Frequency and Period Calculator
Convert between frequency and period, from millihertz to megahertz and cycles per minute, and get the angular frequency and the wavelength for a wave.
Formula
- frequency, in hertz
- period, in seconds
- angular frequency, in radians per second
- wavelength, for a wave of speed v
How it works
The frequency of a repeating signal is the number of cycles per second, and the period is the time one cycle takes: they are reciprocals. The angular frequency, in radians per second, is 2π times the frequency and is the form used in circuit and rotation formulas.
Physiological signals are slow and are often quoted in cycles per minute, for example a heart rate of 72 beats/min is a frequency of 1.2 Hz and a respiratory rate of 15 breaths/min is 0.25 Hz. The wavelength of a wave depends on the medium it travels in.
Worked example
A heart rate of 72 beats per minute.
- f = 72 / 60 = 1.2 Hz.
- T = 1 / 1.2 = 0.8333 s = 833.3 ms.
- ω = 2π × 1.2 = 7.54 rad/s.
The frequency is 1.2 Hz, the period 833.3 ms and the angular frequency 7.54 rad/s.
These are the values the calculator opens with, so you can check its output against this example.
Assumptions
- A periodic signal of a single frequency.
- For the wavelength, a stated speed in a uniform medium.
Common mistakes
- Confusing frequency in hertz with angular frequency in rad/s, which differ by a factor of 2π.
- Mixing milliseconds and seconds for the period.
- Using the speed of sound in air for sound in tissue (about 1,540 m/s).
Related tools
Related equipment
Service documentation, failure modes and parts for the instruments this calculation is used with.