Period to Frequency Converter
This T to f calculator converts any time period (s, ms, µs, ns, ps) to frequency using f = 1/T. The output auto-scales to Hz, kHz, MHz, or GHz — a fast time to Hz conversion for any scale. 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 of a periodic waveform — the duration of one complete oscillation. Frequency (f) is the number of cycles per second, measured in hertz (Hz). They are exact 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. Neither value carries more information than the other — they're two views of the same physical quantity.
Period in oscilloscope analysis
Oscilloscopes are inherently time-domain instruments — they show you period directly on the horizontal axis. To find the frequency of an unknown signal, you measure how long one cycle takes (often using cursor measurements or the automatic period measurement function) and divide 1 by that period. A quick ms to Hz example: a 20 ms cursor readout means 50 Hz. Modern digital storage oscilloscopes (DSOs) and mixed-signal oscilloscopes (MSOs) do this calculation automatically and display both T and f in the measurement pane. This tool replicates that math for any period you can measure, whether from a bench scope, a logic analyzer, or a timing diagram. For comparison across the audio spectrum, you can also explore our audio spectrum analyzer which displays frequency content in real time.
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 electromagnetic signals travel 10 cm in a PCB trace, so signal propagation and transmission-line effects become serious design constraints at this scale. The ns to GHz relationship is the most-used shortcut in RF and digital design: frequency (GHz) = 1 / period (ns). SDRAM tCK timing parameters, DDR4/DDR5 pulse widths, FPGA setup/hold times, and SPI/I2C bus timing are all specified in periods (or fractions thereof). The reciprocal relationship means that tightening timing budgets in nanoseconds directly translates to a higher maximum frequency in MHz.
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, control engineers, and RF designers frequently use ω because it simplifies sinusoidal differential equations: y(t) = A·sin(ωt + φ) completes one cycle when ωt increments by 2π. The phase term φ represents the starting offset within the cycle, a concept central to phase-frequency analysis when comparing two signals.