Distance Calculator

The 2D distance formula is exactly the Pythagorean theorem: the difference in X (Δx) and difference in Y (Δy) form the legs of a right triangle. The distance between the points is the hypotenuse: d² = Δx² + Δy², so d = √(Δx² + Δy²). If you square the distance, you get the sum of the squared coordinate differences — this is the Pythagorean relationship in analytic geometry form.

Yes! 1D distance is simply the absolute difference between two numbers on a number line: d = |x₂ − x₁|. This is useful for finding the distance along a single axis, like temperature differences, time intervals, or positions on a line. The absolute value ensures distance is always non-negative, which matches our intuitive notion that distance cannot be negative.

The midpoint is the point exactly halfway between the two input points. It is calculated by averaging each coordinate: ((x₁+x₂)/2, (y₁+y₂)/2) in 2D, with the same averaging applied to the Z coordinate in 3D. The midpoint is useful for finding center points of line segments, bisectors in geometry, and symmetry axes in design and graphics.

The pattern is simple: for n-dimensional space, add the squared difference of each coordinate under the square root. In 4D: d = √((Δx)²+(Δy)²+(Δz)²+(Δw)²). This extension is used in data science for computing Euclidean distance between data points with many features, and in physics for spacetime intervals in special relativity (though with a sign difference for the time dimension).

Euclidean distance is the straight-line "as the crow flies" distance (the diagonal through space). Manhattan distance (also called L1 distance or taxicab distance) is the sum of the absolute differences along each axis: d = |Δx| + |Δy|. Manhattan distance represents the distance you would travel if you could only move along grid lines, like a taxicab navigating city blocks.