How To Calculate Pendulum Force

When a pendulum moves away from its resting position, gravity forces it to swing back. This force is a function of the earth's constant acceleration due to gravity, the pendulum bob's mass and the angle between the pendulum and the vertical. Specifically, the force equals the mass times gravity times the sine of that angle – (F = mg sinθ). When the string is light, treat it as massless and ignore it in the pendulum force calculation. The string's length has no effect of the force on the pendulum, though it does affect how long the bob takes to swing.

Step 1

Find the sine (sin) of the angle between the string and the vertical. If you don't have a scientific calculator, use the online calculator (see first link Resources section). For example, with an angle of 20 degrees: sin(20) = 0.342.

Step 2

Multiply the result from Step 1 by the earth's gravitational acceleration, which is 9.81 meters per second squared: 0.342 x 9.81 m/s^2 = 3.36 m/s^2.

Step 3

Multiply the result from Step 2 by the bob's mass. For example, if the bob weighs 2 kilograms (kg), the calculation is 3.36 m/s^2 x 2 kg = 6.72. This is the force pushing the pendulum bob, measured in newtons.