Midpoint Calculator
The midpoint of a line segment between two (x, y) points.
Input sheet
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The midpoint is the exact center of a line segment — the point that sits an equal distance from both endpoints. It comes up constantly in geometry, computer graphics, mapping, and any time you need to split a span evenly.
How it works
Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) — the average of the two endpoints' coordinates.
Finding a midpoint is just averaging. You average the two x-coordinates to get the midpoint's x, and average the two y-coordinates to get its y. Because each axis is handled independently, the formula extends cleanly to three dimensions (average the z-values too) or to any higher dimension.
The order of the points never matters: averaging x₁ and x₂ gives the same result as averaging x₂ and x₁. Negative coordinates work exactly the same way — the average simply lands wherever the true center is, above or below zero.
Midpoint = ( (x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2 ) — average the two x-values for the midpoint's x, and average the two y-values for its y.
Worked examples
Midpoint of (2, 3) and (8, 11). → (5, 7)
x = (2 + 8) ÷ 2 = 5, and y = (3 + 11) ÷ 2 = 7.
Midpoint of (−4, 2) and (6, −8), where coordinates can be negative. → (1, −3)
x = (−4 + 6) ÷ 2 = 1, and y = (2 + −8) ÷ 2 = −3.
Tips & gotchas
- Sketch the two points before trusting a number — the midpoint should visually fall halfway between them, which catches sign or transposition slips fast.
- To find one endpoint when you know the midpoint and the other endpoint, reverse the formula: x₂ = 2 × midpoint x − x₁ (same for y).
- For a 3D segment, add a z-coordinate and average it the same way; the 2D formula generalizes directly.
- Don't confuse the midpoint with the centroid of a shape — the midpoint applies to a single segment between two points, not to a triangle or polygon.
FAQ
Is the midpoint always between the two points?
Yes. Because it's the average of the coordinates, it always lands on the segment itself, exactly halfway from each end.
Does it matter which point I enter first?
No. Averaging is order-independent, so swapping point 1 and point 2 produces the identical midpoint.
Can I use the midpoint to find a missing endpoint?
Yes. If you know the midpoint and one endpoint, double the midpoint coordinate and subtract the known endpoint to recover the other one.
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