The frequency formula
Frequency is the number of cycles per second, the reciprocal of the period: f = 1 ÷ T, where T is the period in seconds. A period of 0.02 s gives 50 Hz. Shorter periods mean higher frequencies. Once you know frequency, find the wavelength of the wave.
The relationship follows straight from the definitions. If one cycle takes 0.02 s, then in a full second you fit 1 ÷ 0.02 = 50 of them, which is exactly what 50 Hz means.
How to use this calculator
Enter the period of one full cycle in seconds. The result is frequency in hertz (Hz), where 1 Hz equals one cycle per second. The period must be greater than zero. To convert frequency back into wavelength, use the wavelength calculator.
Measuring a single cycle accurately is difficult by hand, so time several cycles and divide. Timing 10 swings at 0.2 s total gives a period of 0.02 s, and the same 50 Hz, with much less stopwatch error. Note that hertz counts cycles per second, while angular frequency in radians per second is 2π times larger.
Worked example
A pendulum completes one swing every 0.02 s: 1 ÷ 0.02 = 50 Hz. Halve the period to 0.01 s and the frequency doubles to 100 Hz, since frequency and period are inversely related.
That inverse link is a useful sanity check on any result. If a change makes the cycle faster, the frequency must rise, and if the cycle slows the frequency must fall. Everyday scales help too: mains electricity runs at 50 or 60 Hz, audible sound spans roughly 20 Hz to 20,000 Hz, and radio broadcasts are measured in millions of hertz. For a travelling wave, frequency times wavelength gives the wave speed, which is a velocity like any other.
Frequently asked questions
- How do I calculate frequency?
- Take the reciprocal of the period: f = 1 ÷ T.
- What are the units of frequency?
- Hertz (Hz), where one hertz is one cycle per second.
- Why must the period not be zero?
- A period of zero would make frequency undefined, since 1 ÷ 0 is not defined.
- How are frequency and period related?
- They are reciprocals: as one increases the other decreases proportionally.
- What if my period is in milliseconds?
- Convert to seconds first by dividing by 1,000, since the formula returns hertz only for a period in seconds. A period of 20 ms becomes 0.02 s, which gives 50 Hz; entering 20 directly would give 0.05 Hz.