |
|---|---|---|---|
| LF / MF (AM radio) | 300 kHz–3 MHz | 100 m–1 km | AM broadcast, navigation |
| HF (short wave) | 3–30 MHz | 10–100 m | HF radio, amateur bands |
| VHF (FM / TV) | 30–300 MHz | 1–10 m | FM radio, TV, aviation |
| UHF (cellular / TV) | 300 MHz–3 GHz | 10 cm–1 m | TV, 4G LTE, GPS, Bluetooth |
| SHF (microwave) | 3–30 GHz | 1–10 cm | WiFi, radar, satellite |
| EHF (mmWave) | 30–300 GHz | 1–10 mm | 5G mmWave, imaging |
| Infrared | 300 GHz–430 THz | 700 nm–1 mm | Heat, remote controls |
| Visible light | 430–790 THz | 380–700 nm | Vision, photography |
| UV / X-ray | >790 THz | <380 nm | Sterilisation, medical |
Antenna Length from Frequency
| Frequency | Wavelength | Half-wave Dipole | Quarter-wave Monopole |
|---|---|---|---|
| 1 MHz (AM) | 299.8 m | 149.9 m | 75.0 m |
| 100 MHz (FM) | 3.00 m | 1.50 m | 0.75 m |
| 144 MHz (VHF) | 2.08 m | 1.04 m | 52 cm |
| 433 MHz (IoT) | 69.2 cm | 34.6 cm | 17.3 cm |
| 2.4 GHz (WiFi) | 12.5 cm | 6.25 cm | 3.12 cm |
| 5 GHz (WiFi) | 6.00 cm | 3.00 cm | 1.50 cm |
| 28 GHz (5G mmW) | 10.7 mm | 5.36 mm | 2.68 mm |
💡 Quick radio rule: Wavelength in metres ≈ 300 / frequency in MHz. For FM radio at 88 MHz: λ ≈ 300/88 = 3.41 m, half-wave dipole ≈ 1.70 m. This approximation uses c ≈ 3×10⁸ m/s. For precision calculations use the exact value c = 299,792,458 m/s above.
Frequently Asked Questions
Wavelength (λ) = wave speed (v) / frequency (f). For EM waves in vacuum: λ = c/f where c = 299,792,458 m/s. For 100 MHz FM radio: λ = 299792458/100000000 = 2.998 m. For 440 Hz sound in air: λ = 343/440 = 0.780 m. Rearranging gives f = v/λ and v = λ×f.
Visible light: 380 nm (violet) to 700 nm (red). Colours: violet 380–450 nm, blue 450–495 nm, green 495–570 nm, yellow 570–590 nm, orange 590–620 nm, red 620–700 nm. Frequencies: 430–790 THz. Green at 550 nm has frequency = 299792458/(550×10⁻⁹) = 545 THz.
Wavelength (m) ≈ 300 / f(MHz), using c ≈ 3×10⁸ m/s. Examples: AM 1 MHz → 300 m. FM 100 MHz → 3 m. WiFi 2.4 GHz → 12.5 cm. 5G 28 GHz → 10.7 mm. For precision use c = 299,792,458 m/s. A half-wave dipole antenna length ≈ 150/f(MHz) metres.
Sound at 440 Hz (A4) in air at 20°C: λ = 343/440 = 0.780 m (78 cm). In water (1480 m/s): 3.36 m. In steel (5100 m/s): 11.6 m. Sound travels faster in denser media, so the same frequency produces a longer wavelength in water or steel than in air.
Wavelength and frequency are inversely proportional at fixed speed: λ = v/f. Doubling frequency halves wavelength. For EM waves: 1 MHz = 300 m, 100 MHz = 3 m, 1 GHz = 30 cm, 10 GHz = 3 cm, 1 THz = 0.3 mm, 100 THz = 3 µm (infrared), 600 THz = 500 nm (green light).
In vacuum: c = 299,792,458 m/s (exact). In glass (n=1.5): 2.0×10⁸ m/s. In water (n=1.33): 2.25×10⁸ m/s. In diamond (n=2.42): 1.24×10⁸ m/s. Frequency stays constant when entering a medium; only wavelength shortens: λ = c/(n×f).
Half-wave dipole (m) = 150/f(MHz). Quarter-wave monopole = 75/f(MHz). For 144 MHz: half-wave = 1.04 m. For 2.4 GHz WiFi: quarter-wave = 3.1 cm. Practical wire antenna = theoretical × 0.95 (velocity factor). These formulas work for wire dipoles in free space; real installations require correction for nearby objects and feedline effects.
From longest to shortest wavelength: radio waves (>1 mm), microwaves (1 mm–1 m), infrared (700 nm–1 mm), visible light (380–700 nm), ultraviolet (10–380 nm), X-rays (0.01–10 nm), gamma rays (<0.01 nm). All travel at c in vacuum. Photon energy E = hf increases with frequency: gamma rays carry millions of times more energy per photon than radio waves.
WiFi 2.4 GHz: 12.5 cm. WiFi 5 GHz: 6.0 cm. WiFi 6E 6 GHz: 5.0 cm. 5G sub-6 (3.5 GHz): 8.6 cm. 5G mmWave 28 GHz: 10.7 mm. 5G mmWave 60 GHz: 5 mm. Shorter wavelengths allow smaller antennas and wider bandwidth, but penetrate walls less effectively. 5G mmWave requires dense small cells every 100–200 m.
Angular wavenumber k = 2π/λ (rad/m). In spectroscopy, wavenumber = 1/λ (cm⁻¹). For 550 nm green light: k = 2π/(550×10⁻⁹) = 1.14×10⁷ rad/m; spectroscopic wavenumber = 18182 cm⁻¹. Wavenumber is used in quantum mechanics, spectroscopy, and optics as a compact representation of wavelength-dependent quantities.
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