Quick answer
Given a midpoint M and one endpoint A, the other endpoint is B = (2mₓ − x₁, 2m_y − y₁). With midpoint (2, 3) and endpoint (0, 0), the other endpoint is (4, 6).
Enter the midpoint and one endpoint. The calculator returns the other endpoint.
Related tools: Area Calculator: Area of common two-dimensional shapes. Right Triangle Calculator: Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter. Pythagorean Theorem Calculator: Find the hypotenuse or a missing leg of a right triangle.
How to use the Endpoint Calculator
- Enter midpoint x.
- Enter midpoint y.
- Enter known endpoint x.
- Enter known endpoint y.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Midpoint x | A number | — |
| Midpoint y | A number | — |
| Known endpoint x | A number | — |
| Known endpoint y | A number | — |
Formula and method
Formula
(x₂, y₂) = (2mx − x₁, 2my − y₁)
IEEE-754 double precision; shown to at most 6 decimal places.
Reflect the known endpoint through the midpoint.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Midpoint x = 2; Midpoint y = 3; Known endpoint x = 0; Known endpoint y = 0.
| Result | Value |
|---|---|
| Other endpoint | (4, 6) |
Example 2
Inputs: Midpoint x = 1; Midpoint y = 2; Known endpoint x = -2; Known endpoint y = 5.
| Result | Value |
|---|---|
| Other endpoint | (4, -1) |
The first line is the headline result (other endpoint). IEEE-754 double precision; shown to at most 6 decimal places.
Reverse of the midpoint
The midpoint is the average of the endpoints: m = (x₁ + x₂)/2, so x₂ = 2m − x₁. Reflecting A through M gives B: (4 − 0, 6 − 0).
Check
Averaging (0, 0) and (4, 6) gives (2, 3) ✓. The distance from each endpoint to the midpoint is equal. Any real coordinates are accepted.
How the result changes with midpoint x
Holding every other input at the first worked example, this table changes only midpoint x. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Midpoint x | Other endpoint |
|---|---|
| 1 | (2, 6) |
| 2 | (4, 6) |
| 4 | (8, 6) |
| 8 | (16, 6) |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Midpoint x: entering "a" shows "Midpoint x must be a number." beside that field and no result.
Choosing between the Endpoint Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Pythagorean Theorem Calculator](/math/pythagorean-theorem-calculator/) | find, leg a and other side | Hypotenuse c |
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [Circle Calculator](/math/circle-calculator/) | i know the and value | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Any real coordinates
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for midpoint x to confirm this.
Frequently asked questions
What if the midpoint is the origin?
B is the negative of A.
Does it work in 3D?
Apply the same formula to z.
What is a line segment?
The part of a line between two endpoints.
What does the Endpoint Calculator calculate?
Other endpoint of a segment from its midpoint and one endpoint. It returns Other endpoint.
What formula does the Endpoint Calculator use?
(x₂, y₂) = (2mx − x₁, 2my − y₁). Reflect the known endpoint through the midpoint.
What do I need to enter in the endpoint Calculator?
You enter Midpoint x, Midpoint y, Known endpoint x and Known endpoint y.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Any real coordinates.
What is an example of a endpoint result?
With midpoint x 2, midpoint y 3, known endpoint x 0 and known endpoint y 0, the other endpoint is (4, 6).
Related calculators
- Area Calculator — Area of common two-dimensional shapes.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Pythagorean Theorem Calculator — Find the hypotenuse or a missing leg of a right triangle.
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
- Circumference Calculator — Circumference of a circle.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.