Midpoint Calculator

About this tool

The Midpoint Calculator finds the point exactly halfway between two points using M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Type the coordinates of both points to get the midpoint with every substitution shown, the distance between the points from the distance formula, the slope, and the equation of the line through them. Switch to 3D to add z coordinates, or to Find an endpoint when you know one endpoint and the midpoint: each missing coordinate is 2 × midpoint − known endpoint. Coordinates can be integers, decimals, negatives, fractions such as 3/4 or mixed numbers such as 1 1/2, and the arithmetic is exact, so fractions stay fractions and distances appear in simplest radical form when possible, such as √40 = 2√10 ≈ 6.3246. A vertical line gets an undefined slope instead of a division error. Slope and the line equation apply to 2D points only. The calculator runs in your browser.

Why use it

• Shows the midpoint formula with your numbers substituted, step by step.

• Exact answers: fractions stay fractions and distances come in simplest radical form.

• Distance, slope and the line equation arrive with the midpoint, so one entry covers a whole coordinate geometry question.

• Finds a missing endpoint from one endpoint and the midpoint.

• Handles 3D points and reports a vertical line as an undefined slope.

How to use

1. Choose Find the midpoint, or Find an endpoint if you already know the midpoint.
2. Pick 2D for (x, y) points or 3D to add a z coordinate.
3. Type the coordinates of Point 1 and Point 2 (or the midpoint), one number per box. Fractions like 3/4 and negatives like −2.5 are fine.
4. Read the midpoint or the missing endpoint, the distance and the slope in the result cards.
5. Follow the worked formula under the cards to see every substitution and simplification.

When it helps

• Coordinate geometry homework on midpoints, distance and slope.
• Finding the center of a circle from the two ends of a diameter.
• Recovering the other end of a segment when a worksheet gives one endpoint and the midpoint.
• Locating the point halfway between two positions on a map grid, a drawing or a game level.
• Finding the center between two corners of a box in 3D space.

Examples

Tips

• Order does not matter for the midpoint: swapping Point 1 and Point 2 gives the same answer.
• Quick sanity check: the midpoint's x lies between the two x values, and the same goes for y.
• When x₁ = x₂ the line is vertical, so the slope is undefined and the line is x = constant.
• For the center of a circle, enter the two ends of a diameter; the distance shown is the diameter, so halve it for the radius.
• Type one coordinate per box. A pasted pair such as (2, 3) in a single box is not read as a point.

Frequently Asked Questions

Glossary

Midpoint

The point on a line segment that is the same distance from both endpoints.

Endpoint

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

Slope

The steepness of a line: the change in y divided by the change in x.

Distance formula

d = √((x₂ − x₁)² + (y₂ − y₁)²), the straight-line distance between two points.

Coordinate

A number giving a point's position along one axis, such as x or y.