Endpoint Calculator
Find the missing endpoint of a line segment in 2D or 3D when you know one endpoint and the midpoint.
Other endpoint
(8, 9)
X coordinate
8
2 × midpoint x − endpoint x
Y coordinate
9
2 × midpoint y − endpoint y
Given one endpoint and the midpoint of a segment, the missing endpoint is found by doubling the midpoint and subtracting the known endpoint.
Endpoint Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Find the missing endpoint of a line segment in 2D or 3D when you know one endpoint and the midpoint. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: endpoint calculator · find the other endpoint · endpoint from midpoint
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard mathematical formulas — the same ones taught in school and used in exams — verified by our team. All calculations are performed instantly in your browser using JavaScript, so no data is sent to any server.
The formulas follow standard mathematical definitions and conventions used in textbooks and by educational boards. Results are rounded transparently and shown with the exact formula on this page.
When to Use This Calculator
The endpoint formula is used wherever a centre is known but an end is not. Fabricators and furniture makers in India mark symmetric parts by fixing a centre point and computing both ends, so drill holes and hinge positions line up exactly. CAD drafters use it to mirror a component across a centreline when the mirror function is unavailable. Surveyors extend a boundary through a known midpoint to recover a missing corner marker, and civil contractors lay out equal spans by working outward from a centre peg. In graphics and game development, designers reconstruct the second handle of a symmetric curve from its centre and first handle. Students use it to solve 'given one endpoint and the midpoint, find the other endpoint' problems, which appear regularly in coordinate-geometry exams as the inverse of the midpoint question.
How to Use This Calculator
- Step 1: Choose 2D or 3D based on whether your line segment has z-coordinates.
- Step 2: Enter the x and y coordinates of the endpoint you already know.
- Step 3: Enter the x and y coordinates of the midpoint of the segment.
- Step 4: Read the missing endpoint, computed as twice the midpoint minus the known endpoint.
Worked Example
A carpenter in Chennai needs to drill guide holes at both ends of a 6 m shelf whose centre mark is at (5, 6) on his layout grid, with the left hole at (2, 3). Doubling the midpoint x gives 2 × 5 = 10, minus the known x of 2 leaves 8, and the same for y: 2 × 6 − 3 = 9, so the right hole sits at (8, 9). The same rule works in 3D: with endpoint (1, 2, 3) and midpoint (3, 4, 5), the other end is at (5, 6, 7). This is the mirror-image relation every symmetric layout relies on.
Tips and Common Mistakes
- •Tip 1: The midpoint must be the exact middle — if your midpoint is off, the computed endpoint shifts by twice the error.
- •Tip 2: Verify by re-checking that the computed endpoint and the known one average back to your midpoint.
- •Tip 3: In CAD and layout software, this is the fastest way to mirror a point across a centreline by hand.
- ✗Mistake 1: Subtracting the midpoint from the endpoint instead of doubling the midpoint first.
- ✗Mistake 2: Mixing up which input is the midpoint — swapping them produces a different point entirely.
Frequently Asked Questions
What does the endpoint calculator find?
It finds the missing end of a line segment when you know the other end and the midpoint. With endpoint (2, 3) and midpoint (5, 6), the missing endpoint is (8, 9).
How is the missing endpoint calculated?
Double the midpoint coordinate and subtract the known endpoint coordinate: x₂ = 2 × mₓ − x₁ and y₂ = 2 × mᵧ − y₁. For endpoint (2, 3) and midpoint (5, 6): x₂ = 10 − 2 = 8 and y₂ = 12 − 3 = 9.
Does this work in 3D?
Yes — the same doubling-and-subtracting rule applies to the z-coordinate. With endpoint (1, 2, 3) and midpoint (3, 4, 5), the missing endpoint is (5, 6, 7).
What if the midpoint is closer to one endpoint?
That cannot happen — a midpoint is by definition exactly halfway between the ends. If your data says otherwise, one of the two inputs is wrong, since the missing endpoint is fully determined by the formula.
Where is this formula used in practice?
In geometry problems, computer graphics and CAD, where a segment is defined by its midpoint and one endpoint, such as drawing a symmetric object or centring a line between two known anchors.
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