Midpoint Calculator
Find the midpoint between two coordinate points and the straight-line distance between them.
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How to use this calculator
The midpoint is the average of each coordinate pair. The distance formula is an application of the Pythagorean theorem to the horizontal and vertical separations.
- 1
Enter the x and y coordinates of your first point (x₁, y₁).
- 2
Enter the x and y coordinates of your second point (x₂, y₂).
- 3
The midpoint coordinates and the distance between the points are calculated instantly.
Frequently asked questions
Does the order of the two points matter?
Not for the midpoint, distance or slope. Swapping the points changes the sign of Δx and Δy, but their ratio, and therefore the slope, is the same, and the squares in the distance formula remove the sign. Only the printed run and rise flip sign.
How do I find a missing endpoint?
Double the midpoint and subtract the known endpoint. If a segment has midpoint (1, 1) and one end at (−3, 4), the other end is (2·1 − (−3), 2·1 − 4) = (5, −2). Entering (−3, 4) and (5, −2) returns the midpoint (1, 1) as a check.
What does the slope row say for a vertical line?
When both x-values match and the y-values differ, it prints “Undefined (vertical)” because the run is 0. For (1, 1) and (1, 9) the midpoint is (1, 5) and the distance is 8. When the two points are identical, it prints “Undefined (identical points)”: the distance is 0 and no line is determined.
Is the distance a straight line or a road distance?
It is the straight-line Euclidean distance in the plane, √(Δx² + Δy²). It is not the distance along a grid of streets, which would be |Δx| + |Δy|, and it is not corrected for the curve of the Earth, so latitude and longitude values would give meaningless results.
Can I enter negative or decimal coordinates?
Yes. Any real numbers are accepted. (−3, 4) and (5, −2) produce a midpoint of (1, 1), a distance of 10 and a slope of −0.75. Results are rounded to six decimals with trailing zeros removed.
Does it work in three dimensions?
No, it takes only x and y. For a third coordinate you would average the z-values as well and add Δz² under the square root; that step has to be done by hand.
Which units does it use?
The coordinates are unit-free, and the distance comes out in whatever unit the coordinates represent. If x and y are both in metres, the distance is in metres. Mixing units, such as x in feet and y in metres, makes the distance meaningless.
How do I use the output to build a perpendicular bisector?
The bisector passes through the midpoint with slope equal to the negative reciprocal of the slope shown. For (−3, 4) and (5, −2), the slope is −0.75, so the bisector has slope 4/3 and passes through (1, 1). If the slope is 0 the bisector is vertical, and if it is undefined the bisector is horizontal.
Midpoint, distance and slope between two points
Three results from one pair of points
The midpoint is the average of the two x-values and the average of the two y-values. The distance is the hypotenuse of the right triangle whose legs are Δx and Δy. The slope is Δy ÷ Δx. All three are derived from the same two differences, which is why the output also lists run (Δx) and rise (Δy) so you can retrace the arithmetic.
| Points | Midpoint | Distance | Slope |
|---|---|---|---|
| (2, 3) and (8, 7) | (5, 5) | 7.211103 | 0.666667 |
| (−3, 4) and (5, −2) | (1, 1) | 10 | −0.75 |
| (0, 0) and (3, 4) | (1.5, 2) | 5 | 1.333333 |
| (1, 1) and (1, 9) | (1, 5) | 8 | Undefined (vertical) |
Worked example: (2, 3) to (8, 7)
The default pair has Δx = 6 and Δy = 4. The midpoint is ((2 + 8) ÷ 2, (3 + 7) ÷ 2) = (5, 5). The distance is the square root of 36 + 16, which is the square root of 52, shown as 7.211103. The slope is 4 ÷ 6, shown as 0.666667 after rounding. Because the distance is not a whole number, it is the kind of answer you would leave as √52 in a classroom, or round for a drawing.
Worked example: a segment that is easy to check
Points (−3, 4) and (5, −2) have a run of 8 and a rise of −6. The legs 8 and 6 form a 3-4-5 triangle scaled by 2, so the distance is exactly 10. The midpoint is (1, 1), and the slope is −0.75. Since the slope is negative, the segment falls from left to right. Round-number results like this make the quickest sanity check when you are writing your own distance code.
Checking diagonals in a quadrilateral
In coordinate geometry the midpoint formula proves that a four-sided figure is a parallelogram: if its diagonals share the same midpoint, they bisect each other. Run the calculator once for each diagonal and compare the two midpoints. If you also want to test for a rhombus, compare the diagonal slopes: perpendicular lines have slopes whose product is −1.
Edge cases and rounding
Identical points give a midpoint equal to the point, a distance of 0 and an undefined slope. Vertical segments have no slope, but their midpoint and distance are still valid. Displayed numbers are rounded to six decimals, so a repeating value such as 0.666667 is an approximation of 2/3; use the exact fraction in any proof you are writing.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →