# Simple Pendulum Calculator

Welcome to our **simple pendulum calculator**, where you can easily calculate the **period** of a pendulum and its **frequency** from its **length**. You've come to the right place if you want to learn more about a simple pendulum. We shall discuss some fundamentals of a simple pendulum here, including:

- What is a
**simple pendulum**? - How to find its
**frequency**and**period**using the**simple pendulum equation**? - How to find the length of the pendulum?

If you're interested in finding the simple pendulum formula by yourself, then the

may be helpful in the intermediate steps.## How to use this simple pendulum calculator?

This simple pendulum calculator uses the simple pendulum equation to find the pendulum's period and frequency from its length:

- Enter the pendulum's length, and this simple pendulum calculator will determine the pendulum's period and frequency, using a period of a pendulum equation.
- Enter its frequency or period, and the calculator will find the pendulum's length using the pendulum length formula.
- The gravitational acceleration constant is set at $9.807 \text{ m/s}^2$. You can change it to a custom value if you wish.

## What is a simple pendulum?

A pendulum is a **mass** suspended from a **pivot** about which it can swing freely. To classify a pendulum as a **simple pendulum** (or **simple gravity pendulum**), it must satisfy these conditions:

- The
**pivot**must be**frictionless**.**Air resistance**must be**negligible**. - The
**string or rod**used to suspend the mass must be**weightless**.

The inclined plane is another simple structure we often consider in physics problems. The inclined plane calculator is dealing specifically with this issue!

## Frequency and period of a pendulum

For a **simple pendulum** with **small amplitudes** $\theta$ such that $\sin(\theta) \approx \theta$, the **period** of the pendulum is * independent* of the

**mass**and the

**amplitude**. In such cases, the formula for a period of oscillation is given by:

Where:

- $T$ is the pendulum's
**period**; - $L$ is the pendulum's
**length**(length of the string suspending the pendulum mass); - $g$ is the
**gravitational acceleration**, equal to $9.81 \text{ m/s}^2$; and - $\theta$ is the
**amplitude**of the pendulum swing.

We can use this formula for the **period** of a pendulum to calculate its **frequency**:

Here, $f$ is the frequency of the pendulum.

For amplitudes greater than $15 \degree$, the pendulum's period also depends on the moment of inertia of the suspended mass. In such cases, the period of a pendulum formula is given by:

Where:

- $I$ is the
**moment of inertia**about the pivot; - $m$ is the
**suspended mass**; and - $D$ is the
**distance**from the**pivot**to the**center of mass**.

Our calculator does not perform this calculation, but we have the perfect tool for this scenario: physical pendulum calculator.

## Length of a pendulum formula

We can find the length of the simple pendulum by rearranging the formula of a period of oscillation:

If you're now familiar with simple pendulum, why don't you try other calculators explaining **fundamental problems of physics**? Visit our trajectory calculator to learn the vertical distance formula of a thrown object or its angle of trajectory.

*T = 2π√(L/g)*