Maths / Graphs
Midpoint Calculator (and Distance)
Find the point halfway between two points and the distance between them, with the formulas filled in and a plot.
Midpoint Calculator (and Distance): The midpoint averages the coordinates: between (1, 2) and (4, 8) it is ((1 + 4) ÷ 2, (2 + 8) ÷ 2) = (2.5, 5). The distance comes from Pythagoras: √((4 − 1)² + (8 − 2)²) = √45 ≈ 6.708. Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
The midpoint averages the coordinates: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). The distance between the points comes from Pythagoras: d = √((x₂ − x₁)² + (y₂ − y₁)²). Going the other way, if you know one end and the midpoint, the other end is 2M minus the known end.
Worked example
Between (−3, 4) and (5, −2): midpoint ((−3 + 5) ÷ 2, (4 − 2) ÷ 2) = (1, 1), distance √(8² + 6²) = 10.
For the line through the points, use the slope calculator.
On a map
On a flat grid the formulas are exact; between places on the Earth, the curved surface matters, so use a great-circle distance instead.
The distance calculator measures between real places, and the Pythagorean theorem calculator solves the triangle behind the distance formula.
How to use it
- Enter the coordinates of the two points.
- Read the midpoint and the distance, with the working.
- Check the plot.
Privacy & limitations
Everything is calculated in your browser.
Related tools
Frequently asked questions
How do I find an endpoint from the midpoint?
Double the midpoint and subtract the known end: with midpoint (2.5, 5) and end (1, 2), the other end is (5 − 1, 10 − 2) = (4, 8).
Does it work with negative coordinates?
Yes: the formulas are the same.
What about three dimensions?
Average the z-coordinates too, and add (z₂ − z₁)² under the square root for the distance.
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