Wavelength & FrequencyFree online science calculator — instant results, no sign-up
Convert between wavelength and frequency for any wave speed.
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About the Wavelength & Frequency
The Wavelength & Frequency calculator finds a wave’s wavelength from its frequency in MHz and its propagation speed in m/s. Its default speed, 299792458 m/s, is the speed of light in a vacuum, but you can enter another speed for waves in other media. Results show wavelength in both meters and centimeters.
- Frequency (MHz)
- The wave’s oscillation frequency in megahertz, where 1 MHz equals 1000000 Hz; the default is 100 MHz.
- Wave speed (m/s)
- The wave’s propagation speed in meters per second, defaulting to 299792458 m/s for light in a vacuum.
Formula and method
λ = v ÷ f, with f = f_MHz × 1000000; therefore λ = v ÷ (f_MHz × 1000000).
- λWavelength in meters: the distance between successive points at the same phase, such as adjacent crests.
- vWave propagation speed in meters per second.
- fFrequency in hertz, or cycles per second.
- f_MHzThe frequency entered in megahertz.
Convert the entered frequency from MHz to Hz by multiplying by 1000000, then divide wave speed by that frequency to obtain wavelength in meters. Multiply the unrounded wavelength in meters by 100 to obtain centimeters. With the default inputs, 100 MHz becomes 100000000 Hz, and 299792458 ÷ 100000000 gives 2.99792458 m. The displayed results are Wavelength = 2.9979 m and In centimeters = 299.792 cm.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Frequency100 MHz
- Wave speed299792458 m/s
Results
- Wavelength2.9979 m
- In centimeters299.792 cm
- Formulaλ = wave speed ÷ frequency
How to use the Wavelength & Frequency
- 1Enter the frequency in Frequency (MHz), leaving 100 for the default example.
- 2Enter the propagation speed in Wave speed (m/s), leaving 299792458 for light in a vacuum.
- 3Ensure both inputs are positive and that the speed applies to your wave and medium.
- 4Read the wavelength in meters and its equivalent in centimeters; the default results are 2.9979 m and 299.792 cm.
- 5Check the formula row, λ = wave speed ÷ frequency, remembering that the calculation converts MHz to Hz first.
Reading your result
The Wavelength row reports the distance of one complete wave cycle in meters; the default result is 2.9979 m. The In centimeters row expresses the same distance in centimeters, giving 299.792 cm with the default inputs. Each row is rounded independently from the unrounded result. The Formula row, λ = wave speed ÷ frequency, identifies the relationship used, with frequency expressed in Hz for the calculation.
Limitations
The calculation assumes a wave with a well-defined frequency and wavelength and requires positive frequency and speed. Zero frequency causes division by zero. Use the phase speed appropriate to the wave, medium, and frequency; in dispersive media, speed can vary with frequency. The default speed applies to electromagnetic waves in a vacuum, not automatically to sound or waves in materials. Displayed precision does not guarantee equivalent accuracy in the inputs. With the listed inputs, this tool calculates wavelength rather than directly accepting wavelength to calculate frequency.
Common questions
Why must the calculator convert MHz to Hz before dividing?+
Wave speed is entered in meters per second, so frequency must be in cycles per second. The default 100 MHz equals 100000000 Hz; dividing 299792458 m/s by that frequency produces the displayed wavelength of 2.9979 m.
Can I use this calculator for sound or waves in water?+
Yes, if the wave has a well-defined frequency and phase speed. Replace 299792458 m/s with the appropriate speed for that wave and medium, and enter its frequency in MHz rather than Hz.
Why does multiplying the displayed meter result by 100 not exactly reproduce the centimeter row?+
The calculator converts the unrounded wavelength before rounding each output. For the default inputs, 2.99792458 m becomes 299.792458 cm, displayed as 2.9979 m and 299.792 cm respectively.
How would I find frequency from a known wavelength?+
Rearrange the same relationship to f = v ÷ λ, using wavelength in meters to obtain frequency in Hz, then divide by 1000000 for MHz. The listed calculator inputs support the frequency-to-wavelength direction, so this reverse calculation requires a separate calculation.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.