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Results update as values or units change.
Wavelength (λ) is the distance between matching points on adjacent cycles. Frequency (f) is cycles per second, measured in hertz. Period (T) is the time per cycle, so T = 1/f. Wave speed (v) is the speed at which phase propagates through the medium.
Core relation: v = fλ | λ = v/f | f = v/λ
For electromagnetic waves in a material, v = c/n. Frequency normally stays fixed across a stationary boundary, while speed and wavelength change. Spatial frequency is 1/λ in m⁻¹; angular wavenumber is k = 2π/λ in rad/m.
Convert frequency to hertz and wave speed to metres per second, then divide: λ = v/f. For a 100 MHz radio wave in vacuum, λ = 299,792,458 / 100,000,000 = 2.99792458 m.
Convert wavelength to metres, choose the wave speed for the medium, then divide: f = v/λ. For 532 nm light in vacuum, f = 299,792,458 / (532 × 10⁻⁹) ≈ 5.635 × 10¹⁴ Hz.
| Wave and medium | Speed used | Conditions and precision |
|---|---|---|
| Light in vacuum | 299,792,458 m/s | Exact SI defining constant |
| Light in air | 299,709,471 m/s | Approximation from n = 1.000277; refractive index varies with conditions and wavelength |
| Sound in dry air | 343 m/s | Approximate, 20°C; temperature and humidity matter |
| Sound in freshwater | 1,481 m/s | Approximate, 20°C; temperature, pressure, and composition matter |
| Other waves | Custom | Use the applicable phase speed for the material, tension, depth, or other conditions |
| Region | Approximate vacuum wavelength | Typical example |
|---|---|---|
| Radio | Longer than 1 m | Broadcast radio |
| Microwave | 1 mm to 1 m | Wi-Fi and radar |
| Infrared | 700 nm to 1 mm | Thermal radiation |
| Visible | 380 to 700 nm | Human-visible light |
| Ultraviolet | 10 to 380 nm | UV lamps |
| X-ray | 0.01 to 10 nm | Medical imaging |
| Gamma ray | Shorter than 0.01 nm | Nuclear transitions |
Region boundaries are conventional and overlap in some scientific classifications. The calculator classifies electromagnetic results by vacuum wavelength, even when an in-medium wavelength is entered.
Convert: 100 MHz = 100 × 10⁶ Hz = 1.00 × 10⁸ Hz.
Equation: λ = v/f.
Substitute: λ = (299,792,458 m/s) / (1.00 × 10⁸ s⁻¹) = 2.99792458 m.
Answer: λ ≈ 3.00 m. Each cycle spans about three metres in vacuum; the wavelength in air is only slightly shorter.
Convert: 532 nm = 532 × 10⁻⁹ m = 5.32 × 10⁻⁷ m.
Equation: f = v/λ.
Substitute: f = (299,792,458 m/s) / (5.32 × 10⁻⁷ m) = 5.6352 × 10¹⁴ Hz.
Answer: f ≈ 563.5 THz, in the visible green region.
Convert: 440 Hz is already 440 s⁻¹; use v ≈ 343 m/s for dry air at 20°C.
Equation: λ = v/f.
Substitute: λ = (343 m/s) / (440 s⁻¹) = 0.7795 m.
Answer: λ ≈ 0.780 m. The wavelength changes with air temperature because sound speed changes.
Photon energy depends on frequency: E = hf. The familiar form E = hc/λ uses the vacuum wavelength λ₀. If λmedium is measured inside a material with refractive index n, use E = hc/(nλmedium), because λ₀ = nλmedium. The calculator uses E = hf, which remains unambiguous.
Last reviewed: 14 July 2026.
Calculations convert inputs to SI units, solve v = fλ without intermediate rounding, and round only the displayed result. The speed of light c = 299,792,458 m/s, Planck constant h = 6.62607015 × 10⁻³⁴ J·s, and elementary charge e = 1.602176634 × 10⁻¹⁹ C are exact SI-defined constants.
Primary references: BIPM, The International System of Units; NIST SP 330, SI base-unit definitions; NIST refractive-index overview; Georgia Tech, speed of sound in air; and National Physical Laboratory, sound speed in water at 20°C.
Air refractive index and both sound-speed presets are reference estimates, not universal constants. Refractive index varies with wavelength, pressure, temperature, and composition; sound speed varies with the medium and conditions. For precision work, use a measured custom value.
Choose Solve for Wavelength, select the wave speed, and enter the frequency. Convert MHz to Hz by multiplying by 1,000,000, then use λ = v/f. The calculator performs the unit conversion automatically.
Choose Solve for Frequency, enter the wavelength in nm, and select the correct wave speed. The calculator converts nm to metres and applies f = v/λ. For light in vacuum, 532 nm is about 563.5 THz.
Use the phase speed for the wave and medium under your conditions. Light in vacuum uses exactly 299,792,458 m/s; dry-air sound at 20 °C is approximately 343 m/s; freshwater sound near 20 °C is approximately 1,481 m/s. Use Custom speed when the material, temperature, tension, or wave type differs.
Yes. Select Sound in air at 20 °C, Sound in freshwater at 20 °C, or Custom speed. Photon energy and electromagnetic spectrum labels are intentionally omitted for non-electromagnetic waves.
The frequency is set by the source and normally remains continuous across a stationary boundary. If wave speed changes, wavelength changes so that v = fλ still holds.
For light in a material with refractive index n, phase speed is v = c/n. Frequency stays fixed, so the in-medium wavelength is λmedium = λvacuum/n. Material dispersion means n can depend on wavelength and temperature.
In vacuum, 100 MHz corresponds to 2.99792458 m, usually rounded to 3.00 m. In air the result is slightly shorter because light travels slightly slower.
Spatial frequency 1/λ counts cycles per metre and has units m⁻¹. Angular wavenumber k = 2π/λ measures phase change per metre and has units rad/m. They differ by a factor of 2π.
