Distance Between Two Points
d = √((x₂−x₁)² + (y₂−y₁)²). Pythagorean distance in the plane.
Result
Distance
10.000000
From (1,2) to (7,10).
- Point 1(1, 2)
- Point 2(7, 10)
- Δx6
- Δy8
- Distance10.00000000
- Manhattan|Δx| + |Δy|14.0000
Step-by-step
- Δx = 7 − 1 = 6.
- Δy = 10 − 2 = 8.
- d = √(Δx² + Δy²) = √(36 + 64) = √100 = 10.0000.
How to use this calculator
- Enter two points' coordinates.
- Read distance.
About this calculator
The distance formula is the Pythagorean theorem applied to the legs Δx and Δy: d = √(Δx² + Δy²). Foundational for coordinate geometry, GPS, computer graphics, machine learning (Euclidean distance). Manhattan distance |Δx| + |Δy| is an alternative — what a taxi drives on a city grid. Generalizes to 3D: d = √(Δx² + Δy² + Δz²).
Frequently asked
Pythagorean theorem on right triangle with legs Δx and Δy. The hypotenuse is the straight line between points.
Related calculators
Midpoint Calculator
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). The point exactly between two points.
Slope Calculator
m = (y₂−y₁) / (x₂−x₁). Returns slope-intercept form y = mx + b.
Pythagorean Theorem Calculator
a² + b² = c². Solve for hypotenuse or missing leg of a right triangle.
Triangle Perimeter Calculator
P = a + b + c. Sum of all three sides.
Cube Volume Calculator
V = s³. Six equal square faces.
Square Root Calculator (√n)
√n with integer-perfect-square check, simplified surd form, and decimal expansion.