Distance Formula Calculator
Find the straight-line distance between two points on a coordinate plane or in 3D space. The answer is given as a decimal and, when the coordinates are whole numbers, in simplest radical form such as 2√13.
- Exact form
- 5
- Δx
- 3
- Δy
- 4
- Δz
- —
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Formula
How to use it
- Choose 2D or 3D.
- Enter the coordinates of both points.
- Read the distance. The Δ values show how far apart the points are along each axis.
Worked examples
From (1, 2) to (4, 6): √(3² + 4²)
- Distance
- 5
- Exact form
- 5
- Δx
- 3
- Δy
- 4
From (−2, 3) to (4, −1): √(36 + 16) = √52
- Distance
- 7.2111
- Exact form
- 2√13
- Δx
- 6
- Δy
- -4
In 3D from (1, 2, 3) to (4, 6, 15): √(9 + 16 + 144)
- Distance
- 13
- Exact form
- 13
- Δz
- 12
It is the Pythagorean theorem
The horizontal and vertical gaps between the points are the legs of a right triangle, and the distance is its hypotenuse. From (1, 2) to (4, 6) the gaps are 3 and 4, so the distance is 5.
Reading the exact form
When the sum under the square root is not a perfect square, the exact answer is left as a radical with any square factors pulled out: √52 = √(4 × 13) = 2√13 ≈ 7.2111.
Questions people ask
What is the distance between (1, 2) and (4, 6)?
√(3² + 4²) = √25 = 5.
Does the order of the points matter?
No. The differences are squared, so any negative sign disappears.
What is the distance from (1, 2, 3) to (4, 6, 15)?
√(3² + 4² + 12²) = √169 = 13.