Simple Pendulum Period
Also known as swing time of a pendulum
Worked example: 1 m pendulum → T = 2.006409 s — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
The pendulum →
Grade 11Grade 11 Math — Functions & Applications
Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning. Find 1 more lesson on this formula.
share your results
Simple Pendulum Period explained
Galileo noticed — reputedly while timing a swinging cathedral lamp against his own pulse — that a pendulum's period depends on neither its mass nor, for small swings, its amplitude: only on its length and the local pull of gravity. Christiaan Huygens turned that insight into the pendulum clock in 1656, and for nearly three centuries it remained the world's best timekeeper. The solver uses standard gravity, g = 9.80665 m/s², a value exact by definition.
A worked example: a "seconds pendulum" beating once per second has a full period of 2 s, so L = g(T/2π)² = 9.80665 × (2/6.2832)² ≈ 0.994 m — the reason grandfather clocks stand about a metre tall inside. The formula is a small-angle approximation, accurate to about 1% for swings under 15°. Surveyors once ran it in reverse, timing precision pendulums to map tiny local variations in g across the Earth's surface.
Simple Pendulum Period formula
- = Period (s)
- = Pendulum length (m)
Missing one of these? Work it out first, then come back
- Period — Speed in Circular Motion (v = 2πr/T), Angular Velocity from Period
- Pendulum length — Normal Strain (ε = δ/L), Thermal Linear Expansion