Overview
The distance between two points in the plane is the length of the straight segment joining them. Compute it from the horizontal and vertical differences using the Pythagorean theorem; it underlies analytic geometry and navigation.
Formula
d = √((x₂ − x₁)² + (y₂ − y₁)²).
How it works
Read the coordinates
Identify x₁ and y₁ for the first point, x₂ and y₂ for the second.
Compute the differences
Horizontal difference = x₂ − x₁, vertical = y₂ − y₁.
Square and add
Add the squares of both differences.
Take the root
The square root of the sum is the distance.
Worked examples
Example 1: (0, 0) and (3, 4)
d = √(9 + 16) = 5.
Example 2: (1, 2) and (4, 6)
d = √(9 + 16) = 5.
Frequently asked questions
Does the order of points matter?
No. The distance is the same because squaring removes the sign.
What if the points are on a horizontal line?
The vertical difference is zero, and the distance is the absolute horizontal difference.
Does the formula work in three dimensions?
Yes, with the square of the z difference added.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.