The distance between two points is d = √((x₂ − x₁)² + (y₂ − y₁)²). For (1, 2) and (4, 6), the changes are 3 and 4, so d = √(9 + 16) = √25 = 5 units. In three dimensions, add (z₂ − z₁)² under the root before taking the square root.
Students checking coordinate geometry homework, programmers measuring gaps between sprites, and surveyors sanity-checking grid coordinates all need the same number: the straight-line length between two points. Enter the coordinates of both points in a flat plane or in 3D space and the calculator returns the Euclidean distance to four decimals, the change along each axis, the squared distance, the midpoint and, in 2D, the slope of the segment joining them. Every working line is listed, so the arithmetic can be copied straight into a solution. One limit: this is flat (Euclidean) geometry. Two latitude and longitude pairs on the globe need a great-circle formula such as haversine, not this one.
Pick 2D for points on a plane or 3D to reveal the z coordinate for each point.
Type the x and y (and z) coordinates of the first point. Negative values and decimals are accepted.
Type the coordinates of the second point. The order of the points does not change the distance.
The distance updates as you type, with Δx, Δy, the midpoint, the slope and each step of the calculation.
Result Distance between the points: 6.4031
Horizontal change Δx: 5
Vertical change Δy: 4
Distance squared: 41
Midpoint: (-0.5, 1)
Slope of the segment: 0.8
Δx = 5 and Δy = 4, so the distance is √(25 + 16) = √41, a little over 6.4 units.
Result Distance between the points: 5
Horizontal change Δx: 3
Vertical change Δy: 4
Distance squared: 25
Midpoint: (2.5, 4)
Slope of the segment: 1.333333
The legs are 3 and 4, the classic 3-4-5 triangle, so the points sit exactly 5 units apart.
Result Distance between the points: 13
Horizontal change Δx: 3
Vertical change Δy: 4
Distance squared: 169
Midpoint: (2.5, 4, 9)
Slope of the segment: n/a in 3D
Adding the z-axis gives √(9 + 16 + 144) = √169 = 13 units.
d = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²)
dx₁, y₁, z₁x₂, y₂, z₂The segment between two points is the hypotenuse of a right triangle whose legs are the changes along each axis, so the Pythagorean theorem gives its length. Squaring each difference removes the sign, which is why reversing the order of the points gives the same answer. In 3D the theorem is applied twice, adding the z difference under the same root. The midpoint averages each coordinate, and the 2D slope is Δy divided by Δx.
It is the Pythagorean theorem written in coordinates. Draw a horizontal leg of length |x₂ − x₁| and a vertical leg of length |y₂ − y₁|; the segment between the points is the hypotenuse, so its length is the square root of the sum of the squared legs.
No. Each difference is squared, so (4 − 1)² and (1 − 4)² are both 9. The distance and the midpoint are the same either way; only the signs of Δx and Δy flip.
It adds a third squared term, (z₂ − z₁)², inside the square root. For (1, 2, 3) and (4, 6, 15) that is √(9 + 16 + 144) = √169 = 13 units.
The sum of squares is usually not a perfect square. For (−3, −1) and (2, 3) it is 41, so the exact distance is √41, which the calculator shows as 6.4031. The squared distance stat gives the exact value under the root.
The same units as the coordinates. If x and y are in metres, the distance is in metres; on an unlabelled graph it is simply units. Both points must use the same scale on every axis.
When both points share the same x value the segment is vertical, and the slope Δy ÷ Δx would divide by zero. The distance is then just the absolute difference in y.
Only over very short spans after converting to a flat projection in metres. Raw latitude and longitude degrees are not equal lengths, and the Earth curves, so use a haversine or great-circle calculation instead.
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Tools Directory Editorial Team. (2026, October 26). Distance Formula Calculator. Tools Directory. Retrieved October 26, 2026, from https://tools.milunir.com/math/algebra-tools/distance-formula-calculator/
Tools Directory Editorial Team. “Distance Formula Calculator.” Tools Directory, 26 Oct. 2026, https://tools.milunir.com/math/algebra-tools/distance-formula-calculator/. Accessed 26 Oct. 2026.
Tools Directory Editorial Team. “Distance Formula Calculator.” Tools Directory. Last modified October 26, 2026. Accessed October 26, 2026. https://tools.milunir.com/math/algebra-tools/distance-formula-calculator/.
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