DISCOVER

# How to calculate the acceleration due to gravity

Updated February 21, 2017

Science historians credit Isaac Isaac Newton with "discovering" gravity, but Galileo first quantified the process, purportedly by dropping cannon balls from the Leaning Tower of Pisa. Today, the acceleration of a falling object, ignoring air resistance, represents one of the fundamental physical constants: 9.807 meters per second squared (m/s^2) or 32.17 feet per second squared. Many physics students carry out a variety of experiments during their training to verify these constants. One of the more common experiments -- called the "free-fall method" -- involves dropping an object from a height of 10 to 20 feet (3 to 6 m) and measuring the time required for the object to strike the ground. An alternate experiment, called the "pendulum method," involves measuring the time required for a pendulum to travel one full cycle. Students and hobbyists can carry out either experiment using household materials and a stopwatch.

## Free-fall method

Measure the height from a second-story window to the ground using a tape measure. Measure from a convenient reference point, such as the sill, because the object must be dropped from the exact point from where the measurement was taken.

Position the object at the point where the measurement was taken in Step 1 and hold a stopwatch in your other hand. Start the stopwatch at the moment you release the object and stop the stopwatch the instant the object strikes the ground.

Repeat Step 2 at least twice and then average the results to determine the average time, "t."

Measure the height of the window in metres. If you measured in feet, convert the to fractional feet with a decimal. A height of 15 feet, 6 inches, for example, would represent 15.5 feet. Now convert the height to metres by multiplying it by 0.3054. In this case, 15.5 feet * 0.3054 metres per foot = 4.73 m.

Substitute the height in metres as the distance, "d," and the average time as "t" into the equation a = 2d / t^2, where "a" represents the acceleration due to gravity. Using the example of d = 4.73 m from Step 4, and assuming an average time of 0.98 seconds, a = 2d / t^2 = (2 * 4.73m) / (0.98 s)^2 = 9.85m/s^2 (32.32 feet/s^2).

## Pendulum method

Tie or tape a weight to a string and then secure the string to a ceiling so that the weight can swing freely in a pendulum motion.

Measure the length of the string in metres using a tape measure and record this value as length, or "L."

Draw back and release the weight so that it swings freely and start the stopwatch at the moment you release the weight. Allow the pendulum to travel through five complete periods and stop the stopwatch at the height of its travel back to its starting point. Record the time as T (total).

Divide the T (total) by 5 to determine the average period of the pendulum, T (avg).

If you recorded the string length in inches, you need to convert to metres. Multiply the length in inches by 0.0254. For a pendulum length of 37 inches, for example, L = 37 inches * 0.0254m/inches = 0.940 meters.

Substitute L and T(avg) into the equation g = (4 * pi^2 * L) / T(avg)^2. Using the sample data from Step 5 with an average period T(avg) of 1.95 seconds,

g = (4 * pi^2 * L) / T^2 = (4 * 3.14^2 * 0.940m) / (1.95 s)^2 = 9.75m/s^2 (32 feet/s^2).

#### Things You'll Need

• Tape measure
• Small-sized object, such as rock or large marble
• String, 1.2 m (4 feet)
• Tape
• Stopwatch capable of measuring to 0.01 seconds
• Calculator