Pendulum Calculator

This page provides insight into determining the frequency of a pendulum and provides a function to help you calculate it using the pendulum's period.
CalculationPendulum FrequencyInputs﻿﻿T
:50.00s​
﻿
Here are the variables for the equation
Output﻿﻿f
:0.02​
﻿
﻿
f=1Tf =\frac{1}{T}f=T1​
Pendulum Period CalculatorInputs﻿﻿l
:50.00m​
﻿
﻿﻿a, g
:9.81m/s^2​
﻿
Here are the variables for the equation
Output﻿﻿T (1)
:14.19s​
﻿
﻿
T=2π×(lag)12T =2\pi\times(\frac{l}{a_g})^\frac{1}{2}T=2π×(ag​l​)21​
Pendulum Length CalculatorInputs﻿﻿T (2)
:14.20s​
﻿
﻿﻿a, g
:9.81​
﻿
Here are the variables for the equation
Output﻿﻿l (1)
:50.09m​
﻿
﻿
l=(T2π)2×agl =(\frac{T}{2\pi})^2\times a_gl=(2πT​)2×ag​
ExplanationPendulums are used in many scientific instruments, such as accelerometers, seismometers, and gravimeters, to measure the acceleration of gravity in geophysical surveys. They're even used in clocks, so it's important to understand the maths behind them.
The period of the pendulum is the time it takes for a pendulum to complete one cycle, to move left and right.
﻿
Figure 1: Diagram of a Labelled Pendulum Swing
Pendulum FrequencyOne can calculate different things, like the frequency, as seen in the equation below:
﻿
f=1Tf =\frac{1}{T}f=T1​
Pendulum Period CalculatorWe can also calculate the period of the pendulum.
﻿
T=2π×(lag)12T =2\pi\times(\frac{l}{a_g})^\frac{1}{2}T=2π×(ag​l​)21​
Pendulum Length CalculatorFrom this, we can also calculate the length of the pendulum.
﻿
l=(T2π)2×agl =(\frac{T}{2\pi})^2\times a_gl=(2πT​)2×ag​
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