Calculation
f = 1/T
High frequency means short period; the quantities are reciprocals.
f = 1/T
Frequency and Period Calculator
High frequency means short period; the quantities are reciprocals.
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02
Result
Select a target and calculate.
Understand the inputs
- Frequency f — The number of complete oscillations or revolutions per second. Source: measure it directly (frequency counter, tachometer) or compute it as the reciprocal of the period T.
- Period T — The time for exactly one complete cycle (e.g. one full revolution or oscillation). Source: time several cycles with a stopwatch and divide by the number of cycles, or compute it as the reciprocal of f.
Example
A 0.5 s period corresponds to 2 Hz.
Assumptions and limits
Periodic process with constant frequency.
Understand Frequency and Period Calculator
This calculator finds the other quantity from either frequency f or period T. It puts typical frequency values in perspective using heartbeat, a musical note, and mains frequency, and shows why short periods correspond to high frequencies.
What does this quantity describe?
Frequency and period are reciprocals of each other: f = 1/T. Frequency states how many complete cycles occur per second; period states how long a single cycle takes.
Middle C sits at about 264 Hz on many musical instruments — a single oscillation cycle takes only about 3.79 ms. A resting human heartbeat of about 60-100 beats per minute, by contrast, is only 1-1.67 Hz, with a period of about 0.6-1 s per beat — a vivid illustration of how widely frequencies differ across nature and engineering.
Formula and variables
f = 1/T
f = 1/TT = 1/f
| Symbol / input | Meaning |
|---|---|
| Frequency f | The number of complete oscillations or revolutions per second. Source: measure it directly (frequency counter, tachometer) or compute it as the reciprocal of the period T. |
| Period T | The time for exactly one complete cycle (e.g. one full revolution or oscillation). Source: time several cycles with a stopwatch and divide by the number of cycles, or compute it as the reciprocal of f. |
Choose the inputs correctly
Enter one of the two quantities; the other follows as its reciprocal. Watch the time units used — periods are often given in milliseconds, frequencies in hertz (1/s).
How to use the calculator
Select the target quantity and enter the known value with units. The calculator directly computes the reciprocal in the matching unit.
Worked example
Given T = 0.5 s, substitution gives f = 1/0.5 s = 2 Hz.
Understand the result and units
A frequency of 2 Hz means the process being considered fully repeats twice per second. For comparison, the European mains grid runs at 50 Hz, a period of 20 ms per AC cycle.
Frequency is given in hertz (Hz = 1/s), period in seconds or fractions thereof (ms, µs). Higher frequencies such as radio or clock frequencies are commonly given in kHz, MHz or GHz.
Typical applications
Converting between frequency and period is used in vibration and signal analysis, timer and sensor design, acoustics, and assessing mains frequency in electrical engineering.
Assumptions, limits and common mistakes
The formula applies to strictly periodic processes with constant cycle length. For irregular or damped oscillations, the instantaneous period is not constant, and a single frequency value describes the process only approximately.
Common mistake: Do not confuse frequency with angular velocity: ω = 2π·f, not ω = f. Also, time units must be handled consistently in conversion — a period in milliseconds must be converted to seconds before taking its reciprocal if the result should be in Hz.
Frequently asked questions
How are frequency and angular velocity related?
Via ω = 2π·f. Angular velocity in rad/s is therefore 2π times frequency in Hz, not identical to it.
What period does 50 Hz mains frequency have?
T = 1/50 Hz = 0.02 s, or 20 milliseconds per complete AC cycle.
Why does a higher-pitched note have a shorter period than a lower one?
Because pitch relates directly to frequency: a higher frequency means more oscillations per second, and therefore a shorter duration per individual cycle.