Period
Duration of one complete cycle.
Physics · Oscillations & waves
Frequency and period calculator
Convert frequency and the duration of one cycle for any periodic signal, oscillation or rotation. Choose the quantity you know.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Frequency
Number of cycles per second.
Relation and numerical substitution
f = 1 / T ; T = 1 / f—
The phenomenon repeats with a constant period. One cycle means one complete repetition.
01Formulas and symbols
Formulas used
T
T = 1 / fDuration of one cycle from its frequency.f
f = 1 / TCycles per second from the period.02Assumptions and limits
Scope of validity
- The phenomenon repeats with a constant period. One cycle means one complete repetition.
03Validation example
Reference numerical case
- Given f = 50 Hz, find T: T = 1/f = 1/50 = 0.02 s = 20 ms.
- Given T = 0.5 ms = 0.0005 s, f = 1/0.0005 = 2,000 Hz = 2 kHz.
04References
Technical references
FAQ
Can I use this for rotation?
Yes, when one cycle is one revolution. First convert revolutions per minute to revolutions per second: 60 rpm = 1 Hz.
Why is zero frequency rejected?
Zero frequency has no finite period. A nonperiodic signal may have no unique period.
Is frequency the same as angular frequency?
No. f is measured in Hz; angular frequency is ω = 2πf in rad/s. This tool converts f and T only.
05How the relation works
Doubling frequency halves the period. This reciprocal relation depends on neither amplitude nor the kind of phenomenon. The diagram shows one cycle on a normalized time axis.
06Model limits
A changing frequency needs a local period or a signal analysis method. This tool calculates neither wave speed nor wavelength.
07Common mistakes
Convert milliseconds to seconds before taking the reciprocal. Half an oscillation is not a complete cycle.