Frequency Converter

How do you convert frequency units?

To convert, multiply by the starting unit’s value in hertz, then divide by the target unit’s value in hertz. Frequency counts how many times something repeats each second, and one hertz (Hz) is one cycle per second.

SI prefixes: move the decimal point

Kilohertz, megahertz and gigahertz differ by factors of 1,000. 1 kHz = 1,000 Hz, 1 MHz = 1,000 kHz and 1 GHz = 1,000 MHz. Moving up one prefix divides by 1,000; moving down multiplies by 1,000. A Wi-Fi channel centered at 2.412 GHz is 2,412 MHz, and an FM station at 101.1 MHz is 101,100 kHz. The MHz to GHz converter and the Hz to kHz converter handle these instantly.

RPM and hertz

Revolutions per minute measure rotations, and a minute has 60 seconds, so Hz = rpm ÷ 60 and rpm = Hz × 60. Worked example: a motor at 3,000 rpm turns 3,000 ÷ 60 = 50 Hz. A hard drive spinning at 7,200 rpm makes 120 revolutions per second. Try the rpm to Hz converter for any speed.

Angular frequency: ω = 2πf

Physics and engineering often use angular frequency ω, measured in radians per second. One full cycle is 2π radians, so ω = 2πf. The same 3,000 rpm motor has ω = 2π × 50 = 314.1593 rad/s, and 60 Hz mains has ω ≈ 376.9911 rad/s. To go straight from rpm, multiply by 2π/60 ≈ 0.10472; picking rad/s in the converter at the top of this page does it for you. Keep the two apart: the SI Brochure notes that the hertz is for cycles per second and should not be used for angular velocity.

Frequency and period

The period T is the time one cycle takes, the reciprocal of frequency: T = 1/f. A 50 Hz signal repeats every 0.02 s (20 ms), and a 440 Hz tone every 2.2727 ms. For time units, see the time converter.

How are frequency and wavelength related?

Wavelength equals wave speed divided by frequency, λ = v ÷ f, so the higher the frequency, the shorter the wave. Radio waves, Wi-Fi and light travel at the speed of light, exactly 299,792,458 m/s by the SI definition of the meter, while sound in air at about 20 °C travels at roughly 343 m/s.

Wavelength explains a lot of everyday engineering. Antennas are sized as fractions of it, so a quarter-wave antenna for 2.4 GHz Wi-Fi is about 3.12 cm long, and an FM car antenna is far longer than a phone’s Wi-Fi antenna. Low-frequency sound has wavelengths of several meters, long enough to bend around obstacles, which is one reason bass carries through a building more easily than treble. Convert any wavelength result with the length converter.

Which frequency units are used where?

Hertz and kilohertz cover mains power and sound, megahertz and gigahertz cover radio, wireless and processors, and rpm and rad/s describe rotation; the unit usually tells you which field you are in.

• Hertz (Hz): mains electricity (50 Hz or 60 Hz), sound and musical pitch, display refresh rates such as 60 Hz and 144 Hz, and vibration analysis. For AC power calculations, see the electrical calculators.
• Kilohertz (kHz): AM radio dials, audio sampling rates such as 44.1 kHz for CDs and 48 kHz for video, ultrasonic cleaners and switching power supplies.
• Megahertz (MHz): FM radio, aviation and marine radio, RAM speeds and older processor clock speeds.
• Gigahertz (GHz): Wi-Fi (2.4, 5 and 6 GHz bands), mobile networks, GPS, radar, microwave ovens and modern CPU clock speeds, typically in the 3–5 GHz range for desktop chips.
• Revolutions per minute (rpm): car engines and tachometers, electric motors, drills, fans, washing machine spin cycles and record turntables (33⅓ and 45 rpm). The rpm to Hz converter links motor speed to supply frequency.
• Radians per second (rad/s): physics, control systems, signal processing and motor data sheets, where angular frequency appears in formulas. See the angle converter for radians themselves.

Mains frequency varies by country: North America uses 60 Hz, most of Europe, Africa, Asia and Australia use 50 Hz, and Japan uses both, with 50 Hz in the east and 60 Hz in the west.

What does a refresh rate in hertz mean?

A display’s refresh rate is how many times per second it redraws the picture, so a 60 Hz screen refreshes every 16.667 ms and a 144 Hz screen every 6.944 ms. The time per frame is simply the period, T = 1 ÷ f, and it is what gamers and video editors care about: a shorter frame time means smoother motion and less delay.

Frame rate (frames per second, fps) is how often the source produces a new image, while refresh rate is how often the screen shows one. Film is traditionally shot at 24 fps; broadcast television grew up at 30 and 60 in 60 Hz mains regions and at 25 and 50 in 50 Hz regions. The same period math applies to processors: a 4 GHz clock ticks every 0.25 ns. For converting milliseconds, seconds and minutes, use the time converter, and for GHz and MHz clock speeds the MHz to GHz converter.