The inverse relationship between how long one cycle takes (period) and how many cycles happen per second (frequency), applicable to any repeating event.
How it works
Dividing 1 by the period gives frequency; dividing 1 by the frequency gives the period back. Type into either field and the other updates instantly.
What this does not include
This does not include wavelength or wave speed — for the full wave equation relating frequency, wavelength, and speed, use this site’s wave speed calculator instead.
How to use this calculator
- Enter a value in either period or frequency — the other field fills in automatically.
A worked example
A period of 0.01 seconds: frequency = 1 ÷ period = 1 ÷ 0.01 = 100 Hz.
Given a frequency of 50 Hz, the period is 1 ÷ 50 = 0.02 seconds — the reverse calculation.
What the variables mean
| Variable | Meaning |
|---|---|
| Period | Time for one complete cycle |
| Frequency | Cycles per second, in hertz |
Edge cases worth knowing
Frequency and period are reciprocals of each other — a shorter period always means a higher frequency, and there’s no need for two separate formulas, just one inverted.
A period or frequency of zero has no valid reciprocal — the calculator declines to show a result for either, since dividing by zero is undefined.
Frequently asked questions
Why are period and frequency reciprocals of each other?
Frequency counts cycles per second, while period measures seconds per cycle — inverting one directly gives the other, since they describe the same repeating event from opposite angles.
Does this apply to anything besides waves?
Yes — any periodic event (a pendulum swing, a rotating wheel, an electrical signal, a heartbeat) has a period and frequency related this same way.
What unit is frequency measured in?
Hertz (Hz), where 1 Hz means exactly one cycle per second.
