Period and Frequency Converter
Convert instantly between the period, frequency and angular frequency of any oscillation or wave.
Given quantity
s
Oscillations per second
- 1
Angular frequency (ω)
2 × π ÷ 2 = 3.141593ω = 2π / T, in radians per second. - 2
Frequency
1 ÷ 2 = 0.500000
How does this calculator work?
Period and frequency are reciprocals: f = 1/T and T = 1/f. Enter either the period in seconds or the frequency in hertz, and the converter returns the other value plus the angular frequency ω = 2π·f in radians per second. A 2-second period equals 0.5 Hz and about 3.14 rad/s.
Formula
How this is calculated
Pick which quantity you know — the period T (the time in seconds for one complete cycle) or the frequency f (the number of cycles per second, measured in hertz). The calculator then derives the others.
Period and frequency are reciprocals: f = 1 / T and T = 1 / f. The angular frequency, which describes how fast the phase advances in radians, is ω = 2π·f = 2π / T and is reported in radians per second. These relations hold for any periodic motion, from a swinging pendulum to an AC voltage or a sound wave.
Inputs must be positive and non-zero, since a zero period or zero frequency is physically undefined and would require dividing by zero. Make sure your period is in seconds and your frequency in hertz so the converted values carry the correct units; for example a 2 s period gives 0.5 Hz and an angular frequency of about 3.14 rad/s.
Frequently asked questions
They are reciprocals: frequency equals one divided by the period, and the period equals one divided by the frequency. A shorter period means a higher frequency.
Angular frequency ω measures the rate of phase change in radians per second. It equals 2π times the ordinary frequency, ω = 2π·f, because one full cycle spans 2π radians.
Enter the period in seconds and the frequency in hertz (cycles per second). The angular frequency is then returned in radians per second.
Also known as
TG we-Calculate Editorial Team. (2026). Period and Frequency Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/period-frequency-calculator
TG we-Calculate Editorial Team. "Period and Frequency Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/period-frequency-calculator.
TG we-Calculate Editorial Team, "Period and Frequency Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/period-frequency-calculator
@misc{wecalculate_period_frequency_calculator, title = {Period and Frequency Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/period-frequency-calculator}}, year = {2026}, note = {TG we-Calculate} }
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