A simple pendulum is one of the most classic examples of motion in physics. It’s just a weight hanging from a string, swinging back and forth under the pull of gravit. The time it takes to complete one full swing—called the period—depends directly on the length of the string. The longer the pendulum, the slower it swings. Using this relationship, we can calculate exactly how long a pendulum needs to be to achieve a certain period, like the steady tick-tock of a grandfather clock. Here is a free calculator to help you do that with ease.
Pendulum Length Calculator
This calculator determines the length of a pendulum needed for a specific period using the formula for simple harmonic motion.
Result
Example: Grandfather Clock Pendulum
A grandfather clock uses a pendulum with a period of 1 second to measure time. On Earth (g = 9.8 m/s²), the required pendulum length would be:
L = g × (T/(2π))² = 9.8 × (1/(2×3.1416))² ≈ 0.25 meters or 25 centimeters
About Simple Pendulums
A simple pendulum consists of a mass hanging from a massless string of length L that swings from a central pivot point. The motion follows simple harmonic motion, where:
- T = Period (time for one complete cycle)
- L = Length of the pendulum
- g = Acceleration due to gravity
The formula T = 2π√(L/g) shows that the period depends only on the length of the pendulum and gravity, not on the mass of the pendulum bob.