Distance Calculator
2D & 3D Coordinate Tool
Enter two points on a flat plane to find the distance and midpoint between them.
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Enter two points in three-dimensional space to find the distance between them.
Point 1 (x₁, y₁, z₁)
Point 2 (x₂, y₂, z₂)
Understanding the Distance Formula
How far apart are two points? The distance formula answers that question for any two points on a plane or in space, using nothing more than the Pythagorean theorem.
Built directly from the Pythagorean theorem, the distance formula treats the horizontal and vertical gaps between two points as the legs of a right triangle, and the straight-line distance as the hypotenuse.
In 2D, points are located with just x and y. In 3D, a third coordinate, z, locates a point in space — the same Pythagorean idea just gains one more term under the square root.
The Formulas
2D Distance
3D Distance
2D Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)
Reading the Result
The calculated distance is always a non-negative number, since it comes from a square root of a sum of squared differences — it can never be negative, and it's zero only when both points are identical. In 2D mode, the midpoint is also shown: it's the single point exactly halfway along the straight line connecting Point 1 and Point 2, found by averaging the x-coordinates and averaging the y-coordinates separately.
Two coordinates, x and y, plus a midpoint.
Three coordinates, x, y, and z.
Distance is never negative — zero only means the points coincide.
Key Takeaways
- The distance formula is the Pythagorean theorem applied to the coordinate gaps between two points.
- 3D mode simply adds a z-axis term under the same square root used for 2D.
- The midpoint averages each coordinate and marks the exact center of the segment between two 2D points.
- Need slope or a line equation too? Use the Slope Calculator for the same two points.
Frequently Asked Questions
- Pick the 2D tab for two points on a flat plane, or the 3D tab for two points in three-dimensional space.
- Enter the coordinates of Point 1 and Point 2.
- Click "Calculate" to see the distance between the points (and, in 2D mode, their midpoint).
The distance formula is just the Pythagorean theorem applied to a coordinate plane. The horizontal and vertical gaps between two points, (x₂ − x₁) and (y₂ − y₁), form the two legs of a right triangle, and the straight-line distance between the points is the hypotenuse: d = √((x₂−x₁)² + (y₂−y₁)²). Extending to three dimensions simply adds a third leg for the z-axis gap under the same square root.
2D mode finds the distance between two points on a flat plane using only x and y coordinates — useful for maps, graphs, and geometry problems. 3D mode adds a z coordinate for points in three-dimensional space, such as positions in a 3D model, a physical room, or a scientific coordinate system.
The midpoint is the single point exactly halfway between two points — the average of their x-coordinates and the average of their y-coordinates: ((x₁+x₂)/2, (y₁+y₂)/2). It marks the center of the line segment connecting the two points, and this calculator shows it for 2D coordinates.
The distance formula shows up anywhere straight-line separation matters: measuring the length of a segment on a map or blueprint, finding how far apart two GPS-style coordinates are on a flat local grid, computing distances between objects in a video game or 3D simulation, and as a building block in physics for displacement calculations.
No. Distance is always zero or positive because it comes from a square root of a sum of squares, and both squaring and the principal square root always produce non-negative results. A distance of 0 simply means the two points are identical.