Period to Frequency Converter
Convert any time period (s, ms, µs, ns, ps) to frequency using f = 1/T. The output auto-scales to Hz, kHz, MHz, or GHz. Includes a single-cycle visual waveform, angular frequency, and band-aware wavelength. Perfect for oscilloscope readouts and digital-timing analysis.
Input
Result
Single-Cycle Sine Waveform
Period vs Frequency Reference
| Source / Application | Period | Frequency (f = 1/T) | Notes |
|---|---|---|---|
| 1 day (Earth rotation) | 86,400 s | ~11.57 µHz | Sub-audible — circadian scale |
| 1-second tick | 1 s | 1 Hz | Heartbeat tempo (60 BPM) |
| Schumann resonance | ~127.7 ms | 7.83 Hz | Earth-ionosphere cavity mode |
| Sub-bass period | 50 ms | 20 Hz | Lowest audible |
| EU mains cycle | 20 ms exactly | 50 Hz | Europe / Asia grid |
| US mains cycle | ~16.667 ms | 60 Hz | North America grid |
| A4 musical period | ~2.273 ms | 440 Hz | Concert pitch reference |
| 1 kHz audio test | 1 ms exactly | 1 kHz | Audio engineering reference |
| CD sample interval | ~22.676 µs | 44.1 kHz | One audio sample period |
| AM radio cycle | 1 µs | 1 MHz | Mid-AM band |
| FM cycle | 10 ns | 100 MHz | Mid-FM band |
| WiFi 2.4 GHz cycle | ~417 ps | 2.4 GHz | Bluetooth/WiFi band |
| CPU clock tick (3 GHz) | ~333 ps | 3 GHz | One basic CPU cycle |
| WiFi 5 GHz cycle | 200 ps | 5 GHz | WiFi 5/6 band |
| 5G mmWave (28 GHz) | ~35.7 ps | 28 GHz | One mmWave RF cycle |
About Period & Frequency
Period (T) is the time between two consecutive cycles. Frequency (f) is the number of cycles per second. They are reciprocals: f = 1/T and T = 1/f. If your oscilloscope shows a signal completing one cycle in 1 millisecond, that's a 1 kHz signal. If it takes 1 microsecond, that's 1 MHz. If 1 nanosecond, that's 1 GHz.
Period in oscilloscope analysis
Oscilloscopes are inherently time-domain instruments — they show you period directly. To find the frequency of an unknown signal, you measure how long one cycle takes (often using cursor measurements) and divide 1 by that period. Modern DSOs do this calculation automatically and display both T and f. This tool replicates that math for any period you can measure.
Period in digital timing
Digital systems measure time in clock periods. A 3 GHz CPU has a 333 ps clock period — that's roughly the time light travels 10 cm in vacuum, so signal propagation across a chip becomes a serious design constraint. SDRAM tCK timing parameters, DDR pulse widths, FPGA setup/hold times — all expressed in periods.
Period and angular frequency
Angular frequency ω = 2π/T (radians per second). For T = 1 ms (1 kHz signal), ω = 2π × 1000 ≈ 6,283 rad/s. Physicists and control theorists frequently use ω because it simplifies sinusoidal equations: y(t) = sin(ωt) completes one cycle when ωt = 2π.