Frequency Converter

Q: How do I convert a period to a frequency?

Take the reciprocal: f = 1 ÷ T. Choose the period unit in From for example ms and Hz in To ; 20 ms gives 50 Hz.

Frequency Converter

Convert frequency between Hz, kHz, MHz, GHz, RPM and rad/s, and turn a frequency into its period in seconds, milliseconds, microseconds or nanoseconds.

Value

From

–

Formula:

Significant figures

≈ means the result was rounded to the chosen number of significant figures.

1 rpm = 1/60 Hz; ω (rad/s) = 2π × f. The period is the time for one cycle, T = 1/f, so it goes down when the frequency goes up.

{value} in every unit

Unit	Result

Quick conversion table: {from} to {to}

From	To

Common values

Reference	Value	Result

Formula

Unit	Formula

How to use the frequency converter

Type a number in Value and choose its unit in From: hertz and its multiples, revolutions per minute, radians per second, or a period (the time for one cycle).
Choose the unit you want in To. The result appears as you type, with the Formula for the pair and the calculation using your number.
Press Swap units (⇄) to convert the other way, adjust Significant figures, and press Copy to copy a line such as “50 Hz = 3,000 rpm”.

Below the result, the tool lists the value in every unit (grouped as frequency, rotation and period), a quick table for the selected pair, everyday reference frequencies from a heartbeat to Wi-Fi, and the formula from your starting unit to each of the others.

Frequency, rotation speed and angular frequency

A frequency counts how many times something repeats per second. One hertz (Hz) is one cycle per second; the prefixes are powers of ten: 1 kHz = 1,000 Hz, 1 MHz = 10⁶ Hz and 1 GHz = 10⁹ Hz.

Rotating machines are usually rated in revolutions per minute (rpm). One revolution per second is 60 rpm, so:

Hz = rpm ÷ 60
rpm = Hz × 60

Physics and electrical engineering often use the angular frequency ω, in radians per second. One cycle is a full turn of 2π radians, so ω = 2π × f. A 50 Hz mains supply has ω ≈ 314.16 rad/s, and a motor spinning at 3,000 rpm turns at the same 50 Hz, or 314.16 rad/s.

Frequency and period

The period T is the time taken by one cycle. It is the reciprocal of the frequency: T = 1 ÷ f. The higher the frequency, the shorter the period:

50 Hz → T = 1 ÷ 50 = 0.02 s = 20 ms
440 Hz (the tuning note A4) → 2.2727 ms
1 MHz → 1 µs
2.4 GHz → about 0.4167 ns

Because this relation is an inverse, not a multiplication, the formula shown for a period is written as a division, for example “ms = 1,000 ÷ Hz”. A frequency of 0 has no period (it would be infinite), so the tool reports that the value has no equivalent.

Worked example

A hard drive spins at 7,200 rpm. In hertz: 7,200 ÷ 60 = 120 Hz. One revolution therefore takes 1 ÷ 120 s ≈ 8.33 ms, and on average the head waits half a revolution, about 4.17 ms, for the right sector to arrive.

Frequently asked questions

Is rpm the same as Hz?

They measure the same thing on different time scales: rpm counts turns per minute, Hz counts cycles per second. Divide rpm by 60 to get Hz.

What is the difference between Hz and rad/s?

Hertz counts whole cycles per second; radians per second measures the angle covered per second. Since one cycle is 2π radians, 1 Hz ≈ 6.2832 rad/s.

How do I convert a period to a frequency?

Take the reciprocal: f = 1 ÷ T. Choose the period unit in From (for example ms) and Hz in To; 20 ms gives 50 Hz.

Does this tool handle beats per minute?

Yes, indirectly: beats per minute work like rpm. 60 beats per minute is 1 Hz, and 120 bpm is 2 Hz. The rpm unit gives the right figures.

Why do some results use "× 10⁻⁹"?

Very small or very large numbers, such as the period of a GHz signal in seconds, are written in scientific notation to stay readable. Pick ns or µs in To to get a plain number.