Frequency to Period Converter
Free Frequency period Converter for signal & frequency units. Enter a value to see equivalent measurements across systems.
Frequency to Period Converter
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Formula: Period (T) = 1 / Frequency (f)
Worked example โ 60 Hz has a period of 16.667 ms
Formula
Period (T) = 1 / Frequency (f)
The period is the reciprocal of frequency. Divide 1 by the frequency in hertz to get the period in seconds. Angular frequency equals 2 * pi * f in radians per second.
Worked Examples
Example 1: AC Power Line Frequency
Problem:Convert 60 Hz (US power line frequency) to its period.
Solution:Period = 1 / frequency T = 1 / 60 Hz = 0.016667 seconds T = 16.667 milliseconds Angular frequency = 2 * pi * 60 = 376.99 rad/s
Result:60 Hz has a period of 16.667 ms
Example 2: WiFi Signal Frequency
Problem:Find the period of a 2.4 GHz WiFi signal.
Solution:Period = 1 / frequency T = 1 / (2.4 * 10^9) Hz T = 4.1667 * 10^-10 seconds T = 0.41667 nanoseconds
Result:2.4 GHz has a period of 0.4167 ns
Frequently Asked Questions
What is the relationship between frequency and period?
Frequency and period are inversely related. The period is the time it takes for one complete cycle of a wave or oscillation, while frequency is the number of cycles per second. The formula is T = 1/f, where T is the period in seconds and f is the frequency in hertz. If a signal oscillates at 50 Hz, its period is 1/50 = 0.02 seconds or 20 milliseconds.
What units are used for frequency and period?
Frequency is measured in hertz (Hz), which equals one cycle per second. Common multiples include kilohertz (kHz = 1,000 Hz), megahertz (MHz = 1,000,000 Hz), and gigahertz (GHz = 1,000,000,000 Hz). Period is measured in seconds, milliseconds (ms), microseconds (us), or nanoseconds (ns). Higher frequencies correspond to shorter periods, so GHz signals have periods measured in nanoseconds.
How is angular frequency related to regular frequency?
Angular frequency (omega) is related to regular frequency by the formula omega = 2 * pi * f, where f is the frequency in hertz. Angular frequency is measured in radians per second rather than cycles per second. It is commonly used in physics and engineering when working with sinusoidal signals, where the phase angle changes by 2*pi radians for each complete cycle.
Why is frequency-to-period conversion important in electronics?
In electronics and signal processing, converting between frequency and period is essential for designing circuits, analyzing waveforms, and troubleshooting timing issues. For example, a microprocessor running at 3.2 GHz has a clock period of about 0.3125 nanoseconds. Understanding this relationship helps engineers set sampling rates, calculate baud rates for serial communication, and design filters with correct cutoff characteristics.
What is the difference between the period and the wavelength of a wave?
Period is a time: the seconds taken for one full cycle, given by T = 1/f. Wavelength is a distance: how far the wave travels during one cycle, given by lambda = v / f, where v is the propagation speed in the medium. The two are linked by lambda = v x T. Period depends only on the source frequency, while wavelength also changes whenever the wave enters a medium with a different propagation speed.
How do you go the other way and convert a period back into frequency?
Invert the relationship: f = 1/T, with the period expressed in seconds. Watch the prefixes, because that is where errors creep in. A 20 millisecond period is 0.02 s, giving 1/0.02 = 50 Hz. A 4 microsecond period is 4 x 10^-6 s, giving 250,000 Hz or 250 kHz. A quick shortcut for millisecond readings from an oscilloscope is f in Hz equals 1,000 divided by the period in milliseconds.
Does changing the duty cycle of a square wave change its period?
No. Duty cycle is the percentage of each period during which the signal is high, calculated as pulse width divided by period times 100. A pulse-width-modulated signal can swing from a 10 percent to a 90 percent duty cycle while its period, and therefore its switching frequency, stays fixed. That separation is what makes PWM useful: the average delivered power tracks the duty cycle, while the frequency is chosen to suit the load and the switching losses.
How does a signal's period set the sampling interval you need?
The Nyquist criterion says you must sample at more than twice the highest frequency present, so the sampling interval has to be shorter than half the period of the fastest component. A 1 kHz tone has a 1 ms period and needs samples spaced under 0.5 ms. Sampling too slowly folds high-frequency content back into the band as aliases that no later filtering can remove, which is why anti-alias filtering happens before the converter.
Why do 50 Hz and 60 Hz mains supplies behave differently?
A 60 Hz supply has a period of 1/60 = 16.667 ms while a 50 Hz supply has a period of 1/50 = 20 ms, so the 50 Hz waveform spends longer near each zero crossing and produces slightly more visible flicker in simple lighting. Synchronous motor speed also follows frequency: at 120 x f divided by pole count, a four-pole motor turns 1,500 rpm on 50 Hz but 1,800 rpm on 60 Hz.
How do you work out how many cycles occur in a given time span?
Divide the elapsed time by the period, which is the same as multiplying the time by the frequency. A processor clocked at 3.2 GHz has a period near 0.3125 ns, so in one millisecond it completes 0.001 x 3.2 x 10^9 = 3,200,000 cycles. Cycle counting like this underpins instruction timing budgets, watchdog timer settings, and working out how many samples a fixed-length capture window will hold.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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