Midpoint calculator
Enter two points, get the point halfway between.
What is the midpoint formula?
Average the x-coordinates and the y-coordinates: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). The midpoint of (1, 2) and (7, 10) is (4, 6).
How do I find an endpoint from the midpoint?
Double the midpoint and subtract the known end: B = 2M − A. With A = (1, 2) and M = (4, 6), B = (7, 10).
What else does the calculator show?
The length of the segment — 10 in the example, from the distance formula — and its slope, 4/3.
Does it work with negative numbers and decimals?
Yes — any real coordinates.
What is the midpoint of a segment on a number line?
Just the average of the two numbers: halfway between −3 and 9 is 3.
How do I find the center of a circle from the ends of a diameter?
The center is the midpoint of the diameter. In OpenStax Algebra and Trigonometry 2e, Example 8, the endpoints (−1, −4) and (5, −4) give a center of (2, −4). The radius is half the length, 3. The circle equation calculator takes it from there.
How can I check a midpoint?
It must be the same distance from both ends, and each of those distances is half the length of the segment. For (7, −2) and (9, 5) the midpoint is (8, 1.5); it is 3.640 from the first point and 3.640 from the second, and the whole segment is 7.280 long.
The formula and what it assumes
The midpoint is the average of the two points, coordinate by coordinate: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) (OpenStax Algebra and Trigonometry 2e, section 2.1). Solving M = (A + B) ÷ 2 for the unknown end gives B = 2M − A, which is what the “other endpoint” mode computes. Both assume a straight segment on a flat grid with the same unit on both axes. Negative numbers and decimals work without any change.
Worked example: a segment from (7, −2) to (9, 5)
This is OpenStax Example 7. The x-coordinates average to (7 + 9) ÷ 2 = 8 and the y-coordinates to (−2 + 5) ÷ 2 = 3/2 = 1.5, so the midpoint is (8, 1.5). The segment has a length of √(2² + 7²) = √53 = 7.280 and a slope of 3.5. Run it backwards: with A = (7, −2) and the midpoint (8, 1.5), B = (2 × 8 − 7, 2 × 1.5 + 2) = (9, 5), the point you started with.
Common mistakes
The simplest slip is adding the coordinates and forgetting to halve: (16, 3) in place of (8, 1.5). Another is subtracting, which gives the run and rise (2 and 7) instead of the middle. In the “other endpoint” mode the second pair of boxes holds the midpoint, not the second end. And the average does not work for places on Earth: the point halfway along the shortest route between 35° N, 45° E and 35° N, 135° E is near 45° N, 90° E according to Chris Veness, not the 35° N, 90° E that averaging the numbers would give.
Sources: OpenStax, Algebra and Trigonometry 2e, section 2.1 “The Rectangular Coordinate Systems and Graphs” (midpoint formula, Examples 7 and 8); OpenStax, Intermediate Algebra 2e, section 11.1 (Example 11.4); Chris Veness, Movable Type Scripts, “Calculate distance, bearing and more between Latitude/Longitude points” (midpoint on a sphere). Related tools: distance formula calculator, line equation calculator, circle equation calculator and coordinate distance calculator. How we check our calculators.