Frequency to Period Calculator (f = 1/T)
Enter a frequency or a time period and pick its unit. The calculator gives the matching period or frequency, the angular frequency in radians per second and the wavelength of an electromagnetic wave of that frequency in a vacuum.
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Formula
- Period:
T = 1 / fand frequencyf = 1 / T - Angular frequency:
ω = 2π f(radians per second) - Wavelength in a vacuum:
λ = c / fwithc = 299 792 458 m/s
Results are shown with SI prefixes (ms, µs, kHz, MHz, and so on) to six significant digits.
Worked example
50 Hz: T = 1 / 50 = 0.02 s = 20 ms, ω = 2π × 50 = 314.159 rad/s, λ = 299 792 458 / 50 = 5 995 849 m = 5.99585 Mm.
1 MHz: T = 1 µs, ω = 6 283 190 rad/s, λ = 299.792 m.
Frequently asked questions
How do you convert frequency to period?
Period is the reciprocal of frequency, T = 1 / f. A 50 Hz signal has T = 1 / 50 = 0.02 s, which is 20 ms. In the other direction, a 20 ms period is f = 1 / 0.02 = 50 Hz.
What is angular frequency?
Angular frequency is ω = 2π f, in radians per second. At 50 Hz, ω = 2 × 3.14159 × 50 = 314.159 rad/s. It is the ω in expressions such as v(t) = Vp sin(ωt).
How is wavelength found from frequency?
Wavelength = c / f, with c = 299 792 458 m/s in a vacuum. At 1 MHz that is 299.792 m. In a cable or on a circuit board the wave is slower, so the real wavelength is shorter.
What range of values is accepted?
The frequency, or the frequency equal to the period you enter, must be between 0.000001 Hz and 10^15 Hz. Zero is rejected because a frequency of zero has no finite period.