What is the small-angle approximation limit for this calculator?

The small-angle approximation is highly accurate, keeping errors under 0.2% for swing amplitudes of 15 degrees or less.

How does the calculator find the maximum speed of the pendulum bob?

It uses conservation of energy, calculating the height change from the input amplitude and length to find the peak velocity at the lowest point.

Can I use this calculator to find gravity on other planets?

Yes. Select 'Gravity (g)' as the target variable and input the pendulum's length and measured period to find the local gravitational acceleration.

Does the mass of the bob affect the pendulum's period?

No. The period of a simple pendulum depends solely on its length and gravity. Mass is only used to calculate kinetic energy.

What units of measurement should I use?

Input length in meters (m), period in seconds (s), gravity in meters per second squared (m/s²), amplitude in degrees (°), and mass in kilograms (kg).

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Pendulum Period Calculator (T = 2π√(L/g))

Compute period, length, or gravity of a simple pendulum, plus amplitude-based peak speed and energy

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What this tool helps you do

A simple pendulum is a mass on a string of length L swinging under gravity g.

Small-angle equations (given any two of T, L, g — the third follows):

Period: T = 2π · √(L / g)
Length: L = g · (T / 2π)²
Gravity: g = 4π² · L / T²
Frequency: f = 1 / T

With amplitude θ₀: h = L(1 − cos θ₀), vmax = √(2gh), amax = g·sin θ₀.

Small-angle approximation: accurate within 0.2% at θ₀ ≤ 15°. g defaults to 9.80665 m/s².

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Pendulum Period Calculator (T = 2π√(L/g))

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Examples

1. Determining Pendulum Length for a Seconds Pendulum

2. Calculating Peak Velocity of a Physics Lab Pendulum

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