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.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
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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