How to Calculate Acceleration Due to Gravity Using a Pendulum

A simple pendulum is an easy way to calculate the acceleration due to gravity wherever you find yourself.

This can be accomplished because the period of a simple pendulum is related to the acceleration due to gravity by the equation

Simple pendulum period equation

T = period
L = length of the pendulum
g = acceleration due to gravity

This worked example problem will show how to manipulate this equation and use the period and length of a simple pendulum to calculate the acceleration due to gravity.

Calculate Acceleration Due To Gravity Example Problem

Question: Astronaut Spaceman uses a small mass attached to a 0.25 m length of string to figure out the acceleration due to gravity on the Moon. He timed the pendulum’s period to be 2.5 seconds. What were his results?

Start with the equation from above

Square both sides to get

Multiply both sides by g

Divide both sides by T2

This is the equation we need to make our calculation. Plug in the values for T and L where
T = 2.5 s and
L = 0.25 m

g = 1.6 m/s2

Answer: The Moon’s acceleration due to gravity is 1.6 m/s2.

This type of problem is easy to work out and easy to make simple errors. A common error with this problem is not squaring pi when entering the numbers into a calculator. This will result in an answer 3.14 times less than the true answer.

It is also good to keep track of your units. This problem could have had a measurement for the length at 25 cm. instead of 0.25 m. Unless you recorded your acceleration units as cm/s2, the m/s2 value would be 100 times greater than the correct answer.

Other Simple Pendulum Example Problems

Check out another simple pendulum example problem which uses the pendulum period formula to calculate the length when the period is known. Or this example problem to calculate the period when the length is known.