Pendulum Length Calculator

The following calculator is designed to calculate the pendulum length based on inputs acceleration due to gravity and Frequency. The tool can make work easy for students and educators.

Pendulum Length Calculator

Enter the gravity, frequency, or pendulum length to calculate the missing value.










Enter the gravity and period to calculate the pendulum length.










Pendulum Length Calculation tool

A pendulum’s length is the distance between the point of suspension and its center of mass. This length determines the period of the swing, which is the time it takes to complete one full oscillation.

Imputing Guide

Input Action
Gravity (g) Enter gravity in m/s² (e.g., 9.8).
Frequency (f) Enter frequency in Hz (e.g., 0.5).
Pendulum Length (PL) Enter length in meters if known, or leave blank to calculate.
Click Calculate Calculates the unknown value based on inputs.

Calculation Examples

Calculation Type Example Values
Basic g = 9.8, f = 0.5
Advanced g = 9.8, f = 0.5, PL = 0.248

Formula for Pendulum Length

Calculate pendulum length with:

PL=g4π2f2\text{PL} = \frac{g}{4 \cdot \pi^2 \cdot f^2

Variable Description
PL Pendulum Length (meters)
g Acceleration due to Gravity (m/s²)
f Frequency (Hz)

Calculation Example

Step Calculation
Gravity (g) 9.8 m/s²
Frequency (f) 0.5 Hz
Step 1: Square the frequency 0.52=0.250.5^2 = 0.2
Step 2: Multiply by 4π24 \cdot \pi^2 4(3.142)2=39.484 \cdot (3.142)^2 = 
Step 3: Divide gravity by the product 9.839.48=0.248\frac{9.8}{39.48}m

Answer: The pendulum length is approximately 0.248 meters.

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