Quick answer
The midpoint of a segment is the average of its endpoints: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Between (0, 0) and (4, 6) it is (2, 3).
Enter the two endpoints. The calculator returns the midpoint.
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 Midpoint Calculator
- Enter x₁.
- Enter y₁.
- Enter x₂.
- Enter y₂.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| x₁ | A number | — |
| y₁ | A number | — |
| x₂ | A number | — |
| y₂ | A number | — |
Formula and method
Formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
IEEE-754 double precision; shown to at most 6 decimal places.
Average of coordinates.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: x₁ = 0; y₁ = 0; x₂ = 4; y₂ = 6.
| Result | Value |
|---|---|
| Midpoint | (2, 3) |
Example 2
Inputs: x₁ = -2; y₁ = 5; x₂ = 4; y₂ = -1.
| Result | Value |
|---|---|
| Midpoint | (1, 2) |
The first line is the headline result (midpoint). IEEE-754 double precision; shown to at most 6 decimal places.
Average the coordinates
(0 + 4) ÷ 2 = 2 and (0 + 6) ÷ 2 = 3. The midpoint is equally far from both endpoints, 3.606 units here.
Related ideas
To find an unknown endpoint from a midpoint, use the Endpoint calculator. In 3D, average the z-coordinates too. Midpoints are used in geometry proofs, mapping and finding perpendicular bisectors.
How the result changes with x₂
Holding every other input at the first worked example, this table changes only x₂. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| x₂ | Midpoint |
|---|---|
| 2 | (1, 3) |
| 4 | (2, 3) |
| 8 | (4, 3) |
| 16 | (8, 3) |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- x₁: left empty shows "Enter x₁." beside that field and no result.
Choosing between the Midpoint 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 x₁ to confirm this.
Frequently asked questions
What is the midpoint of (−2, 4) and (6, 0)?
The midpoint of (−2, 4) and (6, 0) is ((−2 + 6) ÷ 2, (4 + 0) ÷ 2) = (2, 2).
Does the order matter?
No. Swapping the two points gives the same midpoint.
Can coordinates be negative?
Yes. Coordinates can be negative or decimals.
What does the Midpoint Calculator calculate?
Midpoint of a line segment. It returns Midpoint.
What formula does the Midpoint Calculator use?
M = ((x₁ + x₂)/2, (y₁ + y₂)/2). Average of coordinates.
What do I need to enter in the midpoint Calculator?
You enter x₁, y₁, x₂ and y₂.
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 midpoint result?
With x₁ 0, y₁ 0, x₂ 4 and y₂ 6, the midpoint is (2, 3).
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.