Distance Between Two Points Calculator

Published on: September 15, 2024

This Distance Between Two Points Calculator helps you find the straight-line distance between two points on a coordinate plane. It uses the formula d = √((x₂ − x₁)² + (y₂ − y₁)²), where (x₁, y₁) and (x₂, y₂) are the two points, and the answer is written in units. First find the differences in the x-coordinates and y-coordinates, square them, add them together, and then take the square root. It is a simple way to check answers, understand the distance formula, and practise basic geometry step by step.
Line between two points
Enter the coordinates for (x₁, y₁) and (x₂, y₂).

Step-by-step method

  1. Identify what is given.
  2. Write the formula.
  3. Substitute the values and calculate the distance.

Formula:

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Example 1: (x₁, y₁)=(0.00, 0.00), (x₂, y₂)=(3.00, 4.00)

Step 1 - Identify what is given.

In this problem: The given points are (0.00, 0.00) and (3.00, 4.00).

(x₁, y₁)=(0.00, 0.00),(x₂, y₂)=(3.00, 4.00)

Step 2 - Write the formula.

In this problem: Use the distance formula: d = √((x₂ − x₁)² + (y₂ − y₁)²).

d=√((x₂ − x₁)² + (y₂ − y₁)²)

Step 3 - Substitute the values and calculate the distance.

In this problem: Compute differences: Δx = 3.00 − 0.00 = 3.00, Δy = 4.00 − 0.00 = 4.00. Then d = √(3.00² + 4.00²) = √(25.00) = 5.00.

d=√(3.00² + 4.00²)=√(25.00)=5.00

Final answer: d = 5.00

Example 2: (x₁, y₁)=(-2.00, 1.00), (x₂, y₂)=(4.00, 5.00)

Step 1 - Identify what is given.

In this problem: The given points are (-2.00, 1.00) and (4.00, 5.00).

(x₁, y₁)=(-2.00, 1.00),(x₂, y₂)=(4.00, 5.00)

Step 2 - Write the formula.

In this problem: Use the distance formula: d = √((x₂ − x₁)² + (y₂ − y₁)²).

d=√((x₂ − x₁)² + (y₂ − y₁)²)

Step 3 - Substitute the values and calculate the distance.

In this problem: Compute differences: Δx = 4.00 − -2.00 = 6.00, Δy = 5.00 − 1.00 = 4.00. Then d = √(6.00² + 4.00²) = √(52.00) = 7.21.

d=√(6.00² + 4.00²)=√(52.00)=7.21

Final answer: d = 7.21