Distance Formula

📖 What is the Distance Formula?

The distance formula calculates the straight-line distance between two points on a coordinate plane. It is derived directly from the Pythagorean theorem — the horizontal and vertical gaps between the points form the two legs of a right triangle.

d = √((x₂-x₁)² + (y₂-y₁)²)

🔤 What Each Variable Means

d

DistanceThe straight-line length between the two points

x₁, y₁

First point coordinatesThe x and y values of the starting point

x₂, y₂

Second point coordinatesThe x and y values of the ending point

📝 Step-by-Step Example

Find the distance between points (1, 2) and (4, 6).

1

Label the coordinatesx₁=1, y₁=2, x₂=4, y₂=6

2

Calculate the differences(x₂-x₁) = 3 (y₂-y₁) = 4

3

Square each difference3² = 9 4² = 16

4

Add and take the square rootd = √(9 + 16) = √25

✓

Answer: d = 5 units

The distance between the two points is exactly 5 units.

🧮 Interactive Calculator

x₁ (first point x)

y₁ (first point y)

x₂ (second point x)

y₂ (second point y)

Result will appear here

📖 What is the Distance Formula?

🔤 What Each Variable Means

📝 Step-by-Step Example

🧮 Interactive Calculator

🔗 Related

🎯 Quick Fact