This midpoint calculator finds the exact middle point between two coordinates — plus the distance between them. Enter the two points and get the midpoint, distance and the slope connecting them.
What Is a Midpoint?
The midpoint is the point exactly halfway between two other points — the average of their coordinates. It bisects the segment joining them: the distance from each endpoint to the midpoint is identical. Midpoints appear everywhere from geometry proofs (medians of triangles meet at the centroid, built from midpoints) to real navigation (the midway point of a trip). This calculator is part of our Math Calculators collection.
The Midpoint Formula
Midpoint = ( (x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2 ) — just average the x’s and average the y’s.
Worked example (verified): between (2, 3) and (5, 11): midpoint = ( (2+5)/2, (3+11)/2 ) = (3.5, 7). The distance between the points is 8.544 (so each half is 4.272), and their connecting slope is 2.667 — the same point pair the Slope Calculator uses, so the two tools agree, as they should.
Finding a Missing Endpoint
If you know one endpoint and the midpoint, the other endpoint is: (2×midpoint − known endpoint), coordinate by coordinate. Example: endpoint (2, 3), midpoint (3.5, 7) → other endpoint = (2×3.5 − 2, 2×7 − 3) = (5, 11). This “double the midpoint, subtract the known point” trick solves a whole family of textbook problems instantly.
Where Midpoints Matter
- Triangles: the segment joining two midpoints is parallel to the third side and half its length (midpoint theorem).
- Circles: the midpoint of a diameter is the circle’s center.
- Maps and trips: “meet me halfway” is a midpoint calculation with real distances.
- Data: the midpoint of a class interval represents the whole class in grouped statistics — a cousin of the ideas in our statistics collection.
The distance figure comes straight from Pythagoras — see the Pythagorean Theorem Calculator for the underlying right triangle.
Related Tools
- Slope Calculator — slope, distance, line equation
- Pythagorean Theorem Calculator
- Math Calculators — the full collection
Frequently Asked Questions
How do I find the midpoint between two points?
Add the x-coordinates and halve; add the y-coordinates and halve. Between (2, 3) and (5, 11) that is (3.5, 7).
Can a midpoint have fractions or decimals?
Absolutely — most do. (3.5, 7) is a perfectly ordinary midpoint.
What is the midpoint of a line segment in 3D?
Average all three coordinates: ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). The same averaging idea extends to any dimension.
How is the midpoint different from the average?
It is the average — applied coordinate by coordinate to two points. For lists of numbers instead of points, use an average/statistics calculator.
What if the two points are the same?
The midpoint is that point itself, and the distance is zero.
Is this midpoint calculator free?
Yes — free, instant, no sign-up.