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Frequency to Period Converter

Convert any frequency in Hz, kHz, MHz, or GHz to its time period using T = 1/f. Output auto-scales to seconds, milliseconds, microseconds, or nanoseconds. Includes a visual single-cycle sine waveform, angular frequency, and wavelength.

Input

Frequency

Common Frequencies

Result

Time Period (T = 1 / f)

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Audible

Seconds (s)

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Milliseconds (ms)

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Microseconds (µs)

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Nanoseconds (ns)

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Angular Freq (ω = 2πf)

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Wavelength (sound in air, 20°C)

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Formula

T = 1 / f (period = inverse of frequency)

ω = 2π × f (angular frequency, rad/s)

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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.

Frequency vs Period Reference

Source / Application	Frequency	Period (T = 1/f)	Notes
Earth's rotation	~11.6 µHz	~86,400 s	1 day = one period
Schumann resonance	7.83 Hz	~127.7 ms	Earth-ionosphere cavity
Sub-bass	20 Hz	50 ms	Lowest audible
Mains hum (EU)	50 Hz	20 ms	One cycle = 20 ms
Mains hum (US)	60 Hz	~16.667 ms	1/60 s
Concert A4	440 Hz	~2.273 ms	Standard tuning
1 kHz audio test	1,000 Hz	1 ms exactly	Reference tone
Upper hearing limit	20 kHz	50 µs	Top of audible range
CD sample rate	44.1 kHz	~22.676 µs	Period between samples
AM radio	1 MHz	1 µs	Middle of AM band
FM broadcast	100 MHz	10 ns	Mid-FM
WiFi 2.4 GHz	2.4 GHz	~417 ps	One RF cycle
CPU clock 3 GHz	3 GHz	~333 ps	One clock tick
WiFi 5 GHz	5 GHz	200 ps	One RF cycle
5G mmWave 28 GHz	28 GHz	~35.7 ps	One RF cycle

About Frequency & Period

Period (T) is the time it takes for one complete cycle of a wave or oscillation. Frequency (f) is the number of cycles per second. They are reciprocals: T = 1/f and f = 1/T. A 1 Hz signal completes one cycle every second; a 1 kHz signal completes one cycle every millisecond; a 1 GHz signal completes one cycle every nanosecond.

Why period matters in digital signals

Digital systems measure time in clock periods. A 3 GHz CPU has a clock period of ~333 picoseconds — every basic operation takes one or more of these ticks. Audio sample rates also work this way: 44.1 kHz means a sample every 22.676 µs, 48 kHz every 20.833 µs, 96 kHz every 10.417 µs.

Why period matters in analog and RF

Oscilloscopes display signals in the time domain — they show period directly. A 1 MHz signal will fill one oscilloscope screen division (typically 1 µs/div) with one cycle. Period is the natural unit for measuring rise times, pulse widths, and signal timing.

Period and angular frequency

Mathematics often uses angular frequency (ω) instead of frequency in Hertz. The relationship is ω = 2πf (rad/s), and the period in terms of angular frequency is T = 2π/ω. This is more natural for trigonometric functions: y = sin(ωt) completes one full cycle when ωt = 2π, i.e., when t = 2π/ω = T.

Frequently Asked Questions

How do I convert frequency to period?

Divide 1 by the frequency. For example, a 50 Hz mains signal has a period of T = 1/50 = 0.02 seconds = 20 milliseconds. A 1 MHz radio signal has T = 1/1,000,000 = 1 µs. The reciprocal relationship is exact and lossless — you can always go either direction.

What is the period of 60 Hz mains power?

T = 1/60 ≈ 16.667 milliseconds. That's why oscilloscope traces of US power show a complete cycle every ~16.7 ms. In Europe and most of the rest of the world, 50 Hz means a period of exactly 20 ms.

What's the period of a 440 Hz A4?

T = 1/440 ≈ 2.273 milliseconds (2,273 µs). Every air molecule near a vibrating A-string completes one back-and-forth oscillation in that time. Doubling the frequency to A5 (880 Hz) halves the period to ~1.136 ms; halving to A3 (220 Hz) doubles it to ~4.545 ms.

What does "period" mean for digital signals?

In digital electronics, period is the time between two consecutive clock edges (or one complete cycle of a clock signal). A 3 GHz CPU has a clock period of 1/3 ns ≈ 333 picoseconds. Modern chips run at clock periods so short that signals can't physically propagate across the whole chip in one period — necessitating pipelined design.

What's angular frequency?

Angular frequency ω (omega) measures rate of phase change in radians per second: ω = 2πf. A 1 Hz oscillation has angular frequency 2π ≈ 6.283 rad/s. Angular frequency appears naturally in sinusoidal equations like y = sin(ωt) and in differential equations of oscillation — physicists usually prefer ω; engineers usually prefer f.

Why does the waveform always show one cycle?

The canvas above always renders exactly one period of a sine wave, regardless of the entered frequency. What changes is the time scale of the X-axis — at 1 Hz the canvas represents 1 second; at 1 MHz the same width represents 1 microsecond. The cycle shape is invariant; only the time labels change.

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