Distance Formula Calculator
Calculate the straight-line distance between two points in a coordinate plane.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Distance Formula Calculator
Enter two coordinate points and the distance appears instantly. The breakdown shows all intermediate values.
- Enter Point 1. Type the x and y coordinates of the first point.
- Enter Point 2. Type the x and y coordinates of the second point.
- Read the result. The Euclidean distance is shown along with the horizontal distance (dx), vertical distance (dy), and distance squared.
About the Distance Formula
The distance formula d = sqrt((x2-x1)^2 + (y2-y1)^2) calculates the straight-line (Euclidean) distance between two points in a plane. It is derived from the Pythagorean theorem: the distance is the hypotenuse of a right triangle formed by the horizontal and vertical differences.
This formula is used in geometry, physics, navigation, computer graphics, and machine learning. It generalizes to higher dimensions by adding more squared terms under the square root.
Frequently Asked Questions
What is the distance formula?
The distance formula is d = sqrt((x2-x1)^2 + (y2-y1)^2). It calculates the straight-line distance between two points on a coordinate plane, derived from the Pythagorean theorem.
Can the distance be negative?
No. Distance is always zero or positive. The formula squares the differences before summing, then takes the square root, guaranteeing a non-negative result.
How is the distance formula related to the Pythagorean theorem?
The distance formula is the Pythagorean theorem applied to coordinate geometry. The horizontal difference (dx) and vertical difference (dy) form the legs of a right triangle, and the distance is the hypotenuse.