Pendulum Period Calculator
Calculate the oscillation period and frequency of a simple pendulum from its length. Compare pendulum behavior on Earth, the Moon, Mars, and Jupiter, and animate the swing in real time. No signup, runs entirely in your browser.
Pendulum Physics Tips
Grandfather clocks
A traditional grandfather clock uses a 1-meter pendulum tuned to a 2-second period (1 second per half-swing). This means the tick-tock marks whole seconds precisely.
Measuring g with a pendulum
Rearrange the formula: g = 4π²L/T². Measure the period of a pendulum of known length to estimate local gravitational acceleration — a classic physics lab method.
Double the length
To double the period, you need to quadruple the length, because T ∝ √L. A 4-meter pendulum has exactly twice the period of a 1-meter pendulum.
Temperature sensitivity
Real clock pendulums expand slightly with heat, lengthening the period. Precision clocks use invar (invariant steel) pendulums to minimize this thermal drift.
Frequently Asked Questions
What is the formula for pendulum period?
T = 2π√(L/g), where T is the period in seconds, L is the pendulum length in meters, and g is gravitational acceleration (9.81 m/s² on Earth). This formula is valid for small angles (less than ~15°).
Why does mass not affect the period?
The gravitational force on a pendulum bob is proportional to its mass, but so is its inertia. These cancel out exactly, making the period independent of mass — a result first observed by Galileo.
What length gives a 1-second period?
On Earth with g = 9.81 m/s², a pendulum with T = 1 s has length L = g/(4π²) ≈ 0.2485 m (about 24.9 cm). A 2-second period (grandfather clock standard) requires L ≈ 0.994 m.
How would a pendulum behave on the Moon?
On the Moon (g = 1.62 m/s²), the same 1-meter pendulum would have a period of 2π√(1/1.62) ≈ 4.94 seconds — about 2.46 times slower than on Earth.
What is the small angle approximation?
The formula T = 2π√(L/g) assumes the angle is small enough that sin(θ) ≈ θ. For angles up to ~15° the error is under 1%. For larger amplitudes, the period increases slightly beyond this formula's prediction.
Is my data stored?
No. All calculations run locally in your browser. No data is sent to any server.