Period to Frequency Calculator
Convert period to frequency and frequency to period, both ways, with s, ms, µs and ns against Hz, kHz, MHz and GHz. Also shows angular frequency (ω = 2πf) and vacuum wavelength (λ = c/f).
100% client-side — your numbers never leave this pageCalculator
Enter either side; the other is computed instantly from f = 1/T.
Period in all units
Frequency in all units
Worked examples
Each result below is produced by the same engine that powers the calculator above.
Example 1: period 1 ms to frequency
Given: T = 1 ms = 0.001 s
Formula: f = 1 / T
Compute: f = 1 / 0.001 = 1000 Hz
Answer: 1 kHz
Example 2: 60 Hz to period
Given: f = 60 Hz
Formula: T = 1 / f
Compute: T = 1 / 60 = 0.0166667 s
Answer: 16.6667 ms (period of 60 Hz AC mains)
Example 3: 2.4 GHz to period and wavelength
Given: f = 2.4 GHz = 2,400,000,000 Hz
Period: T = 1 / f = 4.16667 x 10-10 s
Wavelength: λ = c / f = 299792458 / 2400000000 = 0.124914 m
Answer: 0.416667 ns period, 12.4914 cm wavelength
Example 4: 100 MHz wavelength, angular frequency, period
Given: f = 100 MHz = 100,000,000 Hz
Wavelength: λ = 299792458 / 100000000 = 2.99792 m
Angular frequency: ω = 2πf = 628318531 rad/s
Period: T = 1 / f = 10 ns
Answer: 2.99792 m, 628318531 rad/s, 10 ns
Real-world reference table
Common signals, their periods, and vacuum wavelengths.
| Signal | Frequency | Period | Wavelength (vacuum) |
|---|---|---|---|
| AC mains (EU, Asia) | 50 Hz | 20 ms | 5995.85 km |
| AC mains (Americas) | 60 Hz | 16.6667 ms | 4996.54 km |
| Musical note A4 | 440 Hz | 2.27273 ms | 681.346 km |
| Human hearing limit | 20 kHz | 50 µs | 14.9896 km |
| FM radio | 100 MHz | 10 ns | 2.99792 m |
| Wi-Fi / Bluetooth | 2.4 GHz | 0.416667 ns | 12.4914 cm |
| Wi-Fi | 5 GHz | 0.2 ns | 5.99585 cm |
| CPU clock | 3 GHz | 0.333333 ns | 9.99308 cm |
Formulas and method
Results are computed in double precision and displayed rounded to 6 significant digits; the full-precision value is kept internally so chained conversions do not accumulate rounding error. Zero, negative, or non-numeric inputs are rejected with an error because 1/0 is undefined and a negative period has no physical meaning.
Scope boundary
This page is a physics calculator for the period–frequency relationship (T = 1/f), plus angular frequency (ω = 2πf) and vacuum wavelength (λ = c/f), with worked examples and reference tables.
For generic frequency unit conversion — Hz, kHz, MHz, GHz, THz, rpm, rad/s — plus Nyquist rate, motor sync speed and a radio-band finder, use our frequency-converter hub instead. The two tools are complementary, not substitutes.
Frequently asked questions
What is the formula to convert period to frequency?
Divide 1 by the period: f = 1 / T. Use seconds for T to get hertz directly. For example, a period of 1 millisecond (0.001 s) gives f = 1 / 0.001 = 1000 Hz, which is 1 kHz.
What is the formula to convert frequency to period?
Divide 1 by the frequency: T = 1 / f. Use hertz for f to get seconds. For example, 60 Hz gives T = 1 / 60 = 0.0166667 s, which is 16.6667 ms.
What is the period of a 60 Hz signal?
16.6667 milliseconds. T = 1 / 60 Hz = 0.0166667 s = 16.6667 ms. This is the period of AC mains electricity in the Americas.
What frequency corresponds to a period of 1 millisecond?
1 kHz. f = 1 / 0.001 s = 1000 Hz = 1 kHz.
How do I convert GHz to period in nanoseconds?
Take the reciprocal and scale the units: T in nanoseconds equals 1 divided by f in gigahertz. For 2.4 GHz, T = 1 / 2.4 = 0.416667 ns. For 5 GHz the period is 0.2 ns.
What is angular frequency and how is it calculated?
Angular frequency, written as omega, measures rotation in radians per second instead of cycles per second. The formula is omega = 2 x pi x f. For 50 Hz, omega = 314.159 rad/s.
How do I find wavelength from frequency?
Divide the wave speed by the frequency: lambda = c / f. For electromagnetic waves in a vacuum, c = 299792458 m/s exactly. For 100 MHz, lambda = 299792458 / 100000000 = 2.99792 m.
What is the wavelength of a 2.4 GHz Wi-Fi signal?
About 12.4914 cm in a vacuum. lambda = 299792458 / 2400000000 = 0.124914 m = 12.4914 cm.
Can the period or frequency be zero or negative?
No. Both must be positive finite numbers, and the calculator shows an error otherwise, because 1 / 0 is undefined and a negative period has no physical meaning.
What units does this calculator support?
Period: seconds (s), milliseconds (ms), microseconds (µs), nanoseconds (ns). Frequency: hertz (Hz), kilohertz (kHz), megahertz (MHz), gigahertz (GHz). Results also show angular frequency in rad/s and wavelength in km, m, cm or mm.
What is the difference between frequency and angular frequency?
Frequency f counts cycles per second (Hz). Angular frequency omega counts radians per second (rad/s). One full cycle is 2 x pi radians, so omega = 2 x pi x f. A 440 Hz tone has omega = 2764.6 rad/s.
What is the period of 50 Hz mains electricity?
20 milliseconds. T = 1 / 50 = 0.02 s = 20 ms. Its vacuum wavelength is 5995.85 km.
How is this different from the frequency-converter tool?
frequency-converter is a unit-conversion hub: it converts between Hz, kHz, MHz, GHz, THz, rpm and rad/s and bundles extra tabs for Nyquist rate, motor speed and radio bands. This calculator is a focused physics tool for the period-frequency relationship (T = 1 / f), with angular frequency, vacuum wavelength, worked examples and reference tables.
Does the wavelength result apply to sound waves?
The formula lambda = v / f works for any wave, but v must be the wave speed in that medium. This calculator uses c = 299792458 m/s, the speed of light in a vacuum, so its wavelength results describe electromagnetic waves such as radio. For sound in air, use v = 343 m/s instead.
How precise are the results?
Results are computed in double precision and displayed rounded to 6 significant digits, for example 16.6667 ms for 60 Hz. The underlying value keeps full precision, so chained conversions do not accumulate rounding error.
Is my data sent to a server?
No. This tool runs 100 percent in your browser with JavaScript. No input is transmitted, stored, or logged anywhere.
Free tool by NRTechStudio