Choose the quantity to find, then enter the two known quantities. For wavelength or frequency, choose Light in vacuum to use exactly 299,792,458 m/s, or Enter wave speed to supply a speed appropriate to your wave and conditions. The entered-speed option initially shows the same number as the vacuum preset; selecting it does not assume a different medium.
Wave relationship
For a wave with frequency $f$ in hertz, wavelength $\lambda$ in meters, and speed $v$ in meters per second:
One hertz means one cycle per second. Wavelength is the distance between corresponding points of successive wave cycles. This relationship uses the speed of those wave cycles; the calculator does not supply a speed for air, water, cables, or other materials.
Examples and units
Light in vacuum at 1 MHz has a wavelength of 299.792458 m. With an explicitly entered speed of 340 m/s and frequency of 170 Hz, the answer is 2 m. That second example is an arithmetic scenario, not a standard speed for a medium. A vacuum wavelength of 500 nm corresponds to approximately 599.584916 THz.
| Prefix | Factor |
|---|---|
| T (tera) | 10¹² |
| G (giga) | 10⁹ |
| M (mega) | 10⁶ |
| k (kilo) | 10³ |
| c (centi) | 10⁻² |
| m (milli) | 10⁻³ |
| µ (micro) | 10⁻⁶ |
| n (nano) | 10⁻⁹ |
Choose the input units before reading the answer. Changing an input unit assigns the new unit to the number currently shown; it does not convert that number. For example, 500 nm and 500 µm represent different lengths. Result-unit selections are kept separately for each solving mode.
Precision and limits
The calculator normalizes the two known quantities to SI units, calculates without rounding the intermediate values, then converts to your result unit. Supporting rows show all three quantities in SI units and the speed assumption. Ordinary answers show up to six decimal places; scientific notation uses seven significant digits for nonzero magnitudes below 1e-6 or at least 1e12. For example, 1e-200 m/s means 10⁻²⁰⁰ m/s, not zero. Display rounding does not describe measurement accuracy.
Only the visible known quantities affect the calculation. Each must be positive and finite, and must normalize to a value from 1e-100 through 1e100 inclusive. These are software limits, not physical limits. The calculated quantity can fall outside that input range. Invalid inputs clear the answer; Reset restores the vacuum 1 MHz example and the default units.
An entered wave speed is your assumption. Algebraic examples do not establish whether a speed is physically possible or suitable for a particular medium. This tool does not validate propagation models, equipment design, exposure, or safety.
For changing frequency units alone, use the frequency converter. For the duration of one cycle, use the frequency to period calculator. For length units alone, use the distance converter.
Sources
- OpenStax, Traveling Waves, Equation 16.1, supplies the wave relationship.
- NIST, SI Units – Length, supplies the exact speed of light in vacuum used by the preset.
- NIST, SI Units – Time, defines hertz as cycles per second.
- NIST, Metric (SI) Prefixes, supplies the decimal unit factors.