Simple Pendulum Period Calculator

Work out simple pendulum period instantly with clear inputs, formula shown and shareable results.

About Simple Pendulum Period Calculator

For small swings the period of a simple pendulum is 2 pi sqrt(L/g), independent of both mass and amplitude - the isochronism Galileo noticed. A one metre pendulum takes 2.006 s per full swing, which is why the seconds pendulum in a grandfather clock is about 0.994 m long.

Formulas

Period

T = 2 pi sqrt(L / g)

Seconds pendulum

L = g / (4 pi^2) for T = 1 s

Worked example

With the default values below, Simple Pendulum Period Calculator returns Period Of One Full Swing of 2.0064. Change any input above and every figure here is recalculated in your browser.

Inputs used

Pendulum lengthminimum 0 m: 1 m
Local gravitational accelerationminimum 0 m/s2: 9.80665 m/s2

Results

Period Of One Full Swing: 2.0064 s
Frequency: 0.4984 Hz
Length For A One-Second Period: 0.2484 m
Time For One Tick: 1.0032 s

Step by step

1Values used
2Period
3Seconds pendulum
4Period Of One Full Swing= 2.0064 s
5Frequency= 0.4984 Hz
6Length For A One-Second Period= 0.2484 m
7Time For One Tick= 1.0032 s

Assumptions and limits

The result is derived only from the 2 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

Does a heavier bob swing more slowly?

No. Mass cancels out, because gravity provides both the restoring force and the inertia in equal measure.

When does the small-angle assumption fail?

Past about 15 degrees the period grows measurably - roughly 0.5% at 20 degrees and 2% at 40 degrees.