Distance Formula Calculator — Points on a Plane
Quick answer: Enter (x₁, y₁) and (x₂, y₂) to calculate distance, midpoint, and deltas.
Calculate the exact distance between any two points on a coordinate plane using the distance formula: d = √((x₂−x₁)² + (y₂−y₁)²). Also returns the midpoint, horizontal distance (Δx), and vertical distance (Δy).
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Last reviewed: April 2026Report an error
Formula: d = √((x₂−x₁)² + (y₂−y₁)²)
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Distance
5
Distance = √(3² + 4²) = √(25) = 5. Midpoint: (2.5, 4).
Distance
5
Midpoint
(2.5, 4)
Δx, Δy
3, 4
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How to Use This Distance Formula Calculator
- 1Enter the x and y coordinates of the first point.
- 2Enter the x and y coordinates of the second point.
- 3Read the distance, midpoint, Δx, and Δy.
Frequently Asked Questions
- d = √((x₂−x₁)² + (y₂−y₁)²). It's derived from the Pythagorean theorem: the distance is the hypotenuse of a right triangle with legs Δx and Δy.
- d = √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5. The distance is exactly 5 units.
- Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). It's the average of the x-coordinates and the average of the y-coordinates.
- Midpoint = ((0+6)/2, (0+8)/2) = (3, 4). Distance = √(6² + 8²) = √100 = 10.
- Yes. The horizontal change Δx is one leg, the vertical change Δy is the other leg, and the distance is the hypotenuse. They are mathematically identical.
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