Pendulum Calculator - Period, Length & Gravity
How to Use This CalculatorEnter any two of the three values — period, length, or gravity — and the third is calculated instantly. Or enter just a length with gravity pre-filled to get the period immediately. Use the planetary preset buttons to explore how the same pendulum would behave on other worlds. Adjust the amplitude slider and click Animate to watch the pendulum swing in real time at the correct speed. Quick examples: L = 1 m on Earth → T ≈ 2.006 s — L = 1 m on the Moon → T ≈ 4.94 s — T = 1 s, g = 9.807 m/s² → L ≈ 24.8 cm. Period
T
Length
L
Gravity
g
15 deg
(small angle approximation valid below ~15 deg)
Enter any two values above - or just a length - to calculate the period.
EquationsT = 2π √(L / g) (simple pendulum, small angles)L = g (T / 2π)² g = L (2π / T)² f = 1 / T (frequency in Hz) Valid for swing angles below ~15° — error < 0.5% About the Simple PendulumA simple pendulum consists of a mass (the bob) suspended from a fixed point by a massless, inextensible string. When displaced from its equilibrium position and released, it swings back and forth in a nearly perfect periodic motion. For small angles (below about 15°), the restoring force is approximately proportional to the displacement, making the pendulum a classic example of simple harmonic motion described by T = 2π√(L/g). Galileo Galilei is credited with discovering the isochronism of the pendulum around 1602 - the remarkable property that the period is independent of the amplitude (for small swings) and independent of the mass of the bob. Legend holds he noticed a swinging lamp in the Pisa cathedral keeping time with his pulse. This insight led directly to Christiaan Huygens' invention of the pendulum clock in 1656, which remained the world's most accurate timekeeping device for nearly 300 years. The pendulum equation also reveals that gravity itself can be measured precisely by timing a pendulum of known length - a technique used by scientists to map gravitational variations across the Earth's surface, detect underground density anomalies, and even confirm that gravity is slightly stronger at the poles than at the equator. The classic 1-second pendulum (half-period = 1 s, so T = 2 s) has a length of almost exactly 99.4 cm on Earth - very close to 1 metre, which is not a coincidence: the original definition of the metre in 1791 was proposed to be the length of a seconds pendulum.
Hands-On Physics in the Lab:
Build and time your own pendulums with Physics Kits and Physics Lab Supplies from xUmp.com — curated by a physicist for students, educators, and science enthusiasts. Related Reference Pages |