Distance Formula Calculator
Find the straight-line distance between two points in the coordinate plane — uses the Pythagorean-derived distance formula.
What is Distance Formula Calculator?
The distance formula calculator finds the straight-line distance between any two points (x₁, y₁) and (x₂, y₂) in the coordinate plane. The formula is the Pythagorean theorem applied to the horizontal and vertical legs of the imaginary right triangle between the two points.
Formula
Distance formula:
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
It is just √(Δx² + Δy²) — the hypotenuse of the right triangle whose legs are the horizontal and vertical separations.
Worked example
Points (1, 2) and (4, 6):
- Δx = 4 − 1 = 3
- Δy = 6 − 2 = 4
- d = √(9 + 16) = √25 = 5
Classic 3-4-5 triangle in disguise.
How to use this calculator
- Enter the coordinates of two points.
- The calculator returns the straight-line distance plus the horizontal and vertical components (Δx and Δy).
Frequently asked questions
Is the order of points important?
No. (x₂ − x₁)² is the same as (x₁ − x₂)² because squaring eliminates the sign. The distance is always positive.
Can I use this for 3D distance?
This calculator handles 2D. For 3D add a Δz term: d = √(Δx² + Δy² + Δz²).
Is "distance" the same as "displacement"?
In straight-line terms, yes for two specific points. In motion problems, distance is the total path length while displacement is the straight-line endpoint difference — they differ only along curved paths.
What if the two points are the same?
The distance is 0. The calculator handles this case correctly.