Frequency to period: turning a rate into a length of time
What this conversion does
It takes the number of cycles completed in a second and reports how long one of them lasts, using the relationship T = 1/f. The two quantities carry exactly the same information in opposite directions: a rate tells you how often something happens, a period tells you how much time you have between occurrences. Engineers reach for one or the other depending on which makes the arithmetic simpler.
Why the answer is scaled for you
A period can be anything from a fraction of a nanosecond to several seconds, and writing all of those in seconds would mean either very long decimals or a column of exponents. The converter therefore picks the unit: a frequency of 1 Hz gives a period of 1 second, 50 Hz gives 20 milliseconds, and a gigahertz gives something in the picosecond range. The underlying value never changes — only the way it is written.
Frequency to period conversion table
Frequencies from the mains supply upwards, with the period each one implies and the unit it is naturally written in.
| Hertz (Hz) | Period (seconds) |
|---|---|
| 1 | 1 s |
| 50 | 20 ms |
| 60 | 16.67 ms |
| 100 | 10 ms |
| 440 | 2.273 ms |
| 1000 | 1 ms |
| 10000 | 100 us |
| 1000000 | 1 us |
The mains supply, and why 50 and 60 both exist
Mains electricity alternates at either 50 or 60 Hz depending on the region, which is a period of 20 or about 16.7 milliseconds. Neither number is round in the other unit, and the choice was made long ago for reasons of generator design rather than convenience. What matters in practice is that the period sets the timing of anything synchronised to the supply, from a clock that counts cycles to a dimmer that switches at the zero crossing.
Fifty gives twenty, sixty gives about seventeen
The two figures worth memorising are the ones you will meet most often: 50 Hz is a period of 20 ms, and 60 Hz is a period of about 16.67 ms. Everything else follows from dividing one by the frequency, and the converter does the division without rounding.
Frequently asked questions
How do I convert a frequency to a period?
Divide one by the frequency: T = 1/f. A frequency of 50 Hz therefore has a period of 0.02 seconds, which is 20 milliseconds. The converter does the same division and picks the unit that keeps the result readable.
What is the period of 60 Hz?
About 16.67 milliseconds, since 1 ÷ 60 is 0.01666 recurring seconds. The value does not terminate in decimal, which is one of the reasons the mains period is usually quoted as a fraction of a second rather than a whole number.
Why does the output show milliseconds instead of seconds?
Because the converter scales the result to keep it readable, and for anything in the audible or mains range the natural unit is a millisecond or a microsecond. The same period can always be written in seconds as a decimal — the scaling changes the notation, not the value.
Is the period simply the inverse of the frequency?
Yes, exactly, with no constant involved. That is what distinguishes this conversion from the wavelength one, where the speed of light enters the calculation. A frequency of zero has no period for that reason: division by zero is undefined.
What period does a gigahertz have?
One nanosecond, since a gigahertz is a billion cycles per second and a billionth of a second is a nanosecond. Values above that produce periods in the picosecond range, which the converter shows with the unit already chosen.