Frequency to Period Calculator
Enter a frequency in hertz to get the period of one cycle in seconds — plus the angular frequency in radians per second — using the simple relationship T = 1 / f.
Period and angular frequency at once
Enter the frequency in hertz and the calculator returns the period (1/f) in seconds and the angular frequency (2πf) in radians per second together.
Use hertz
Frequency must be in hertz (cycles per second) for the period to come out in seconds — a kilohertz is 1000 Hz and a megahertz is 1,000,000 Hz.
What is the period of a frequency?
Time for one full cycle
A frequency to period calculator turns how often something repeats into how long a single repetition takes. Frequency, measured in hertz (Hz), counts the cycles a periodic signal completes each second; the period is the time of one of those cycles, measured in seconds. The two are reciprocals, so a higher frequency always means a shorter period. This is the number behind the tick of an oscillator, the swing of a pendulum, the pitch of a sound wave, and the cycle of the AC voltage in your wall socket. Alongside the period the calculator also returns the angular frequency, the same rhythm expressed in radians per second.
Enter a frequency in hertz to get the period of one cycle in seconds and the angular frequency in radians per second instantly.
The period is one divided by the frequency, and the angular frequency is two pi times the frequency.
T = 1 / fBecause period and frequency are reciprocals, doubling the frequency halves the period. The angular frequency (ω = 2πf) measures the same oscillation in radians per second rather than cycles per second, which is the form used throughout the mathematics of waves and rotation. Take the European mains frequency of 50 Hz: the period is 1 ÷ 50 = 0.02 s, one full voltage cycle every 20 milliseconds, and the angular frequency is 2π × 50 ≈ 314.159265 rad/s. Feed in hertz and the period comes back in seconds and the angular frequency in radians per second.
The relationship is exact, but a couple of practical points are worth keeping in mind.
Constant frequency and hertz in, seconds out
The formula T = 1 / f describes a steady, repeating signal with a single, constant frequency. A signal whose frequency drifts, or a complex waveform built from many frequencies, has no single period — analyse each component separately. Keep your unit in hertz so the period lands in seconds: convert kilohertz and megahertz to hertz first, and remember the angular frequency is in radians per second, not cycles per second.