Waves & Oscillations
Pendulum Period Calculator
Calculate period, frequency or length for a simple pendulum. Works on any planet. Live pendulum animation shows your result in real time.
Solve for
Quick examples
Live pendulum
Period T
2.0061
s
Frequency f
0.4985
Hz
Length L
1
m
Same length (1m) on different planets
Earth
2.01 s
Moon
4.94 s
Mars
3.26 s
Jupiter
1.26 s
Venus
2.11 s
Step-by-step solution
Formula
T = 2π × √(L / g)Substituted
T = 2π × √(1 / 9.81)
T = 2π × √(0.10194)
T = 2π × 0.31928
T = 2.0061 s
Frequency
f = 1 / T = 1 / 2.0061 = 0.4985 HzPendulum equations
Period
T = 2π√(L/g)
Frequency
f = 1/T = (1/2π)√(g/L)
Length from period
L = g(T/2π)²
Gravity from period
g = L(2π/T)²
Angular frequency
ω = 2π/T = √(g/L)
Small-angle approx
Valid for θ < 15°
The simple pendulum
A simple pendulum consists of a mass (the bob) on a string of fixed length. For small angles (less than about 15°), it undergoes simple harmonic motion with a period that depends only on length and gravity — not on mass or amplitude. This is called isochronism, discovered by Galileo.
The independence from mass is what made pendulums so useful for timekeeping — a 1-metre pendulum has a period of almost exactly 2 seconds on Earth, regardless of how heavy the bob is. For the full treatment including large-angle corrections, see our article on Simple Harmonic Motion.
Why doesn't mass affect the period?↓
A heavier bob has more inertia (harder to accelerate) but also more gravitational force (pulled back harder). These two effects exactly cancel — the ratio F/m = g is the same regardless of mass.
What is the small-angle approximation?↓
The exact pendulum equation is nonlinear: d²θ/dt² = −(g/L)sinθ. For small angles, sinθ ≈ θ, giving simple harmonic motion with period T = 2π√(L/g). Above about 15° the true period is slightly longer than this formula predicts.
How do pendulum clocks work?↓
A pendulum provides isochronous (constant-period) timing pulses. An escapement mechanism counts these pulses and moves the clock hands. The length is adjusted to set the period — making it slightly longer slows the clock; shorter speeds it up.