Frequency and period are the two most fundamental descriptors of any repeating signal or oscillation — and they are each other’s exact reciprocal. Whether you are analysing mains electricity, tuning an audio filter, designing an LC oscillator, computing the clock speed of a CPU, or studying electromagnetic waves, the same pair of formulas governs the calculation:
T = 1 / f f = 1 / T ω = 2πf
This calculator lets you convert in either direction across a span of 24 orders of magnitude — from a heartbeat period measured in seconds down to a visible-light period measured in femtoseconds — with automatic unit selection so you never have to mentally juggle powers of ten.
How it works
Core formulas. Frequency f (SI unit: hertz, Hz = cycles per second) and period T (SI unit: seconds) satisfy the exact inverse relationship T = 1/f. No approximation is ever applied. Enter either quantity and the other follows immediately.
Angular frequency. Many physics and engineering equations use angular frequency ω (omega, unit: rad/s) rather than f. One full cycle subtends 2π radians, so ω = 2πf. The Angular tab shows all three quantities simultaneously alongside the cycles-per-minute (rpm) value.
Unit handling. The calculator accepts frequency in Hz, kHz, MHz, GHz, THz, and rpm. Periods can be entered in ps, ns, µs, ms, s, min, or h. Internally every value is converted to SI (Hz and seconds) before computation. The displayed result is then automatically scaled to the most human-readable unit — a 1 GHz clock is shown as a 1 ns period rather than 0.000000001 s.
Precision. All arithmetic uses IEEE 754 double precision (64-bit), giving 15-17 significant digits. Results are displayed to 6 significant figures; the raw SI value is also shown for direct copy-paste into equations or spreadsheets.
Worked example
UK mains electricity (50 Hz):
- Select “Period T (from frequency f)”.
- Enter f = 50 Hz.
- Read off: T = 1/50 = 0.02 s = 20 ms.
- Angular frequency: ω = 2π × 50 = 314.159 rad/s.
CPU clock (3 GHz):
- Enter f = 3, unit = GHz.
- Period T = 1/(3 × 10^9) = 0.333 ns (about one-third of a nanosecond).
- ω = 2π × 3 × 10^9 = 1.885 × 10^10 rad/s.
Green visible light (~545 THz):
- Enter f = 545, unit = THz.
- Period T = 1/(545 × 10^12) = 1.835 × 10^-15 s = 1.835 fs (femtoseconds).
| Signal | Frequency | Period | ω (rad/s) |
|---|---|---|---|
| UK mains | 50 Hz | 20 ms | 314.2 |
| US mains | 60 Hz | 16.67 ms | 376.99 |
| Concert A4 | 440 Hz | 2.273 ms | 2764.6 |
| FM radio | 100 MHz | 10 ns | 6.283 × 10^8 |
| Wi-Fi 5 GHz | 5 GHz | 0.2 ns | 3.142 × 10^10 |
| Green light | 545 THz | 1.835 fs | 3.424 × 10^15 |
All numbers are computed in your browser. No figures are transmitted to any server.
Formula reference
The three relations form a closed triad — knowing any one gives all three:
T = 1 / f— period from frequencyf = 1 / T— frequency from periodomega = 2 * pi * f = 2 * pi / T— angular frequency from either
In simple harmonic motion the displacement is x(t) = A * cos(omega * t + phi), so omega directly enters the equation of motion. In AC circuits, capacitive reactance is X_C = 1 / (omega * C) and inductive reactance is X_L = omega * L — both require omega, not f. Knowing how to move fluently between f, T, and omega is therefore an essential everyday skill in physics, electronics, acoustics, and signal processing.