Frequency and Period Calculator

Turn frequency in Hz into period, angular speed, and kHz.

What it does

Frequency counts cycles per second, period times one cycle. Mains at 60 Hz repeats every 1/60 second. Audio at 440 Hz repeats far faster. The two are reciprocals.

The tool above takes Hz and returns period seconds, angular rad/s, and kHz. The default 60 matches the worked example, so the page opens showing 0.016667 s. Type a new Hz to update all three results.

Period T = 1/f. Angular omega = 2 pi f tracks phase for waves and AC. Kilohertz divides by 1000 for compact readouts. A 1000 Hz tone has 0.001 s period and 6283.19 rad/s.

Use Hz for mains, audio, and clocks. Use period for timing gates and oscilloscope divisions. Use angular for wave equations where sine takes radians.

This page shows the formulas, one full hand checked example at 60 Hz, a reference table, and practice checks that run through the tool.

How to use

1. Type frequency in Hz above 0.
2. Read Period as seconds per cycle.
3. Read Angular as radians per second.
4. Read kHz as Hz over 1000.
5. For period to frequency, enter 1 over period as Hz.
6. Check mains: 50 or 60 Hz by region.

Formula

f

Frequency in hertz.

T

Period in seconds.

omega

Angular frequency in rad/s.

Positive Hz only. Zero or negative stops with an error. Radians are unit free as arc over radius.

Worked example

Reference table

Limits

• Single sine only. Modulated signals need spectra.
• Positive Hz only.
• Ideal timing. Jitter and drift sit outside.
• No medium model. Wave speed needs separate v = f lambda.

Common mistakes

• Entering 0 Hz and expecting infinite period here.
• Mixing kHz with Hz by 1000 times.
• Reading angular rad/s as rev/s. Divide by 2 pi for rev/s.
• Using period as frequency.
• Forgetting mains is 50 in many regions, 60 in others.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• NIST
• BIPM: SI Brochure

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