Convert frequency to period online: tap a beat or drag the slider.
Frequency and Period simulator
Tap a steady beat to set the frequency
This simulation needs a modern browser with canvas support. The measurements and formula below still describe the physics.
Live measurements
Controls
Graph
Formula
T = 1 / f
- T Period
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Observations
What's happening
Real-world examples
Mains electricity
European mains runs at 50 Hz, so its period is 1 / 50 = 0.02 seconds, or 20 milliseconds per cycle.
Resting heart rate
A heart at 60 beats per minute beats at 1 Hz, so the period is 1 second between beats.
Metronome
Tap a steady tempo and the simulator reads both the frequency in hertz and the period in seconds.
Simple harmonic motion
A mass on a spring or a pendulum repeats at its own frequency, and its period follows the same T = 1 / f idea.
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Uses of frequency and period
- Converting a metronome tempo in beats per minute into a frequency
- Understanding why mains electricity at 50 Hz has a 20 ms period
- Relating a heart rate to the time between beats
- Preparing for a physics topic on simple harmonic motion
frequency and period pitfalls
- Thinking a higher frequency means a longer period
- Confusing angular frequency (rad/s) with ordinary frequency (Hz)
frequency and period questions (5)
How do I convert frequency to period?
Use T = 1 / f. Divide one by the frequency in hertz to get the period in seconds. At 50 Hz the period is 0.02 seconds. At 1 Hz it is 1 second. Equivalently, frequency is f = 1 / T. Open the calculator, set frequency with the slider or tap-the-beat, and read period and angular frequency together.
What is the relationship between frequency and period?
They are exact reciprocals: T = 1 / f, and equivalently f = 1 / T. Frequency counts cycles per second (hertz); period measures seconds per cycle. Multiply them together and you always get one. At 2 Hz the period is 0.5 seconds; at 0.25 Hz it is 4 seconds. The simulator shows both at once so you can watch one shrink as the other grows.
What is angular frequency?
Angular frequency, written omega, measures how fast the oscillation advances in radians per second: omega = 2 pi f. One full cycle is 2 pi radians, so a 1 Hz oscillation has an angular frequency of about 6.28 rad/s. It is the natural unit for the sine function that describes the motion, which is why it appears throughout wave and oscillation equations.
If I double the frequency, what happens to the period?
The period halves. Because T = 1 / f, frequency and period always move in opposite directions by the same factor. Double the frequency and each cycle has half as much time; halve the frequency and each cycle lasts twice as long. Drag the frequency slider and watch the period reading move the opposite way.
How does the tap-the-beat feature work?
Tap or click the canvas in a steady rhythm and the simulator measures the time between your taps, then sets the frequency to match. Tapping once a second gives 1 Hz; tapping twice a second gives 2 Hz. It is a hands-on way to feel that frequency is simply how often something repeats, turned into a number.