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Simple Pendulum Calculator

Estimate the period and frequency of an ideal simple pendulum from its pivot-to-center-of-mass length and local gravity.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the stated units and domain limits.

Period (s)2.006409293
Frequency (Hz)0.4984027953

How to use this calculator

  1. Enter every quantity in the unit printed beside its field.
  2. Select Calculate or press Enter.
  3. Read the labeled results and compare them with the assumptions below.

Formula and method

For small angles, period T = 2π√(L/g) and frequency f = 1/T.

The calculation runs locally in your browser. If any entry is invalid or a mathematical condition is undefined, the prior result is hidden so it cannot be mistaken for a new answer.

Worked example

Using Pendulum length (m) = 1, Gravitational acceleration (m/s²) = 9.80665, the formula returns Period (s) = 2.006409293, Frequency (Hz) = 0.4984027953. The displayed default result is generated from these same inputs.

Limitations and safety

The small-angle approximation is most accurate at modest amplitudes (commonly below about 15°). Air drag, pivot friction, string mass and large swings are omitted. Results use floating-point arithmetic and are displayed to about 10 significant digits; measurement uncertainty usually supports fewer. Verify units before relying on a result.

Frequently asked questions

Where is pendulum length measured?

Measure from the pivot to the bob’s center of mass, not merely the visible string length.

Why might a measured result differ?

The formula isolates the stated model. Real systems can add uncertainty, losses, changing properties, geometry or forces that are not among the inputs.

How should I handle units?

Convert every value to the unit shown beside its field before calculating. A numerically valid value in the wrong unit will still produce a wrong result.

Review notes and reference

Reviewed October 3, 2026. The default example and an independent edge or scaling case were checked against expected values. The live script was also checked for blank, text, comma-formatted, non-finite and out-of-range entries. Method reference. Constants use the values stated in the formula. This page’s explanation and example are original.

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