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Pendulum Period Calculator

Find a pendulum’s swing period.

How it is calculated

For a simple pendulum, a small mass on a light string swinging through a small angle, the time of one full swing is T = 2π × √(L ÷ g). L is the length from the pivot to the centre of the mass in metres, and g is gravitational acceleration, fixed in this tool at 9.81 m/s². The period comes out in seconds. Length must be above zero. The mass does not appear in the formula, so a heavier bob swings at the same rate. The formula holds only for small swings (roughly under 15°); larger angles make the real period slightly longer.

Worked example

A pendulum 1 m long. Divide by gravity: 1 ÷ 9.81 = 0.10194. Square root: 0.3193. Multiply by 2π (6.2832): 6.2832 × 0.3193 ≈ 2.01 s. It takes about two seconds to swing out and back, so each one-way swing takes about one second.

Try this example →

Common mistakes

  • Entering the length in centimetres. The field expects metres, so 50 cm is 0.5.
  • Measuring to the end of the bob instead of its centre, or from the wrong pivot point.
  • Expecting a heavier weight to change the period. Only length and gravity matter.
  • Counting the one-way swing as the period. The period covers a full back-and-forth cycle.
  • Using large swing angles, where the small-angle formula under-estimates the time.

Sources

About this calculator

This calculator applies the simple-pendulum formula T = 2π√(L/g), which holds for small swing angles (roughly under 15°) and assumes an idealized point mass on a massless string, giving the period — the time for one full back-and-forth swing.

It's used by physics students verifying lab measurements, hobbyists and clockmakers designing pendulum clocks where the length directly sets the tick rate, and anyone using a pendulum's known period to estimate local gravitational acceleration experimentally.

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Comments (1)

  • Editorial team

    To check the result with a real pendulum, measure from the pivot to the centre of the bob. A length near 0.994 m gives a period of 2.00 s, the classic seconds pendulum. Time 20 full swings with a stopwatch and divide by 20, which spreads your reaction-time error over many swings. Note that the tool fixes gravity at 9.81 m/s². What length did you use, and how close was your timing?

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