# Simple Pendulum

Exact formula : `T = 4*sqrt(L/g)*K(sin(theta/2))` K is the complete elliptic integral of first kind (see below).

Approximative formula : `T_a = 2*pi*sqrt(L/g)`

## Period and frequency of a simple Pendulum

This tool is a simple pendulum calculator. It calculates the pendulum period using two different equations.

L: length of the pendulum in meter (m)

`theta`: angular amplitude of the pendulum in radian (rad)

g: gravitational acceleration in meter per second squared (m/s2)

The first equation is the exact solution derived from the equation of motion of a simple pendulum.

`T = 4 * sqrt (L / g) * K (sin (theta / 2))`

K is the complete elliptic integral of first kind.

The second equation is an approximation of the first equation that simplifies calculations. This approximation is valid only for "small angles" (generally less than 15 degrees, `theta <15 °`).

`T_a = 2 * pi * sqrt (L / g)`

The frequency is deduced from the period using the following formula :

`f = 1 / T`

## See also

Complete elliptic integral of first kind

Motion Calculators

Physics Calculators