How to Calculate the Period of Pendulum

By Jack Brubaker
The period of a pendulum depends on its length, not its mass.

Galileo first discovered that experiments involving pendulums provide insights into the fundamental laws of physics. Foucault’s pendulum demonstration in 1851 proved the Earth completes one rotation per day. Since then, physicists have used pendulums to investigate fundamental physical quantities, including the mass of the Earth and the acceleration due to gravity. Physicists characterize the motion of a simple pendulum by its period -- the amount of time required for the pendulum to complete one full cycle of motion.

Determine the length of the string or wire that connects the mass on the end of the pendulum to its tether point. If you are working a problem from a textbook, this information may be stated directly, usually in units of inches, feet, centimeters or meters. If you are constructing your own pendulum, measure the length of the wire or string that connects the weight to its tether point using a ruler or tape measure.

Convert the length of the pendulum to units of meters with an online conversion tool. You will determine the period of the pendulum in units of seconds, but you must use length units of meters for the units in the calculation to cancel properly.

Divide the length of the pendulum in meters by 9.81 meters per second per second -- the acceleration due to gravity. Take the square root of this value and multiply the result by 2 * pi, where pi is 3.14. A pendulum length of 1.6 meters, for example, results in a period, T, of T = 2 * 3.14 * (1.6 / 9.81)^0.5 = 2 * 3.14 * (0.16)^0.5 = 2 * 3.14 * 0.40 = 2.5 seconds.

Tip

The equation T = 2 * pi * (L/g)^0.5 relates the pendulum’s period, T, to the length, L, and the acceleration of gravity, g, or 9.81 meters per second per second.