Endpoint Calculator

Solve coordinate geometry in either direction. In “missing endpoint” mode, enter the midpoint and one endpoint to find the other. In “midpoint” mode, enter both endpoints. Every result shows the substitution steps and a self-check line proving the answer is right.

Worked example, checked against this exact tool

Midpoint (5, 7), known endpoint (2, 3). Missing x = 2 × 5 − 2 = 8. Missing y = 2 × 7 − 3 = 11. Missing endpoint = (8, 11). Self-check: midpoint of (2, 3) and (8, 11) = ((2+8)÷2, (3+11)÷2) = (5, 7), which matches. Enter the same numbers above and you will get exactly these figures.

The formula, derived in one line

The midpoint averages the two endpoints: M = ((x1+x2)÷2, (y1+y2)÷2). Solve for the missing endpoint and the 2 moves to the other side: x2 = 2mx − x1, y2 = 2my − y1. That is the whole trick, and it is why the calculator’s steps show the doubling first: it mirrors exactly what you would write on paper.

The self-check: trust but verify

Every result recomputes the midpoint from the two endpoints and shows it matches your input. This catches the most common error, swapping which endpoint is known, because a swapped input produces a midpoint that does not match. If the check line ever disagrees with your midpoint, your inputs are wrong, not the math.

When you need the other direction

Sometimes the question gives both endpoints and asks for the midpoint, the average of each coordinate pair. Switch to midpoint mode and the tool averages directly. Students hit this version when bisecting segments; builders and designers hit it when finding centres.

What competing calculators miss

Rival endpoint tools compute one direction only, and the midpoint specialists never look backward from a midpoint at all. None of them verify their own answer. This page solves both directions in one tool and adds the self-check line that proves every result against your inputs.

Frequently asked questions

How do you find the endpoint given the midpoint?

Double the midpoint and subtract the known endpoint: x2 = 2mx − x1, y2 = 2my − y1.

How do you find the midpoint of two points?

Average each coordinate: ((x1+x2)÷2, (y1+y2)÷2).

What if the midpoint is the same as the endpoint?

Then the missing endpoint equals the known one: the segment has zero length.

Can coordinates be negative or decimals?

Yes. The formulas work for any real numbers.

What is the self-check line?

The tool recomputes the midpoint from both endpoints to prove the answer matches your input.

Does this work in 3D?

The same formulas extend to z: z2 = 2mz − z1. This tool covers the 2D case.

Why double the midpoint?

Because the midpoint formula divides the sum by 2; solving for the missing term undoes that division.

What if I mix up the two endpoints?

The midpoint is symmetric, so midpoint mode is unaffected; in endpoint mode the check line will disagree and flag it.

Is an endpoint the same as a vertex?

An endpoint is where a segment stops; a vertex is where polygon edges meet. The math here is for segment endpoints.

Can I use this for line segments on a map?

For small areas on a flat projection, yes. For real distances on a curved Earth, use geodesic tools.