Find the duration of one cycle from a frequency, or reverse the calculation to find frequency from a known period. Results include seconds, milliseconds, microseconds, and nanoseconds per cycle.
How to use this calculator
Choose Hz to seconds when you know the frequency. Choose Seconds to Hz when you know the duration of one complete cycle. Select the matching prefix before entering the number. The Number of cycles input adds a total-duration result without changing the period of a single cycle.
Frequency and period are reciprocals
Frequency counts cycles per second; period is the time taken for one cycle. Doubling the frequency halves the period. This reciprocal relationship differs from a simple fixed-factor unit conversion.
A hertz is one cycle per second. A kilohertz is 1,000 cycles per second, so a 1 kHz signal has a 1 ms period. A clock frequency does not directly describe application performance: an operation may require multiple cycles, and real systems can wait on memory or other components.
Examples
A 50 Hz signal
50 Hz has a period of 0.02 seconds, or 20 milliseconds. Ten cycles take 0.2 seconds.
A very short period
A period of 500 nanoseconds corresponds to 2 MHz. Select Nanoseconds before entering 500 in the reverse tab.
Formula
period in seconds = 1 / frequency in hertz
frequency in hertz = 1 / period in seconds
total duration = number of cycles × period
Precision and interpretation
Frequency and period must be positive. At zero frequency, there is no finite repeating-cycle period, so the tool returns an input error instead of a misleading zero. The total-duration calculation assumes a steady periodic signal and a whole number of cycles. Results use up to 12 significant digits.
Definitions and further reading
Unit and quantity reference provides the underlying definitions. The examples above are worked calculations for this tool.