If the midpoint is halfway, the missing end is as far beyond the midpoint as the known end is before it. This is the midpoint formula solved backwards.
How to use the Endpoint Calculator
- Starting point A – x
- Starting point A – y
- Midpoint M – x
- Midpoint M – y
Results update as you type, and everything is calculated in your browser.
How it works
Each coordinate of the midpoint is the average of the endpoints, so the missing coordinate is twice the midpoint minus the known coordinate.
Inputs explained
| Field | What to enter |
|---|---|
| Starting point A – x | A number |
| Starting point A – y | A number |
| Midpoint M – x | A number |
| Midpoint M – y | A number |
What each result means
- Endpoint B – x₂ = 2×[Midpoint M – x] – [Starting point A – x]
- Endpoint B – y₂ = 2×[Midpoint M – y] – [Starting point A – y]
- Length of AB = 2×sqrt(([Midpoint M – x] – [Starting point A – x])^2 + ([Midpoint M – y] – [Starting point A – y])^2)
Example values
How the main result changes when Starting point A – x changes and everything else stays at the example values above:
| Starting point A – x | Endpoint B – x₂ |
|---|---|
| 1 | 9 |
| 1.5 | 8.5 |
| 2 | 8 |
| 2.5 | 7.5 |
| 3 | 7 |
| 4 | 6 |
Formula
x₂ = 2x − x₁, y₂ = 2y − y₁
Worked example
Inputs — Starting point A – x: 2; Starting point A – y: 3; Midpoint M – x: 5; Midpoint M – y: -1.
Results — Endpoint B – x₂ = 8; Endpoint B – y₂ = -5; Length of AB = 10.
Key terms
- Midpoint
- The point halfway along a segment.
Frequently asked questions
How do I find an endpoint from a midpoint?
Double the midpoint and subtract the known endpoint, coordinate by coordinate.
Does it work in 3D?
Yes: z₂ = 2z − z₁.
What is the length of the segment?
Twice the distance from A to M.
Can the endpoint have negative coordinates?
Of course.