Midpoint Calculator
Find the midpoint between two coordinate points.
Results update as you type.
How it works
The midpoint of a line segment is the point that sits exactly halfway between its two endpoints, splitting the segment into two equal halves. It is found with the midpoint formula, which averages the x-coordinates and averages the y-coordinates of the two ends. This midpoint calculator takes two points and returns the midpoint as a coordinate pair, along with its x and y values separately so you can use them elsewhere. The logic is intuitive: to land halfway between two positions along a single axis, you take their average, and doing that independently for the horizontal and vertical directions gives the point centred between them in the plane. For the points (0, 0) and (4, 6), the midpoint is the average of the x-values, which is 2, and the average of the y-values, which is 3, giving the point (2, 3). Midpoints matter in geometry for bisecting segments, finding the centre of a shape, or locating the middle of a path. Students, designers aligning elements, and mapmakers finding a central location all use a midpoint calculator to pinpoint the exact centre between two coordinates without arithmetic slips.
midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
The midpoint is the point exactly halfway between two others, so its coordinates are simply the averages of the endpoints' coordinates. Adding the two x-values and dividing by two lands halfway along the horizontal direction, and doing the same with the y-values lands halfway vertically. Averaging each axis independently works because the midpoint splits the segment evenly, sitting the same distance from both ends in every direction at once.
Source:Standard mathematics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter x₁, y₁, x₂ and y₂.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Midpoint updates instantly as you type — no button to press.
Frequently asked questions
What is the midpoint formula?
The midpoint formula finds the centre point of a segment by averaging the coordinates of its two endpoints. You add the two x-values and divide by two to get the midpoint's x-coordinate, then add the two y-values and divide by two for its y-coordinate. The result is the single point that lies exactly halfway between the ends, the same distance from each along the line joining them.
Why do you average the coordinates?
The average of two numbers is the value exactly halfway between them, which is precisely what a midpoint needs along each axis. By averaging the x-coordinates you find the horizontal centre, and by averaging the y-coordinates you find the vertical centre. Combining those two halfway positions gives a point equidistant from both endpoints in every direction, which is the definition of the midpoint of the segment.
Does the order of the points matter?
No, the midpoint is the same regardless of which point you enter first. Addition is commutative, so adding the two x-values or the two y-values gives the same total no matter the order, and dividing by two produces the identical result. This matches intuition, because the centre of a segment does not depend on which end you start measuring from. The calculator returns the same midpoint either way.
Can the midpoint have decimal coordinates?
Yes, and it often does. Whenever the sum of two coordinates is odd, dividing by two produces a value ending in a half, so the midpoint sits between whole-number grid lines. For example, the midpoint of points with x-values 1 and 4 has an x-coordinate of 2.5. This is perfectly normal; the midpoint is a precise geometric location and does not have to fall on integer coordinates.
What is the midpoint used for?
Midpoints are used to bisect line segments, locate the centre of a shape, and find a point equidistant from two locations. In geometry they help construct perpendicular bisectors and identify centres of circles from endpoints of a diameter. In practical work they place a label or object halfway between two others, or find a fair meeting point between two map positions. The midpoint is a building block for many further constructions.