How To Convert Frequency Units

Frequency is the number of cycles of a repeating event per second. The SI unit is the hertz, which is one cycle per second, and it is the base for every other frequency unit.

A kilohertz is a thousand hertz, a megahertz is a million hertz and a gigahertz is a billion hertz. These SI prefixes appear everywhere from audio and radio to computer clocks.

The prefix steps are powers of a thousand, so one gigahertz is a thousand megahertz and a megahertz is a thousand kilohertz. Miscounting a prefix is a common source of large errors.

Revolutions per minute, or RPM, measures rotation rather than cycles. One revolution per minute is one sixtieth of a cycle per second, so one hertz equals 60 RPM.

Radians per second measures angular speed rather than cycle count. One full cycle is two pi radians, so one hertz equals two pi radians per second, about 6.2831853.

Because a cycle is a full rotation, hertz and radians per second differ by the factor two pi. Forgetting that factor is the most common mistake when converting angular speed.

Going from hertz to RPM multiplies by sixty, because a minute has sixty seconds. Going the other way divides by sixty. The direction matters, so it helps to check that a faster spin gives a larger number.

The converter expresses every unit as a size in hertz and converts by multiplying the value by the source factor and dividing by the target factor. That keeps every pair consistent.

Radio and audio use the SI-prefixed hertz almost exclusively. A station at 1000 kilohertz is the same as one at 1 megahertz, and a processor clocked at 3 gigahertz runs three billion cycles a second.

Mechanical work uses RPM, so converting between hertz and RPM appears whenever an electrical frequency drives a motor or a tachometer reading is compared with a drive frequency.

Physics and signal processing use radians per second, where the angular frequency is the cycle frequency multiplied by two pi. The distinction between frequency in hertz and angular frequency in radians per second matters in every wave equation.

A related trap is the difference between frequency and period. The period is the time for one cycle, the reciprocal of the frequency, so a 50 hertz supply has a period of 0.02 seconds.

Audio engineers move between hertz and kilohertz constantly, since human hearing spans about 20 hertz to 20 kilohertz. A thousand-fold slip is the difference between a bass note and a bat call.

In signal processing the angular frequency appears in every sine and cosine, so hertz is converted to radians per second before the maths begins. Skipping the two pi factor changes the result by about six point three.

Motors and drives quote speed in RPM while the electrical supply is in hertz, so the conversion appears whenever a variable-speed drive is configured. A four-pole motor at 50 hertz runs at about 1500 RPM.

Radio bands are named by wavelength but tuned by frequency. A station at 100 megahertz has a wavelength of about three metres, and the two descriptions are linked by the speed of light.

Clock speeds in computing are quoted in gigahertz, and one gigahertz is a billion cycles a second. Comparing a 3 gigahertz processor with a 2.4 gigahertz one uses the same unit, so no conversion is needed there.

The calculator models the fixed relationships between the units and nothing more. It does not know the measurement's accuracy or whether the quantity is a cycle rate or an angular rate, so treat the output as exact arithmetic on the number you entered.