Distance Calculator
Calculate the straight-line distance between two points on a 2D plane using the Pythagorean theorem. Enter the x and y coordinates of both points to get the exact distance.
Calculator Inputs
The x-coordinate of the first point. Can be negative.
The y-coordinate of the first point. Can be negative.
The x-coordinate of the second point. Can be negative.
The y-coordinate of the second point. Can be negative.
- Distance
- 5.00
About these results
CalcSpectrum calculators produce automated estimates using established formulas and the specific values you enter. Because real-world outcomes depend on input accuracy, mathematical assumptions, and rounding conventions, please verify critical figures with an appropriately qualified financial, tax, medical, legal, or other professional, as relevant.
How It's Calculated
Formula
The distance between two points on a 2D plane is a direct application of the Pythagorean theorem. Picture the two points connected by a straight line, then draw a right triangle underneath it: one leg runs horizontally (the difference between the x-coordinates), the other runs vertically (the difference between the y-coordinates), and the straight-line distance is the triangle's hypotenuse. That means distance = sqrt((x2 - x1)^2 + (y2 - y1)^2) is exactly a^2 + b^2 = c^2 solved for c, with a = the horizontal difference and b = the vertical difference. Enter the coordinates of both points — any real numbers, positive or negative — and this calculator returns the straight-line distance between them.
Worked Examples
Classic 3-4-5 case: (0, 0) to (3, 4)
- Find the horizontal difference: x2 - x1 = 3 - 0 = 3
- Find the vertical difference: y2 - y1 = 4 - 0 = 4
- Apply the Pythagorean theorem: d = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25)
- d = 5
Negative coordinates: (-3, -4) to (0, 0)
- Find the horizontal difference: x2 - x1 = 0 - (-3) = 3
- Find the vertical difference: y2 - y1 = 0 - (-4) = 4
- Apply the Pythagorean theorem: d = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25)
- d = 5
Frequently Asked Questions
Does the order of the two points matter?
No. Swapping Point 1 and Point 2 flips the sign of each difference (x2 - x1 becomes x1 - x2), but both differences get squared in the formula, so the result is identical either way.
Can the coordinates be negative?
Yes. Coordinates can be any real number — positive, negative, zero, or fractional. There's no requirement that points sit in a particular quadrant; the formula works the same everywhere on the plane.
What if both points are the same?
The distance is 0. Both the horizontal and vertical differences are 0, so sqrt(0^2 + 0^2) = 0 — a valid result, not an error.
Does this work for points in 3D space or on a globe?
Not this calculator. This is a 2D Cartesian (flat-plane) distance calculator. Distance between points in 3D space, or between two locations on the Earth's curved surface (geodesic distance), requires a different formula and a different tool.
How is this related to the Pythagorean theorem?
Directly. The horizontal and vertical differences between the two points form the two legs of a right triangle, and the straight-line distance between the points is that triangle's hypotenuse — so this calculator's formula is simply a^2 + b^2 = c^2 solved for c.