Calculate the Euclidean distance between two points in 2D or 3D space, with midpoint and step-by-step work.
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Dimensions
Point 1
Point 2
Euclidean Distance
Step-by-step
d = √(9 + 16) = √(25) = 5
Midpoint = (2.5, 4)
Also in Functions
Algebra
A distance formula calculator computes the Euclidean distance between two points in 2D or 3D space. It also finds the midpoint and shows step-by-step work using the Pythagorean-based distance formula.
The distance between two points (x₁, y₁) and (x₂, y₂) in 2D is d = √((x₂ − x₁)² + (y₂ − y₁)²). This extends to 3D by adding a z-component: d = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²).
The midpoint between the two points is found by averaging each coordinate: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Euclidean distance in 2D.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint formula.
Frequently asked questions
Yes — the distance formula is a direct application of the Pythagorean theorem. The horizontal and vertical differences form the legs of a right triangle, and the distance is the hypotenuse.
No. Distance is always non-negative because it involves squaring the differences and taking a square root. A distance of zero means the two points are the same.
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