Wavelength and Frequency: formula
Enter the frequency in megahertz. The wavelength is the speed of light, 299,792,458 meters per second, divided by the frequency, and the period is the inverse of the frequency. Convert other units first: 1 gigahertz is 1,000 megahertz.
The relationship holds for radio waves and light in a vacuum, and slightly slower speeds apply in cables and materials.
Wavelength and Frequency: worked example
| Frequency (MHz) | 100 |
|---|---|
| Wavelength (m) | 3 |
| Period (nanoseconds) | 10 |
Speed in cable is 60% to 90% of the speed of light, changing the effective wavelength. Sound waves travel at about 343 meters per second, so their wavelengths differ. Real antennas are trimmed for the surroundings.
Results are for waves in a vacuum or air.
Wavelength and Frequency: changing Frequency (MHz)
| Frequency (MHz) | Wavelength (m) | Period (nanoseconds) |
|---|---|---|
| 80 | 3.7 | 12.5 |
| 90 | 3.3 | 11.1 |
| 100 (example) | 3 | 10 |
| 110 | 2.7 | 9.1 |
| 120 | 2.5 | 8.3 |
Wavelength and Frequency: compare input ranges
| Input | Tested from | To | Wavelength (m): low input | Wavelength (m): high input | Swing |
|---|---|---|---|---|---|
| Frequency (MHz) | 90 | 110 | 3.3 | 2.7 | 0.606 (20%) |
Wavelength and Frequency: individual input comparisons
| Input | Value | Wavelength (m) | Period (nanoseconds) |
|---|---|---|---|
| Frequency (MHz) | 80 | 3.7 | 12.5 |
| 90 | 3.3 | 11.1 | |
| 100 | 3 | 10 | |
| 110 | 2.7 | 9.1 | |
| 120 | 2.5 | 8.3 |
Wavelength and Frequency: which assumptions move the result?
Wavelength and Frequency: values and definitions
| Quantity and definition | Value used |
|---|---|
| Frequency (MHz) — An FM radio station at 100 MHz is a typical example. | 100 |
| Wavelength (m) | 3 |
| Period (nanoseconds) | 10 |
Wavelength and Frequency: half and double Frequency (MHz)
| Frequency (MHz) | Wavelength (m) |
|---|---|
| 50 | 6 |
| 100 | 3 |
| 200 | 1.5 |
Common error: Using the speed of sound. Radio and light travel at about 300 million meters per second, nearly a million times faster than sound in air.
Physics & Mechanics calculators: Projectile Motion Calculator, Free Fall Calculator, Centripetal Force Calculator, Pendulum Period Calculator, Horsepower Calculator, Speed, Distance and Time Calculator.
Waves that travel at the speed of light trade frequency for length: the higher the frequency, the shorter the wave. A radio station at 100 megahertz has a wavelength of about 3 meters, and each cycle takes 10 nanoseconds. That relationship sets the length of an antenna, and a Wi-Fi signal at 2.4 gigahertz is only about 12 centimeters long.
Enter the frequency in megahertz. A value in kilohertz or gigahertz needs converting first, or the wavelength lands a thousand times off.
See the pendulum period on the pendulum period calculator, unit changes on the frequency and length converters and speed on the speed, distance and time calculator. The uniform acceleration and Hooke's law pages cover oscillation and motion, and the bandwidth calculator covers data rates.
How do I convert frequency to wavelength?
Divide the speed of light, about 300 million meters per second, by the frequency in hertz.
Why do antennas depend on wavelength?
An antenna works best near a fraction of the wavelength, such as a half or quarter, so lower frequencies need longer antennas.
What is the wavelength of Wi-Fi?
About 12.5 centimeters at 2.4 gigahertz and about 6 centimeters at 5 gigahertz.