Midpoint Calculator
Find the exact midpoint between two points on a coordinate plane. Enter (x₁, y₁) and (x₂, y₂) to get the midpoint with each coordinate's step shown.
Enter the coordinates of two points to find the midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
Quick answer
The midpoint of two points (x₁, y₁) and (x₂, y₂) is M = ((x₁ + x₂)/2, (y₁ + y₂)/2). You average the two x-values to get the midpoint's x-coordinate and average the two y-values to get its y-coordinate. For example, the midpoint of (2, 3) and (8, 7) is (5, 5).
Formula & method
The midpoint of a line segment is the point exactly halfway between its two endpoints. To find it, average the x-coordinates and average the y-coordinates separately: take x₁ + x₂ and divide by 2 for the midpoint's x-coordinate, then take y₁ + y₂ and divide by 2 for the midpoint's y-coordinate. The result M = ((x₁ + x₂)/2, (y₁ + y₂)/2) is always equidistant from both endpoints and lies directly on the segment connecting them. This calculator accepts negative and decimal coordinates and shows the arithmetic for each coordinate so you can follow the work.
Examples
- Input
- (2, 3) and (8, 7)
- Result
- Midpoint = (5, 5)
- Why
- x = (2 + 8)/2 = 10/2 = 5 and y = (3 + 7)/2 = 10/2 = 5, so the midpoint is (5, 5).
- Input
- (-4, 1) and (2, -5)
- Result
- Midpoint = (-1, -2)
- Why
- x = (-4 + 2)/2 = -2/2 = -1 and y = (1 + (-5))/2 = -4/2 = -2, giving the midpoint (-1, -2).
- Input
- (0, 0) and (10, 4)
- Result
- Midpoint = (5, 2)
- Why
- x = (0 + 10)/2 = 5 and y = (0 + 4)/2 = 2, so the midpoint is (5, 2) — half of each coordinate of the second point.
- Input
- (1.5, 2.5) and (4.5, 7.5)
- Result
- Midpoint = (3, 5)
- Why
- x = (1.5 + 4.5)/2 = 6/2 = 3 and y = (2.5 + 7.5)/2 = 10/2 = 5, so the midpoint is (3, 5).
- Input
- (-3, 8) and (9, -2)
- Result
- Midpoint = (3, 3)
- Why
- x = (-3 + 9)/2 = 6/2 = 3 and y = (8 + (-2))/2 = 6/2 = 3, giving the midpoint (3, 3).
When to use this tool
- Finding the center point of a line segment in geometry, drafting, or coordinate proofs.
- Locating the center of a circle when you know the two endpoints of a diameter.
- Splitting a distance evenly on a map, chart, or design grid to place a marker exactly halfway.
- Checking homework or test answers for midpoint-formula problems with step-by-step work.
- Computing the centroid step of a midsegment, perpendicular bisector, or median in a triangle.
Common mistakes
- Subtracting the coordinates instead of adding them. The midpoint formula adds the two x-values (and the two y-values) before dividing by 2 — subtracting gives the distance components, not the midpoint.
- Forgetting to divide by 2. Adding x₁ + x₂ alone gives twice the midpoint's x-coordinate; you must divide each sum by 2.
- Mishandling negative coordinates. Remember that adding a negative is subtraction: (1 + (-5)) = -4, not 6. Keep the signs when summing.
- Mixing up the axes — pairing an x-value with a y-value. Always average the two x's together and the two y's together separately.
- Confusing the midpoint with the slope or distance. Those use subtraction (x₂ − x₁); the midpoint uses addition and an average.
Frequently asked questions
What is the midpoint formula?
The midpoint formula is M = ((x₁ + x₂)/2, (y₁ + y₂)/2). You average the x-coordinates of the two endpoints and average their y-coordinates to get the point exactly halfway between them.
How do I find the midpoint of two points by hand?
Add the two x-coordinates and divide the sum by 2 to get the midpoint's x-value. Then add the two y-coordinates and divide by 2 for the midpoint's y-value. Write the answer as an ordered pair (x, y).
Does the midpoint calculator work with negative numbers?
Yes. Just enter negative coordinates as-is, for example -4. The formula adds the values keeping their signs, so the midpoint of (-4, 1) and (2, -5) is (-1, -2).
Can I use decimals or fractions?
Decimals work directly — for example (1.5, 2.5) and (4.5, 7.5) give a midpoint of (3, 5). For fractions, convert them to decimals first (½ = 0.5) before entering them.
What is the difference between the midpoint and the distance between two points?
The midpoint is the point halfway between two endpoints and uses addition: ((x₁ + x₂)/2, (y₁ + y₂)/2). The distance is how far apart they are and uses subtraction inside a square root: √((x₂ − x₁)² + (y₂ − y₁)²).
How do I find an endpoint if I know the midpoint and one endpoint?
Rearrange the formula: if M is the midpoint and A is the known endpoint, the other endpoint B = (2·Mₓ − Aₓ, 2·M_y − A_y). Double the midpoint's coordinates and subtract the known endpoint's coordinates.
Is the midpoint always on the line segment?
Yes. The midpoint always lies exactly on the segment joining the two endpoints and is equidistant from both, dividing the segment into two equal halves.
Sources & references
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