Electronics Timing Tool

Frequency ↔ Period Converter

Convert frequency to period or period to frequency instantly. Use the reciprocal relationship T = 1/f for clocks, oscillators, PWM signals, digital electronics, communications and other periodic signals.

Frequency ↔ Period Converter

Enter either frequency or period and the other value will be calculated automatically.

Frequency represents cycles per second.
Period is the time required for one complete cycle.
Period
1 ms
1000 Hz = 1 ms
Frequency 1 kHz
Period 1 ms
Period in seconds 0.001 s
Angular frequency 6283.19 rad/s

T = 1 / f    |    f = 1 / T

Frequency and Period Formula

Frequency and period describe the same repeating behavior from two different perspectives. Frequency tells you how many cycles occur each second, while period tells you how long one complete cycle takes.

Frequency to Period

T = 1 / f

Convert the frequency to hertz first. The reciprocal gives the period in seconds.

  • T = period in seconds
  • f = frequency in hertz
  • 1 Hz = 1 cycle per second
  • 1 kHz = 1,000 cycles per second
  • 1 MHz = 1,000,000 cycles per second

Period to Frequency

f = 1 / T

Convert the period to seconds first, then take its reciprocal to obtain frequency in hertz.

  • f = frequency in hertz
  • T = period in seconds
  • 1 ms = 0.001 s
  • 1 µs = 0.000001 s
  • 1 ns = 0.000000001 s

Common Frequency ↔ Period Conversions

These examples show the reciprocal relationship between frequency and period across common electrical and electronic signal frequencies.

Frequency Period Typical Context
1 Hz 1 s Very slow periodic signal
10 Hz 100 ms Low-frequency control
50 Hz 20 ms AC power systems
60 Hz 16.667 ms AC power systems
100 Hz 10 ms Power/control signals
1 kHz 1 ms Audio/control electronics
10 kHz 100 µs PWM and switching
100 kHz 10 µs Switching converters
1 MHz 1 µs Digital electronics
10 MHz 100 ns Clocks and RF
100 MHz 10 ns High-speed digital/RF
1 GHz 1 ns RF and high-speed electronics
2.4 GHz 416.67 ps Common wireless band

Applications of Frequency and Period

Frequency and period calculations are fundamental to timing, signal processing, communications and digital electronics.

Digital Clocks

Determine the duration of each clock cycle from a processor, microcontroller or oscillator frequency.

RF Electronics

Convert MHz and GHz carrier frequencies into the corresponding signal period for timing analysis.

PWM Signals

Determine PWM period from switching frequency before calculating duty cycle and pulse duration.

Oscilloscopes

Convert measured signal period into frequency when analyzing repetitive waveforms.

Practical Notes

Unit Conversion

Always convert frequency to Hz or period to seconds before applying the reciprocal formula. The calculator handles these conversions automatically.

Higher Frequency

A higher frequency means a shorter period. For example, increasing frequency from 1 MHz to 10 MHz reduces the period from 1 µs to 100 ns.

Timing Accuracy

Real oscillators and clocks have tolerance, jitter and frequency drift. A calculated period represents the nominal value from the specified frequency.

Important: The reciprocal relationship applies to periodic signals. For real clock and oscillator circuits, the actual period can vary because of oscillator tolerance, temperature, supply voltage, aging and phase or timing jitter.

Worked Examples

Example 1: 1 kHz Signal

Find the period of a 1 kHz signal.

T = 1 / 1,000

Therefore:

T = 0.001 s = 1 ms

Example 2: 10 µs Period

Find the frequency of a signal with a 10 µs period.

f = 1 / 10 µs

Convert 10 µs to seconds:

f = 1 / 0.00001 = 100,000 Hz

Therefore: f = 100 kHz.

Example 3: 2.4 GHz

Find the period of a 2.4 GHz signal.

T = 1 / 2.4×10⁹

The result is approximately:

T ≈ 416.67 ps

Example 4: 50 Hz

Find the period of a 50 Hz AC waveform.

T = 1 / 50

Therefore:

T = 0.02 s = 20 ms

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Frequency & Period FAQ

Use T = 1/f, where T is the period in seconds and f is the frequency in hertz. For example, 1 kHz corresponds to a period of 1 ms.

Use f = 1/T, where f is frequency in hertz and T is the period in seconds. For example, a 10 µs period corresponds to 100 kHz.

Frequency and period are reciprocals. Increasing frequency decreases the period, while decreasing frequency increases the period.

The period of a 50 Hz signal is T = 1/50 = 0.02 seconds, or 20 ms.

The period of a 60 Hz signal is approximately 0.01667 seconds, or 16.67 ms.

A 1 MHz signal has a period of 1 microsecond (1 µs), because 1 MHz is 1,000,000 cycles per second.

A 1 ns period corresponds to a frequency of 1 GHz.

The converter supports Hz, kHz, MHz, GHz and THz for frequency, and seconds, milliseconds, microseconds, nanoseconds, picoseconds and minutes for period.