Pendulum: Calculate Length and Period of Oscillation

Name: Pendulum: Calculate Length and Period of Oscillation
Author: Jürgen Kummer

Stopwatch and calculator for the length and oscillation period of a thread pendulum. A thread pendulum is a weight on an as light as possible string. An oscillation is a swing back to the starting point, e.g. from the far left to the far right and back again. The length of the pendulum is measured from the point of attachment to the center of gravity of the weight. If the angle at which the swing takes place is small (less than 10° for practical measurements), then the duration of an oscillation depends only on the length of the pendulum, but not on the length of the deflection, the amplitude.
You can stop the time or enter the duration directly. With number of swings you can specify the oscillations during this time. With a larger number of measured oscillations, the measurement error over time decreases. If the duration is given, then the length is calculated, if the length is given, the duration is calculated.

Stopwatch

Calculator

Time t:		s
Number of swing n:
Gravitational acceleration g:		m/s²
Length l:

The formula is t = 2 π n √ l/g

Example: a pendulum swings back and forth 10 times in 9 seconds. Then it is a little over 20 centimeters long.

The acceleration due to gravity, g, averages approximately 9.81 m/s² on the Earth's surface, but can vary slightly depending on geographical location (9.78 at the equator, 9.80 in Central Europe, 9.83 at the poles). This value can be adjusted for precise calculations. The formula is only valid for small oscillations. At larger angles, the oscillation period increases, and the motion is no longer harmonic. To improve measurement accuracy, it is recommended to time at least 10 to 20 oscillations. Air resistance and friction in the suspension can slightly lengthen the oscillation period but are not considered in this calculation. For experiments in the classroom or at home, a simple stopwatch and a ruler for measuring length are usually sufficient.

Last updated on 03/08/2026. Author: Jürgen Kummer

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