Frequency to Wavelength Calculator: Exact Speed of Light
Convert frequency to wavelength with the exact SI speed of light. Set a medium by velocity factor or refractive index, with RF band presets, a reverse mode, and photon energy.
At a glance
- Computes
- Frequency to wavelength and back with the exact speed of light, plus photon energy.
- You supply
- A frequency or a wavelength, and the medium as velocity factor or refractive index.
- Use when
- An electromagnetic wave in vacuum or a medium whose slowing factor you know.
- Not for
- Sound or any wave whose speed is not derived from the speed of light.
electromagnetic spectrum band (log10 of the wavelength in metres); reference at Example
Wavelength
Enter a value
| Quantity | Value |
|---|
v = VF * c; lambda = v / f (forward); f = v / lambda (reverse); E = h * f
How?
How this is calculated
Wavelength and frequency are related by the wave speed, v = f times lambda. In vacuum the wave speed is the exact SI speed of light, c = 299,792,458 m/s. In a medium the wave slows by the velocity factor, v = VF times c, where VF = 1 in vacuum and VF = 1 / n for a stated refractive index n. Frequency is invariant across media, so only the speed and the wavelength change; a medium-measured wavelength still maps back to frequency by f = VF times c / lambda.
Photon energy, E = h times f, is always computed from frequency (in both directions) and converted to electronvolts by dividing by the elementary charge. It is shown only when the wavelength is at or below 1 mm (frequency at or above 300 GHz), the far-infrared boundary where the quantity is physically salient; on RF results it is computed but not displayed.
To see how a wavelength sets measurable fringe positions rather than only its frequency, use the double slit experiment simulator.
Formula: v = VF * c; lambda = v / f (forward); f = v / lambda (reverse); E = h * f
The 3e8 shortcut and the 300 / f(MHz) mnemonic
Textbook homework keys and the ham-radio mnemonic both round the speed of light to c ~ 3e8 m/s, which gives the quick estimate lambda(m) ~ 300 / f(MHz). That shortcut is accurate to about 0.07%, close enough for most antenna work but not exact. This tool computes with the defined SI value c = 299,792,458 m/s, so the last digits differ from the rounded shortcut: 2.45 GHz computes to 12.236 cm exact, versus 12.2 cm from the 3e8 approximation.
How wavelength relates to antenna length
Wavelength is not antenna length. A resonant half-wave element is shortened from a free-space half wavelength by a wire end-effect factor, k ~ 0.95 for a thin-wire half-wave dipole, giving element length ~ 0.5 times k times lambda. This shortening factor k is a different quantity from the medium velocity factor VF this tool's Medium input uses (VF ~ 0.66 for RG-58 coax): k accounts for the physical wire's end effects in free space, VF accounts for a wave's propagation speed through a transmission line or dielectric. The familiar empirical formula 468 / f(MHz) feet for a half-wave dipole is the same k ~ 0.95 shortening baked into a unit conversion: a free-space half wavelength is 492 / f(MHz) feet, and 468 / 492 is about 0.951.
Sources
- BIPM SI Brochure, 9th edition (speed of light, defining constant). BIPM. Retrieved .
- NIST CODATA, Value of c. NIST. Retrieved .
- OpenStax College Physics 2e, Wave Properties, Speed, Amplitude, Frequency, and Period. OpenStax. Retrieved .
Method last reviewed