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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

Common Periods (Oscilloscope & Timing)

Result

Frequency (f = 1 / T)
Audible
Hertz (Hz)
Kilohertz (kHz)
Megahertz (MHz)
Gigahertz (GHz)
Angular Freq (ω = 2πf)
Wavelength
Formula
f = 1 / T   (frequency = inverse of period)
ω = 2π × f   (angular frequency, rad/s)

Single-Cycle Sine Waveform

Each tick (0, T/4, T/2, 3T/4, T) marks one quarter of the period. The full canvas width represents one complete oscillation.

Period vs Frequency Reference

Source / ApplicationPeriodFrequency (f = 1/T)Notes
1 day (Earth rotation)86,400 s~11.57 µHzSub-audible — circadian scale
1-second tick1 s1 HzHeartbeat tempo (60 BPM)
Schumann resonance~127.7 ms7.83 HzEarth-ionosphere cavity mode
Sub-bass period50 ms20 HzLowest audible
EU mains cycle20 ms exactly50 HzEurope / Asia grid
US mains cycle~16.667 ms60 HzNorth America grid
A4 musical period~2.273 ms440 HzConcert pitch reference
1 kHz audio test1 ms exactly1 kHzAudio engineering reference
CD sample interval~22.676 µs44.1 kHzOne audio sample period
AM radio cycle1 µs1 MHzMid-AM band
FM cycle10 ns100 MHzMid-FM band
WiFi 2.4 GHz cycle~417 ps2.4 GHzBluetooth/WiFi band
CPU clock tick (3 GHz)~333 ps3 GHzOne basic CPU cycle
WiFi 5 GHz cycle200 ps5 GHzWiFi 5/6 band
5G mmWave (28 GHz)~35.7 ps28 GHzOne 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.

Frequently Asked Questions

How do I convert a period to frequency?
Divide 1 by the period in seconds. Examples: T = 1 ms → f = 1/0.001 = 1,000 Hz = 1 kHz. T = 1 µs → f = 1,000,000 Hz = 1 MHz. T = 1 ns → f = 1 GHz. The reciprocal relationship is exact and lossless — you can always recover one from the other.
What frequency is a 20 ms period?
f = 1 / 0.020 = 50 Hz. That's the EU mains frequency — every cycle of the European power grid lasts exactly 20 ms. In North America, the period is ~16.667 ms (1/60 s) for 60 Hz mains.
My oscilloscope shows a 500 µs period — what frequency?
f = 1 / 500 × 10⁻⁶ = 1 / 0.0005 = 2,000 Hz = 2 kHz. To do this quickly in your head: when period is in microseconds, frequency in kHz = 1000 / T(µs). So 500 µs → 2 kHz, 10 µs → 100 kHz, 1 µs → 1 MHz.
What's the frequency of a CPU clock at 333 ps?
f = 1 / (333 × 10⁻¹²) = 1 / 3.33 × 10⁻¹⁰ ≈ 3 × 10⁹ Hz = 3 GHz. Modern desktop CPUs run at 3–6 GHz clock frequencies, corresponding to clock periods of 333 ps down to 167 ps.
Quick rule-of-thumb: period units to frequency units?
The reciprocals scale predictably: 1 s ↔ 1 Hz, 1 ms ↔ 1 kHz, 1 µs ↔ 1 MHz, 1 ns ↔ 1 GHz, 1 ps ↔ 1 THz. For other values, divide: 5 ms → 200 Hz (since 1/0.005 = 200), 250 ns → 4 MHz (1/250e-9 = 4e6).
Why does the wavelength label change depending on period?
Wavelength uses the speed of the relevant wave. For audio (frequency below 20 kHz, period above 50 µs), the tool uses speed of sound (343 m/s in air). For RF and above (period 50 µs and below — corresponding to ≥ 20 kHz, where electromagnetic interpretation is meaningful), it uses the speed of light (299,792,458 m/s). So 20 ms → sound wavelength 6.86 m; 10 ns → EM wavelength 3 m.