# Force Calculator

Welcome to our **force calculator**, where you can calculate the **force** acting on a body using **Newton's second law**. We shall address some fundamentals regarding force calculations, so read through this article if you have any of the following nagging questions:

- What is
**force**? - What is the
**formula for force**? - What is
**Newton's second law of motion**? - Is
**force**a**scalar**or a**vector**quantity? - How do you calculate
**net force**?

## How to use this force calculator?

This force calculator is a simple tool to determine how much force is acting on a system.

- Enter the
**mass**and**acceleration**of the body, and the calculator will do the rest. - Use the different units in the tool to avoid unit conversion hassle.

You can also use this calculator to find the acceleration or the mass of the body by providing the remaining two variables!

## What is force? Newton's second law of motion

A **force** is any action on a body (with **mass**) that can change its **motion**. We perceive this change in motion through a change in the object's **velocity** (or ). Newton's second law states that * "the change in the object's momentum is directly proportional to the force applied"*.

For a constant mass system, the formula for force is given by:

Where:

- $\vec{F}$ is the
**force**acting on a body of**mass**$m$; - $\vec{p}$ is the
**momentum**of the body; - $\vec{v}$ is the
**velocity**of the body; and - $\vec{a}$ is the
**acceleration**of the body.

As the arrows indicate, force is a **vector** quantity, acting in the same direction as the **acceleration**. Use our acceleration calculator to find the acceleration in your case.

The SI unit of force is **Newton** $(\text{N})$, while the imperial system uses units such as **pound-force** $(\text{lbf})$ and **dynes** $(\text{dyn})$.

## Examples using force equation to find force, mass and acceleration

Let us understand this concept of force through some examples:

- You need to stop a
**mass**of $200 \text{ kg}$ moving at $25 \text{ m/s}$. Use the force equation to find how much force you need to apply to stop it in $5 \text{ s}$.

Let us list out everything given to us first:

1. **Mass**, $m = 200 \text{ kg}$.

2. **Initial velocity**, $u = 25 \text{ m/s}$.

3. Desired **final velocity**, $v = 0 \text{ m/s}$.

4. **Time period** in which the velocity changes, $\Delta t = 5 \text{ s}$.

We will need **acceleration** to calculate force:

The **negative** symbol indicates the **direction** of acceleration; In this case, the acceleration is * opposite* to the

**direction**of

**velocity**.

Using this information, we can determine the force required:

Note that this **force** with the **negative sign** acts in the **same direction** as the **acceleration**.

If you need to find the velocity from distance and time, use our velocity calculator.

Now let's learn how to find acceleration with mass and force using the force formula.

- A shopping cart weighing $70\text{ lb}$ is pushed with a force of $35 \text{ N}$. Calculate the cart's
**acceleration**.

Again, let's list out the given data:

1. **Mass**, $m = 70 \text{ lb}$.

2. **Force**, $F = 35 \text{ N}$.

Now how do we find acceleration with this mass and force information? Let's rearrange the force equation to get:

Using this equation, we get:

You can avoid all these unit conversions using our calculator instead! Now you know how to find acceleration with mass and force.

## Calculating net force

When multiple forces act on a body, the **net force** shall determine the body's motion. Since force is a vector quantity, we determine the net force acting on a body using the vector addition:

Where:

- $R$ is the
**resultant force**or**net force**; - $F_i$ are
**individual forces**acting on the body.

Head to our net force calculator to calculate the net force acting on a body.