Frequency Converter
Convert frequency between hertz, kHz, MHz, GHz, rpm, beats per minute and radians per second, with the period of one cycle.
Period of one cycle: 1 s
Updated Formula covered by automated tests
Frequency counts how many times something repeats each second, whether that is a guitar string, an AC power line, a spinning drill chuck or a radio carrier. Engineers write it in hertz and its multiples, mechanics in revolutions per minute, musicians and cardiologists in beats per minute, and physicists often in radians per second. This converter moves between all of them and also shows the period, the time one cycle takes, which is often the number you actually need.
Typical questions it answers: what rotational speed in rpm corresponds to a vibration peak at 50 Hz, how many radians per second a motor shaft turns for a control-system model, how long one cycle of a 2.4 GHz Wi-Fi signal lasts, or what a resting pulse of 60 bpm is in hertz.
The formula
- f
- Frequency in hertz, cycles per second
- rpm
- Revolutions per minute; bpm (beats per minute) uses the same factor of 60
- ω
- Angular frequency in radians per second; one full cycle sweeps 2π radians
- T
- Period, the duration of a single cycle, in seconds
The hertz honors Heinrich Hertz, who demonstrated electromagnetic waves in the 1880s; the name was adopted by the IEC in 1930 and became part of the SI in 1960, replacing "cycles per second". Converting per-minute counts is simply division by 60, since a minute holds 60 seconds.
Angular frequency is a different way of describing the same motion. Instead of counting whole cycles, it measures how many radians of phase pass each second, and because each cycle is 2π radians, ω = 2πf. Formulas for oscillators, AC circuits and rotating shafts usually use ω, which is why mixing up hertz and radians per second gives answers off by a factor of about 6.28. The SI Brochure recommends reserving the hertz for periodic phenomena and using rad/s for angular velocity.
Worked example
Alex is reading a hard-drive spec sheet that lists a spindle speed of 7200 rpm and wants the rotation in hertz, in radians per second, and the average time the drive waits for a sector to come round.
- 1 Convert rpm to hertz: 7200 ÷ 60 = 120 Hz, so the platters turn 120 times per second.
- 2 Find the period: T = 1 ÷ 120 = 0.008333 s, or 8.333 ms per revolution.
- 3 Convert to angular frequency: ω = 2π × 120 = 753.98 rad/s.
- 4 On average the wanted sector is half a turn away: 8.333 ÷ 2 = 4.17 ms.
Result: A 7200 rpm drive spins at 120 Hz (753.98 rad/s), and its average rotational latency is about 4.17 ms, the figure often quoted in drive specifications.
Before you rely on the result
- The converter treats every input as a steady, periodic rate. Signals whose frequency drifts, or random events such as radioactive decay, need averaging or statistics rather than a single conversion.
- Beats per minute is converted as a simple rate; a heart rate is not perfectly regular, so its period varies beat to beat.
Frequently asked questions
Why is mains power 50 Hz in some countries and 60 Hz in others?
Both frequencies were settled on by early electrical companies in the late 1800s and then locked in by the equipment built around them. Most of Europe, Asia and Africa use 50 Hz (a 20 ms cycle); North America and parts of South America use 60 Hz (16.67 ms), and Japan is split, with 50 Hz in the east and 60 Hz in the west.
How do I convert engine rpm to a vibration frequency?
Divide rpm by 60 to get the shaft frequency in hertz. Many vibrations occur at a multiple of that: in a four-stroke four-cylinder engine the main firing pulse happens twice per crankshaft revolution, so 3000 rpm gives 50 Hz shaft rotation and 100 Hz firing frequency.
Is rad/s the same as Hz?
Both have the dimension of 1 per second, but they count different things. 1 Hz is one full cycle per second, which equals 2π ≈ 6.283 rad/s. A 50 Hz motor supply therefore has ω = 314.16 rad/s.
What is the period of a 2.4 GHz Wi-Fi signal?
T = 1 ÷ 2,400,000,000 Hz ≈ 4.17 × 10⁻¹⁰ s, or about 0.417 nanoseconds. In that time light travels about 12.5 cm, which is roughly the wavelength of the signal.
Sources
- BIPM: The International System of Units (SI Brochure) (bipm.org)
- NIST: SI Units (nist.gov)