Frequency ↔ Period Calculator
Convert between frequency and period instantly. Enter a positive value, choose your units, and click calculate.
Period T (seconds) = 1 / f (Hz)
Frequency f (Hz) = 1 / T (seconds)
What is frequency and what is period?
Frequency and period describe the same repeating motion from two different angles. Frequency tells you how many cycles happen each second, while period tells you how long one cycle takes. If you are working with sound waves, AC electricity, rotating motors, vibration, clocks, or digital signals, this relationship appears everywhere.
In physics and engineering, frequency is usually measured in hertz (Hz), where 1 Hz means 1 cycle per second. Period is measured in seconds (s). Because they are inverses of each other, high frequency means short period, and low frequency means long period.
Quick formulas you should remember
- T = 1 / f (period from frequency)
- f = 1 / T (frequency from period)
- ω = 2πf (angular frequency, radians per second)
These equations only work directly when frequency is in hertz and period is in seconds. If your input is in kHz, ms, µs, rpm, or any other unit, you must convert units first. The calculator above handles this for you.
How to use this frequency calculator period tool
1) Choose the conversion direction
Pick Frequency to Period if you know how often a signal repeats. Pick Period to Frequency if you know cycle time.
2) Enter your number and unit
You can use units like Hz, kHz, MHz, GHz, and rpm for frequency; or s, ms, µs, ns, min, and h for period.
3) Click calculate
The tool returns the main answer plus several equivalent unit conversions so you can use the result directly in your project, lab notes, or homework.
Worked examples
Example A: 60 Hz power line frequency
If f = 60 Hz, then period is T = 1/60 = 0.016666... seconds. That is 16.67 ms per cycle.
Example B: A digital pulse every 2 ms
If T = 2 ms, convert to seconds first: 0.002 s. Then f = 1 / 0.002 = 500 Hz.
Example C: A 2.4 GHz signal
2.4 GHz = 2.4 × 109 Hz. So period is about 4.167 × 10-10 s, or 0.4167 ns.
Common mistakes to avoid
- Mixing milliseconds and seconds without converting.
- Entering 0 or negative values (period and frequency must be positive for physical cycles).
- Using rpm as if it were Hz (remember: 1 rpm = 1/60 Hz).
- Rounding too early when working with very high or very low values.
Where this conversion is useful
- Electronics: oscillators, filters, PWM, clocks.
- Audio: tone frequency and waveform timing.
- Mechanical systems: shaft rotation, vibration, resonance checks.
- Physics labs: pendulum, wave, and periodic motion analysis.
- Communications: carrier signals and symbol timing.
Final takeaway
The frequency-period relationship is simple but foundational: one is the reciprocal of the other. With a reliable calculator and correct units, you can move between time-domain and frequency-domain thinking in seconds. Bookmark this page whenever you need a fast, accurate frequency calculator period conversion.