Midpoint Calculator
Enter two coordinate points to find the midpoint of the segment, the average of each coordinate, the distance to each endpoint, and clear substitution steps.
M = ((0 + 3)/2, (0 + 4)/2)
Embed Midpoint Calculator
Copy this iframe code into a page that permits embeds.
All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Midpoint Calculator
Enter the x-coordinate and y-coordinate for each point. Keep each coordinate pair together. Select Calculate Midpoint or press Enter. The calculator reports the midpoint, coordinate changes, half-distance to each endpoint, a location classification, and substitution steps.
- Label the points (x₁, y₁) and (x₂, y₂).
- Enter all four values, including any negative signs.
- Average the x-coordinates: (x₁ + x₂) / 2.
- Average the y-coordinates: (y₁ + y₂) / 2.
- Write the midpoint as the ordered pair M = (x-average, y-average).
Swapping the two points does not change the midpoint. If both points are identical, the midpoint is that same point, which is a valid result.
Midpoint Formula Between Two Points
The formula averages each coordinate independently. The x-coordinate of M is halfway between x₁ and x₂. The y-coordinate of M is halfway between y₁ and y₂. Together those averages locate the unique point that splits the segment into two equal lengths.
The same idea is the two-dimensional case of a section formula with equal weights. If a point divided the segment in a ratio other than 1:1, the weights would no longer both be 1/2.
Half-distance
The distance from M to either endpoint is half of d = √((x₂ − x₁)² + (y₂ − y₁)²). The calculator reports that half-length so you can check the geometry without leaving the page. Distance answers “how far.” Midpoint answers “where.”
Coordinate changes
Δx = x₂ − x₁ and Δy = y₂ − y₁ describe the displacement from point 1 to point 2. Adding half of each change to point 1 also produces the midpoint: (x₁ + Δx/2, y₁ + Δy/2). That identity is a useful check against the averaging formula.
Midpoint Formula Examples
A 3-4-5 segment
Between (0, 0) and (3, 4), the midpoint is ((0 + 3)/2, (0 + 4)/2) = (1.5, 2). The full distance is 5, so each half is 2.5.
Two general points
Between (2, 3) and (7, 6), M = ((2 + 7)/2, (3 + 6)/2) = (4.5, 4.5). The point sits on y = x in this example, but that is a coincidence of the inputs.
Negative coordinates
Between (−2, −3) and (4, 5), M = (1, 1). Negative values change the sums, not the formula.
A vertical segment
Between (2, 1) and (2, 9), the x-coordinates are equal, so the midpoint stays on the same vertical line: (2, 5).
The same point twice
Between (7, 7) and (7, 7), both averages equal 7. The midpoint is (7, 7) and the segment length is 0.
How to Interpret a Coordinate Midpoint
The result is the center of the straight segment joining two points in a flat coordinate plane. Units come from the coordinate axes, so coordinates measured in meters produce a midpoint measured in meters.
Midpoints appear in geometry proofs, coordinate graphing, computer graphics, physics, and mapping. They can locate a segment center, find the center of a circle from a diameter, or split a path into two equal parts.
Midpoint and distance
Use the distance formula calculator when the length of the segment is the main goal. The two tools share the same inputs and should agree that each endpoint is equally far from M.
Midpoint and slope
Slope measures direction. The midpoint does not depend on slope, and a vertical segment still has a midpoint even though its slope is undefined. Use the slope calculator when the rate of change is the main goal.
Three-dimensional extension
For points in three dimensions, average the z-coordinates as well: M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2). This page handles two-dimensional coordinates only.
Common Midpoint Formula Mistakes
Averaging the wrong pairs
Average x with x and y with y. Do not mix an x-value from one point with the y-value from the other.
Subtracting instead of averaging
Distance uses differences. Midpoint uses averages. (x₂ − x₁)/2 is a half-change, not the midpoint x-coordinate.
Forgetting parentheses around negatives
Write negative coordinates in parentheses before adding. For example, (−2 + 4)/2 equals 1.
Reporting only one coordinate
A midpoint is an ordered pair. Both the x-average and the y-average are required.
Confusing midpoint with the intersection of axes
The midpoint does not have to be the origin. It lands at the origin only when the two points are opposites through (0, 0).
Using the 2D formula for a path on a sphere
Latitude and longitude over large regions need a geographic midpoint model, not this flat-plane average.
Midpoint Calculator FAQs
What is the midpoint formula?
The midpoint of (x₁, y₁) and (x₂, y₂) is M = ((x₁ + x₂)/2, (y₁ + y₂)/2). Average the x-coordinates and average the y-coordinates separately.
Does the order of the two points change the midpoint?
No. Addition is commutative, so swapping the points leaves both averages unchanged.
What happens when both points are the same?
The midpoint is that same point. The segment has length zero, and each “half” is also zero.
Can I use negative or decimal coordinates?
Yes. The calculator accepts finite positive, negative, zero, and decimal coordinates.
Is the midpoint always on the segment?
Yes, for two points in a flat coordinate plane. It is the point halfway along the straight segment joining them.
How is midpoint different from distance?
Midpoint names a location. Distance names a length. The two results are related: each endpoint is half the full distance from the midpoint.
Are my coordinates sent to a server?
No. The calculation runs locally in your browser.
Related Algebra Calculators
Explore More Algebra Tools
Continue with coordinate, equation, and polynomial tools in the SolverCalc algebra collection.
Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.