Simple Pendulum Calculator

A simple pendulum's swing period depends only on its length (for small swings).

How the Math Works

The Simple Pendulum Calculator uses the formula T = 2π√(L ÷ g) to determine the period of a pendulum, which is the time it takes to complete one full swing. This formula assumes the pendulum swings at a small angle (less than 15 degrees) and that air resistance is negligible. The period (T) depends directly on the square root of the pendulum's length (L) and inversely on the square root of gravitational acceleration (g). Since g is constant on Earth (approximately 9.8 m/s²), the period increases as the pendulum's length increases, meaning longer pendulums swing more slowly. The frequency, calculated as 1/T, represents how many swings occur per second.

Practical Applications

To use this calculator, input the pendulum's length in meters or feet (ensure units match the gravitational constant used). The calculator will output the period in seconds and the frequency in hertz (Hz). For example, a 1-meter-long pendulum on Earth has a period of about 2.01 seconds and a frequency of 0.5 Hz. This is useful for designing pendulum clocks, where adjusting the length fine-tunes the timekeeping accuracy. In physics experiments, it helps verify the principles of harmonic motion or calibrate equipment like metronomes.

Day-to-Day Use

Understanding pendulum motion helps explain everyday phenomena, such as why grandfather clocks use long pendulums for stable, slow swings that ensure precise timekeeping. It also applies to hobbies like building model clocks or kinetic sculptures that rely on pendulum motion. Additionally, knowing how length affects period can inform practical tasks, like adjusting a playground swing's rope length to change its swinging rhythm or optimizing the design of chandeliers that sway gently due to pendulum-like motion.

Worked example

1 m pendulum → period 2.01 s.

FAQ