Midpoint Calculator
Enter two points' x and y coordinates — decimals and negatives included — to get their midpoint to 3 decimals, plus the segment length, slope, and both quarter points.
Example: with Point 1 — x₁ 2 · Point 1 — y₁ 4 · Point 2 — x₂ 8 · Point 2 — y₂ 10 → Midpoint (x, y): (5, 7).
- Segment length8.485 units
- Slope of the segment1
- Quarter points (25% and 75%)(3.5, 5.5) and (6.5, 8.5)
Computed by the calculator below using its default values. Change any input to see your own numbers.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2) — average the x's, average the y's.
Average the coordinates
The midpoint of a segment is the plain average of its endpoints: M = ((x₁ + x₂)/2, (y₁ + y₂)/2). No square roots, no slopes — just add each pair of coordinates and halve. For (2, 4) and (8, 10): x = (2 + 8)/2 = 5 and y = (4 + 10)/2 = 7, so M = (5, 7). The formula works in every quadrant; negatives simply ride along through the addition.
Because averaging is symmetric, the order of the two points never matters — a useful sanity check when a homework answer key seems to disagree with you.
Length, slope, and the quarter points
The same Δx and Δy that build the midpoint also give the segment's length √(Δx² + Δy²) and slope Δy/Δx, so this page reports both. It also shows the quarter points — the spots 25% and 75% of the way along, computed as weighted averages (3P₁ + P₂)/4 and (P₁ + 3P₂)/4. Halve the halves and you can subdivide a segment as finely as a problem demands.
How it’s calculated
M = ((x₁ + x₂)/2, (y₁ + y₂)/2). Segment length = √(Δx² + Δy²); slope = Δy/Δx, reported as undefined when Δx = 0. Quarter points weight the ends 3:1 — ((3x₁ + x₂)/4, (3y₁ + y₂)/4) and ((x₁ + 3x₂)/4, (y₁ + 3y₂)/4). Displayed to 3 decimals.
Straight-line midpoint on a flat plane; latitude/longitude pairs need great-circle math instead.
Worked examples
| Point 1 | Point 2 | Midpoint |
|---|---|---|
| (0, 0) | (10, 6) | (5, 3) |
| (2, 4) | (8, 10) | (5, 7) |
| (-3, 5) | (7, -1) | (2, 2) |
| (1.5, 2) | (4.5, 9) | (3, 5.5) |
Computed with M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
Common mistakes
- Subtracting the coordinates instead of adding — subtraction belongs to distance and slope, not the midpoint.
- Averaging only the x-coordinates and carrying one endpoint's y unchanged.
- Sign slips with negatives: (−3 + 7)/2 is 2, not 5.
- Using the midpoint formula for an uneven split — 25/75 points need weighted averages, shown in the quarter-points row.
Frequently asked questions
What is the midpoint formula?
M = ((x₁ + x₂)/2, (y₁ + y₂)/2): average the two x-coordinates, average the two y-coordinates. The result is the point exactly halfway along the segment.
Does it matter which point I call Point 1?
No. Averages are symmetric, so swapping the points gives the identical midpoint. (Slope is also unchanged, since both Δx and Δy flip sign.)
How is the midpoint formula different from the distance formula?
They answer different questions from the same inputs: the midpoint formula averages coordinates to locate the halfway point, while the distance formula √(Δx² + Δy²) measures how long the segment is.
How do I find a point 25% of the way along a segment?
Weight the near end 3-to-1: ((3x₁ + x₂)/4, (3y₁ + y₂)/4). This page prints that and the 75% twin automatically as the quarter points.