Pendulum Calculator

Calculate pendulum period from length.

About Pendulum Calculator

The pendulum period for Pendulum depends only on length and gravity at small angles, so longer pendulums swing slower regardless of the bob's mass. A pendulum's period is set by geometry and gravity alone, which is why it became a reliable clock.

Formula

Pendulum

T = 2*pi*sqrt(L/g); large amplitude adds a small correction

small angle: Below about 15 degrees, the correction is negligible

Worked example

With the default values below, Pendulum Calculator returns Period of 2.0099. Change any input above and every figure here is recalculated in your browser.

Inputs used

Lengthminimum 0 m: 1 m
Gravityminimum 0 m/s^2: 9.81 m/s^2
Amplitudeminimum 0 deg: 10 deg

Results

Period: 2.0099 s
Frequency: 0.4975 Hz
Small-Angle Period: 2.0061 s

Step by step

1Values used
2Pendulum
3Period= 2.0099 s
4Frequency= 0.4975 Hz
5Small-Angle Period= 2.0061 s

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Pendulum calculated?

T = 2*pi*sqrt(L/g); large amplitude adds a small correction The pendulum period for Pendulum depends only on length and gravity at small angles, so longer pendulums swing slower regardless of the bob's mass.

Why does Pendulum matter?

A pendulum's period is set by geometry and gravity alone, which is why it became a reliable clock.

What values do I need to enter?

This calculator takes 3 inputs: Length, Gravity, Amplitude. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.