Midpoint Calculator

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Enter two endpoints to find their coordinate-plane midpoint as an ordered pair and see each matching coordinate averaged.

Advanced options
Paste ordered pairs
Midpoint ordered pairThe first number is halfway between the x-coordinates. The second is halfway between the y-coordinates.
Midpoint x-coordinateThis is Point A's x-coordinate and Point B's x-coordinate averaged together.
Midpoint y-coordinateThis is Point A's y-coordinate and Point B's y-coordinate averaged together.
How the midpoint x-coordinate was foundOnly the two x-values are used in this line.
How the midpoint y-coordinate was foundOnly the two y-values are used in this line.
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How to use our Midpoint Calculator

  1. Enter Point A and Point B from your problem: put each first number in its x-coordinate field and each second number in its y-coordinate field.
  2. Use signed whole numbers, decimals, or simple fractions such as -3/4. Keep every minus sign shown in the original point.
  3. If the problem already shows both points as ordered pairs, open Advanced options and paste both complete pairs in the form (x, y).
  4. Click Calculate to get the midpoint ordered pair, followed by the separate x-coordinate and y-coordinate work.
  5. Check that each midpoint coordinate is between the two matching endpoint coordinates. For example, a value halfway between -4 and 2 is -1.
Example inputs for Midpoint Calculator
Example inputs for Midpoint Calculator

Definitions

Ordered pair: Two coordinates written as (x, y). The first value is the horizontal x-coordinate, and the second is the vertical y-coordinate.

Endpoint: One of the two points at the ends of a line segment.

Midpoint: The point exactly halfway between the two endpoints of a line segment.

x-coordinate: The first number in an ordered pair. It shows horizontal position on a coordinate plane.

y-coordinate: The second number in an ordered pair. It shows vertical position on a coordinate plane.

Simple fraction: A number with one slash, such as 1/2 or -3/4, whose denominator is not zero.

Common mistakes and quick fixes

Mistake: Reversing the numbers in an ordered pair.
Fix: Check Point A x-coordinate (x1) and then recalculate. Put the number before the comma in the x field and the number after the comma in the y field.

Mistake: Losing a minus sign while copying a coordinate.
Fix: Check Point A x-coordinate (x1) and then recalculate. Copy the sign with its number. One missing minus sign changes the midpoint.

Mistake: Subtracting the endpoint coordinates.
Fix: Check Point A x-coordinate (x1) and then recalculate. Add the two x-values and divide by 2. Do the same separately for the two y-values.

Mistake: Pasting only one ordered pair.
Fix: Check Point A x-coordinate (x1) and then recalculate. Paste both complete points, or clear both paste fields and use the four separate coordinate fields.

Mistake: Rounding a fractional or decimal midpoint to a whole number.
Fix: Check Point A x-coordinate (x1) and then recalculate. Keep the exact fraction or decimal shown. A midpoint coordinate does not have to be a whole number.

Limitations & Key Assumptions / Boundary Conditions

  • This calculator finds the midpoint of two points in a two-dimensional coordinate plane. It does not calculate 3D midpoints, distance, or a missing endpoint.
  • Point A and Point B must use the same coordinate system and, if units are given, the same units.
  • Each coordinate must be one finite whole number, decimal, or simple fraction. Expressions, ranges, mixed numbers, and fractions with a zero denominator are not accepted.
  • Coordinates are treated as unitless unless the source problem supplies a unit.
  • If both endpoints are the same point, that point is also the midpoint.

Methodology

Calculation method

The calculator averages matching coordinates. It uses the two x-coordinates to find the midpoint x-coordinate and the two y-coordinates to find the midpoint y-coordinate.

xM = (x1 + x2) / 2

yM = (y1 + y2) / 2

M = (xM, yM)

For Point A = (-4, 6) and Point B = (2, -2), the midpoint x-coordinate is (-4 + 2) / 2 = -1. The midpoint y-coordinate is (6 + -2) / 2 = 2, so the midpoint is (-1, 2).

Pasting ordered pairs

When both pasted pairs are valid, the calculator reads the first value of each pair as x and the second as y, then fills the four coordinate fields before calculating. It accepts signed whole numbers, finite decimals, and simple fractions with one slash.