# Distance Between Two Points Calculator

Our **distance between two points calculator** can quickly find the distance between any two points confined to a two-dimensional plane.

Within this short text, we will cover:

- How to
**find the distance between two points**; - How to use the distance between two points formula; and
- What is the
**shortest distance**between two points.

Let's start!

**Prefer watching** rather than reading? Learn all you need in 90 seconds with this video **we made for you**:

## What is distance? Distance between two points definition

In its simplest definition, the **distance between two points** in a **2D** plane is **the length of the line segment connecting them**.

For example, if we put into a graph the points $(0, 4)$ and $(4, 4)$, draw a line between them, and measure this line segment's length, we would get $4$ as a result.

This definition is derived from the **Euclidean distance** definition, and we can also define **1D**, **3D**, **4D**, and **any finite dimension** Euclidean distance.

*Of course, plotting and measuring lines anytime we want to find the distance between two points is not practical*. That's where the **distance between two points formula** comes in.

## Distance between two points formula

We can obtain the mathematical distance definition from the Euclidean distance formula for a two-dimensional plane:

where:

- $x_{1}$ and $y_{1}$ are the coordinates of any of the two points;
- $x_{2}$ and $y_{2}$ are the coordinates of the other point; and
- $d$ is the distance between them.

💡 This definition is what makes the shortest distance between two points on a two-dimensional plane **always a line**! **Don't worry**. We won't dwell deeper into math in this distance between two points calculator 😉.

## How do you find the distance between two points?

To find the distance between two points, simply follow these steps:

- Find the
**XY**coordinates of the first point**(x₁, y₁)**. It doesn't matter which point we choose as long as we don't mix coordinates between them. - Find the
**XY**coordinates of the other point**(x₂, y₂)**. - Replace these values in the distance between two points formula:
`√[(x₂ - x₁)² + (y₂ - y₁)²]`

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## Other useful tools

If you enjoyed this distance between two points calculator and want to learn more about other distance definitions, check any of our other distance calculation tools:

- Distance;
- 2D distance;
- Length of a line segment;
- Coordinate distance; and
- Euclidean distance.

🙋 Give it a try! Type any two points' coordinates in the distance between two points calculator, and it will automatically output the distance between them.

## FAQ

### What is the shortest distance between two points?

**The shortest distance between two points is a straight line connecting them**. This definition only applies to flat surfaces or spaces. In a sphere, for example, the shortest distance between two points is an arc called **great circle distance**.

### What is the distance between (5, 10) and (8, 9)?

**3.16228**. We can find the distance between points **(5, 10)** and **(8, 9)** by replacing them in the distance between two points formula: `√[(8 - 5)² + (9 - 10)²] = 3.16228`

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