Free Endpoint Calculator

Built and fact-checked by the DocNectar team — see our editorial standards

Thanks for rating!

Key Features

Instant Calculation

Get accurate results in real time with our optimized algorithm.

Mobile Friendly

Fully responsive design. Works on all devices & screen sizes.

Privacy Focused

Your data stays on your device. We don't store any inputs.

100% Free

No hidden costs. This tool is completely free forever.

This tool reverses the familiar midpoint formula: instead of finding the midpoint from two endpoints, you're given one endpoint and the midpoint and need to work backward to the other endpoint. This comes up constantly in coordinate geometry homework, in CAD and drafting when a symmetric feature's center and one edge are known, and in navigation or surveying problems where a known reference point and a halfway marker are used to project a destination.

How it works

Enter the known endpoint (x1, y1) and the midpoint (mx, my). Since the midpoint formula states mx=(x1+x2)/2 and my=(y1+y2)/2, solving for the unknown endpoint just requires rearranging: multiply the midpoint by 2 and subtract the known endpoint, giving x2=2mx-x1 and y2=2my-y1.

Enter known endpoint — x1.
Enter known endpoint — y1.
Enter midpoint — x.
Enter midpoint — y.
Click Calculate to see your results.

Examples

Endpoint (1,2), midpoint (4,5)

x2 = 2(4)-1 = 8-1 = 7. y2 = 2(5)-2 = 10-2 = 8. The other endpoint is (7, 8).

Endpoint (-3,6), midpoint (0,0)

x2 = 2(0)-(-3) = 3. y2 = 2(0)-6 = -6. The other endpoint is (3, -6) — the exact reflection of the first point through the origin, as expected when the midpoint is the origin.

Common mistakes to avoid

Swapping the roles of the known endpoint and the midpoint in the formula — the "2×" multiplier always applies to the midpoint, never to the known endpoint.
Forgetting to subtract the known endpoint after doubling the midpoint (computing 2mx instead of 2mx-x1).
Mixing up x and y coordinates between the two input points.
Assuming the known point given is the midpoint when it's actually the endpoint, or vice versa.

Frequently asked questions

Average the two endpoints — (x1+x2)/2 and (y1+y2)/2 should reproduce the original midpoint exactly.

Yes, conceptually — you'd just add a z2=2mz-z1 term. This particular tool is built for the 2D case, which is by far the more common classroom and drafting scenario.

Then the missing endpoint is also that same point — the segment has zero length, which is a degenerate but mathematically valid case.

Yes exactly — finding the missing endpoint given one endpoint and the midpoint is identical to reflecting the known endpoint through the midpoint (a 180° rotation about that center).

It's a direct algebraic rearrangement of the midpoint formula. Since the midpoint is defined as the average of the two endpoints, isolating the unknown endpoint just requires undoing that averaging step by doubling and subtracting.

Yes — the missing endpoint equals the midpoint plus the vector from the known endpoint to the midpoint, which is mathematically identical to the coordinate formula but sometimes more intuitive when visualizing the segment.

Yes — the formula x2=2mx-x1 and y2=2my-y1 handles negative coordinates automatically, since it's pure arithmetic that works the same regardless of sign.