Frequency to Period Converter
Free Frequency period Converter for signal & frequency units. Enter a value to see equivalent measurements across systems.
Reviewed by Manoj Kumar, Mathematics Educator
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\nT = 1 / 60 Hz = 0.016667 seconds\nT = 16.667 milliseconds\nAngular 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\nT = 1 / (2.4 * 10^9) Hz\nT = 4.1667 * 10^-10 seconds\nT = 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.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy