Frequency, Period & Time Conversion Guide | Hz, kHz, MHz, GHz

Introduction

Frequency and time are fundamental to oscillators, PWM, clocks, microcontrollers, communication systems, filters, switching power supplies, sensors, RF systems, and lab measurement. The core relationship is simple: f = 1 / T and T = 1 / f. Higher frequency means shorter period.

This guide builds on Engineering Unit Conversions for Electronics. That guide covers SI prefixes and engineering notation; this one focuses on signal-specific relationships where the correct formula matters as much as the units.

Frequency and Period Basics

Frequency is the number of complete cycles per second. Its SI unit is hertz, where 1 Hz means 1 cycle per second. Period is the time required for one complete cycle. Its symbol is T and its SI unit is the second.

Frequency ↔ Period Quick Reference

Converting Frequency to Period

The standard workflow is: convert frequency to hertz, apply T = 1 / f, then convert seconds to the best display unit. For 25 kHz, the base frequency is 25,000 Hz. The period is 1 / 25,000 seconds, or 0.00004 s, which is 40 µs.

Converting Period to Frequency

For period-to-frequency conversion, convert the period to seconds, apply f = 1 / T, then convert hertz to a suitable output unit. A 20 µs period is 20 × 10^-6 s, so the frequency is 50,000 Hz, or 50 kHz.

How the ECParts Frequency to Period Converter Works

The Frequency to Period Converter supports frequency inputs in Hz, kHz, MHz, GHz, and THz, and period outputs in ps, ns, µs, ms, and s. In reverse mode, it accepts period in ps, ns, µs, ms, and s, then displays frequency as Hz, kHz, MHz, GHz, or THz.

The implementation normalizes frequency to hertz or period to seconds, applies the reciprocal formula, and formats results using shared engineering-number helpers. It accepts decimal and scientific notation, rejects zero or negative frequency/period values, and warns when values are extremely high or low.

Digital Electronics, Clocks, and PWM

Clock frequency describes cycles per second. A 16 MHz clock has a 62.5 ns clock period, and a 100 MHz clock has a 10 ns period. This does not mean every CPU instruction takes exactly one clock cycle; instruction timing depends on architecture, pipeline, memory, and peripherals.

PWM uses frequency, period, and duty cycle together. For 20 kHz PWM, T = 50 µs. With 25% duty, TON = 12.5 µs and TOFF = 37.5 µs. With 60% duty at 25 kHz, T = 40 µs, TON = 24 µs, and TOFF = 16 µs.

Signal-Specific Relationships

Not every signal conversion is a prefix conversion. Angular frequency, phase delay, wavelength, duty cycle, bandwidth, and RPM each use their own physical relationship. Choose the relationship first, then handle units.

Angular Frequency, Phase Delay, and Wavelength

Angular frequency is ω = 2πf, so 1 kHz is about 6283.1853 rad/s. One cycle is 2π radians, which is why 1 Hz is not 1 rad/s. For phase delay, a complete cycle is 360°. At 10 MHz, T = 100 ns, so 45° represents 12.5 ns. At 100 MHz, a 1 ns delay is 36°.

Wavelength uses λ = v / f. In free space, v is approximately 3 × 10^8 m/s, so 100 MHz is about 3 m and 2.4 GHz is about 0.125 m, or 12.5 cm. On a PCB, propagation velocity is lower and depends on effective dielectric constant, geometry, and stackup. Do not use free-space wavelength as an exact PCB guided wavelength.

Related Timing Concepts

When Not to Use f = 1 / t

Do not automatically invert every time value. Propagation delay, rise time, fall time, pulse width, setup time, hold time, latency, and capture window are not necessarily periods. You can use a reciprocal only when that time value truly represents one complete repeat cycle or when you have defined a meaningful rate.

Practical Examples

Common Frequency and Time Conversion Mistakes

• Forgetting that frequency and period are reciprocals.
• Treating kHz ↔ ms as a normal prefix conversion instead of a reciprocal shortcut.
• Using microseconds directly as seconds.
• Confusing MHz and GHz.
• Using f = 1 / t for any time value, including delay or rise time.
• Confusing clock period with instruction execution time.
• Treating baud rate as always identical to hertz.
• Treating rotational frequency and motor electrical frequency as always identical.
• Forgetting the 2π relationship between hertz and radians per second.
• Assuming PCB wavelength always equals free-space wavelength.
• Displaying more precision than the source value justifies.

Practical Engineering Tips

• Convert frequency to hertz before using the base reciprocal formula.
• Convert period to seconds before using f = 1 / T.
• Remember that higher frequency means shorter period.
• Use kHz ↔ ms and MHz ↔ µs shortcuts only when the units match correctly.
• Do not use f = 1 / t unless t actually represents a period.
• Keep frequency and angular frequency separate.
• Remember the 2π relationship between Hz and rad/s.
• Use RMS concepts only where relevant; do not mix them into frequency conversion.
• Distinguish clock frequency from instruction rate.
• Distinguish baud rate from frequency.
• Use actual propagation velocity when calculating wavelength in a medium.
• Treat free-space wavelength as an approximation only for free-space propagation.
• Check pulse width and duty cycle separately from period.
• Preserve meaningful precision.
• Verify results with the ECParts Frequency to Period Converter.

Summary

Reliable signal conversion requires the correct quantity, correct units, and correct physical relationship. Use T = 1 / f for period, f = 1 / T for frequency, ω = 2πf for angular frequency, λ = v / f for wavelength, TON = D × T for PWM pulse width, and Δt = φ/(360f) for phase delay in degrees. The hard part is not moving the decimal point; it is choosing the right relationship for the time or signal quantity you actually have.