Frequency & PeriodFree online science calculator — instant results, no sign-up
Convert between frequency and period (T = 1/f).
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About the Frequency & Period
The Frequency & Period calculator converts a frequency in hertz into the time required for one complete wave cycle. It reports the period in seconds and milliseconds, along with the equivalent number of cycles per minute. With the default frequency of 60 Hz, it shows a period of 0.016667 s, or 16.6667 ms, and 3,600 cycles per minute.
- Frequency (Hz)
- Frequency is the number of complete cycles per second, measured in hertz (Hz), with a default value of 60.
Formula and method
T = 1/f; T_ms = 1000T = 1000/f; C = 60f. The inverse relationship is f = 1/T.
- fFrequency in hertz (Hz), equivalent to cycles per second.
- TPeriod, or duration of one complete cycle, in seconds (s).
- T_msPeriod expressed in milliseconds (ms); there are 1,000 milliseconds in one second.
- CEquivalent number of cycles per minute; there are 60 seconds in one minute.
Take the reciprocal of the entered frequency to find the period in seconds. Multiply the unrounded period by 1,000 to express it in milliseconds, and multiply the frequency by 60 to obtain cycles per minute. For f = 60 Hz, T = 1/60 s rounds to 0.016667 s, T_ms = 1000/60 ms rounds to 16.6667 ms, and C = 60 × 60 = 3,600 cycles per minute.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Frequency60 Hz
Results
- Period0.016667 s
- In milliseconds16.6667 ms
- Cycles per minute3,600
How to use the Frequency & Period
- 1Enter a positive frequency in the Frequency (Hz) field, or keep the default value of 60.
- 2Read the Period output: at 60 Hz, one cycle takes 0.016667 s.
- 3Read the In milliseconds output: the same cycle duration is 16.6667 ms.
- 4Read the Cycles per minute output: a constant frequency of 60 Hz corresponds to 3,600 cycles per minute.
Reading your result
Period gives the duration of one complete cycle in seconds. In milliseconds expresses that same duration in a smaller time unit, not a different physical quantity. Cycles per minute expresses the frequency on a one-minute basis. For the default input, the output rows are Period = 0.016667 s; In milliseconds = 16.6667 ms; Cycles per minute = 3,600. Higher frequencies produce shorter periods, while lower positive frequencies produce longer periods.
Limitations
The calculation assumes a repeating signal with a constant, positive frequency. Zero frequency has no finite period under T = 1/f, and negative frequency is not meaningful as a cycle-count rate for this tool. For a varying frequency, the result does not describe every cycle's duration. Displayed periods are rounded independently from unrounded calculations, so converting the displayed seconds value back to milliseconds may give a slightly different last digit. This tool does not determine wavelength, wave speed, or amplitude.
Common questions
Why does 60 Hz give a period of 0.016667 s?+
60 Hz means 60 complete cycles occur each second. Dividing one second by 60 gives the duration of one cycle, which rounds to 0.016667 s.
Why is the millisecond result 16.6667 ms rather than the result of multiplying the displayed seconds by 1,000?+
The calculator converts the unrounded value of 1/60 s to milliseconds before rounding. Using the already rounded display value of 0.016667 s introduces a small rounding difference.
How are 3,600 cycles per minute obtained from 60 Hz?+
Multiply 60 cycles per second by 60 seconds per minute. The result is 3,600 cycles per minute, assuming the frequency stays constant.
Can I recover frequency from a known period?+
Yes. Use f = 1/T with the period expressed in seconds; if the period is in milliseconds, use f = 1000/T_ms. This page's listed input is frequency, so the inverse formula explains the relationship rather than implying a separate period input.
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.