Midpoint Calculator
Find the exact midpoint between two coordinate points, calculate the distance between them, or divide the segment in any ratio using the section formula.
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How It Works
Average the x-coordinates and the y-coordinates of the two endpoints. The result is the point exactly halfway between them.
M = ((x1+x2)/2, (y1+y2)/2)(2,4) and (8,10): M=(5,7)Compute distance from each endpoint to the midpoint. Both should equal half the total segment length: d(P1,M) = d(M,P2) = d(P1,P2)/2.
d(P1,M) = d(M,P2)(0,0)→(3,2)→(6,4): each = √13Dividing P1P2 in ratio m:n: x=(m·x2+n·x1)/(m+n). Midpoint is the special case m=n=1.
((m·x2+n·x1)/(m+n), (m·y2+n·y1)/(m+n))(0,0) to (6,9) in ratio 2:1 → (4,6)The midpoint is used to find perpendicular bisectors (lines perpendicular to a segment at its midpoint), circumcenters, and in coordinate proofs.
Perpendicular bisector passes through midpointMidpoint of hypotenuse = circumcenter of right triangleAdd the z-coordinates: M = ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2).
M = (avg_x, avg_y, avg_z)(0,0,0) and (4,6,8): M=(2,3,4)If midpoint M=(mx,my) and one endpoint P1=(x1,y1): x2=2·mx−x1, y2=2·my−y1.
P2 = 2M − P1M=(5,6), P1=(3,4): P2=(7,8)Quick Reference
Common examples — verify instantly above.
Center
(0,0) and (6,4)
(3,2)
Center
(1,3) and (5,7)
(3,5)
Center
(−2,4) and (6,−2)
(2,1)
Center
(0,0) and (10,10)
(5,5)
Distance
(0,0) to (3,4)
5
Distance
(1,1) to (4,5)
5
Section 2:1
(0,0) to (9,9)
(6,6)
Find endpoint
M=(5,5), P1=(3,3)
P2=(7,7)
Tips & Shortcuts
The midpoint formula is just averaging: add coordinates and divide by 2. Simple but powerful.
To find a missing endpoint: if you know the midpoint and one endpoint, double the midpoint coordinates and subtract the known endpoint.
The midpoint of a segment is always inside the segment — between the two endpoints, never outside.
For the section formula: m applies to the SECOND point, n to the FIRST. Ratio 2:1 means the point is 2/3 of the way from P1 to P2.
Centroid of a triangle: average all three x-values, average all three y-values. Extension of the midpoint concept.
The perpendicular bisector of any segment passes through its midpoint and is perpendicular to it.
Common Mistakes
Adding instead of averaging: (x1+x2) instead of (x1+x2)/2
Always divide the sum by 2. The midpoint is the average, not the sum.
Averaging the distances instead of the coordinates
Average the x-coordinates separately and y-coordinates separately. Do not find individual distances and average those.
Thinking the midpoint must have integer coordinates
The midpoint may have decimal or fractional coordinates. (1,0) and (2,1) have midpoint (1.5, 0.5).
Confusing section formula ratio direction
In ratio m:n, m is applied to the endpoint you are heading toward, n to the starting point.
Not verifying the midpoint
Always verify: distance from P1 to midpoint should equal distance from midpoint to P2.
Extending midpoint formula to 3+ points
Midpoint only works for 2 points. For 3 points, use centroid: average all x, all y, all z separately.
Frequently Asked Questions
Midpoint = ((x1+x2)/2, (y1+y2)/2). Average the x-coordinates and average the y-coordinates to find the center point.
No. The midpoint is always between the two endpoints. It divides the segment in a 1:1 ratio.
Midpoint is the center of a line segment (2 points). Centroid is the center of a triangle (3 points), found by averaging all three vertices.
Check that the distance from each endpoint to the midpoint is equal. Both should equal half the total segment length.
The section formula finds a point dividing a segment in ratio m:n: ((m·x2+n·x1)/(m+n), (m·y2+n·y1)/(m+n)).
Yes — for two points, the midpoint is the arithmetic mean of coordinates.
Midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2). Rearranging: x₂ = 2×Mx − x₁, y₂ = 2×My − y₁. Example: one endpoint (2, 3) and midpoint (5, 7). Other endpoint: x₂ = 2(5)−2 = 8, y₂ = 2(7)−3 = 11. Result: (8, 11). Verify: midpoint of (2,3) and (8,11) = ((2+8)/2, (3+11)/2) = (5, 7) ✓.
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