About the Midpoint Calculator
This midpoint calculator finds the point exactly halfway between two coordinates on a plane. Enter the endpoints (x₁, y₁) and (x₂, y₂) and it applies the midpoint formula, then also reports the length of the segment and its slope, which are usually the next things a geometry or algebra problem asks for.
It also works in reverse. If you know one endpoint and the midpoint, switch to “find the missing endpoint” and the calculator doubles the distance from the known end through the midpoint to locate the other end — a common textbook question and a handy check when reflecting a point through another.
Coordinates can be negative, decimal or fractional (enter fractions as decimals). Outside the classroom the same idea finds the centre of a wall between two studs, the halfway stop between two map grid references, or the centre of a bounding box.
How to use the midpoint calculator
- 1Choose whether you want the midpoint or a missing endpoint.
- 2Enter the coordinates of the known endpoint (x₁, y₁).
- 3Enter the second endpoint, or the midpoint if you are solving for the other end.
- 4Read the answer, plus the segment length and slope.
Formula and method
The midpoint is the average of the endpoints’ coordinates: add the two x-values and halve them, then do the same for the y-values. Because it is an average, the midpoint is always the same distance from both ends.
To find a missing endpoint, rearrange the same formula: the unknown end is twice the midpoint minus the known end. The segment length uses the distance formula √((x₂ − x₁)² + (y₂ − y₁)²), and the slope is (y₂ − y₁) ÷ (x₂ − x₁), which is undefined for a vertical segment.
- (x₁, y₁), (x₂, y₂)
- The two endpoints of the segment
- M = (Mx, My)
- The midpoint
Worked examples
Midpoint of (2, 3) and (8, 11)
Average the x-values: (2 + 8) ÷ 2 = 5. Average the y-values: (3 + 11) ÷ 2 = 7. The midpoint is (5, 7), and the segment is √(6² + 8²) = 10 units long.
Missing endpoint from (1, −2) and midpoint (4, 3)
The other end is twice the midpoint minus the known end: x = 2·4 − 1 = 7 and y = 2·3 − (−2) = 8. The full segment from (1, −2) to (7, 8) is about 11.66 units.
Decimals and negatives: (−3.5, 2) and (6, −4.5)
x = (−3.5 + 6) ÷ 2 = 1.25 and y = (2 − 4.5) ÷ 2 = −1.25. The segment falls 6.5 units over a run of 9.5, a slope of about −0.684.
Frequently asked questions
What is the midpoint formula?+
M = ((x₁ + x₂)/2, (y₁ + y₂)/2). You simply average the x-coordinates and average the y-coordinates of the two endpoints.
How do I find an endpoint if I know the midpoint?+
Double the midpoint and subtract the known endpoint: x₂ = 2·Mx − x₁ and y₂ = 2·My − y₁. For example, with endpoint (1, 2) and midpoint (3, 5), the other end is (5, 8).
Does the midpoint formula work in 3D?+
Yes. Average the z-coordinates too: M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2). This calculator handles the 2D case, so run the z-values separately.
Is the midpoint the same as the average?+
Yes — each coordinate of the midpoint is the arithmetic mean of the endpoints’ coordinates. That is why the midpoint is equidistant from both ends.
How do I find the perpendicular bisector?+
The perpendicular bisector passes through the midpoint with a slope equal to the negative reciprocal of the segment’s slope. Use the midpoint and that slope in the slope-intercept form calculator.