📋

Walk-through

How to Use This Calculator

4 steps

1

Pick 2D or 3D

Leave the dimension on 2D for ordinary (x, y) points, or switch to 3D to add a z-coordinate. The extra z fields appear or hide instantly, and every tab follows your choice.

2

Enter the two points

Type the coordinates of point A and point B. Negatives and decimals are fine. The midpoint, segment length, and slope update as you type — no Calculate button to press.

3

Read the midpoint, distance, and slope

The headline card shows the midpoint, with the segment length and slope just below it. The coordinate sketch plots A, B, and the midpoint M so you can see the result. Open Distance & Slope for the step-by-step working.

4

Or work backwards with Find Endpoint

Know the midpoint and one end? Open the Find Endpoint tab, enter the midpoint and the known endpoint, and the calculator returns the other endpoint using B = 2M − A.

⚡

Reference

Formula & Methodology

4 formulas

Midpoint of a segment

M = ( (x1 + x2)/2 , (y1 + y2)/2 ) [3D: add (z1 + z2)/2 ]

The midpoint is just the average of the two endpoints, taken one coordinate at a time. Averaging the x-values gives the midpoint's x, averaging the y-values gives its y, and (in 3D) averaging the z-values gives its z. It is always exactly halfway along the straight segment from A to B.

Distance (segment length)

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 ) [3D: + (z2 - z1)^2 ]

The distance formula is the Pythagorean theorem applied to the coordinate differences Δx, Δy (and Δz in 3D). Square each difference, add them, and take the square root to get the straight-line length of the segment.

Slope of a 2D line

m = (y2 - y1) / (x2 - x1) = Δy / Δx

Slope is rise over run: how much the line climbs (Δy) for each unit it moves sideways (Δx). When Δx = 0 the line is vertical and the slope is undefined (you cannot divide by zero). When Δy = 0 the line is horizontal and the slope is 0. Slope is a 2D idea only — a line in 3D needs a direction vector instead.

Finding a missing endpoint

B = 2M - A (per coordinate: x_B = 2*M_x - x_A)

Because the midpoint M is the average of A and B, rearranging M = (A + B)/2 gives B = 2M − A. Double the midpoint's coordinates and subtract the known endpoint's coordinates to recover the other end of the segment.

📖

Glossary

Key Terms Explained

8 terms

Midpoint The point exactly halfway between two endpoints of a segment. Its coordinates are the averages of the endpoints' coordinates.

Coordinate A number that locates a point along one axis. A 2D point has two coordinates (x, y); a 3D point has three (x, y, z).

Line segment The straight piece of a line bounded by two endpoints A and B. Unlike a full line, it has a definite, finite length.

Distance The straight-line length of the segment between two points, found with the distance formula (an application of the Pythagorean theorem).

Slope The steepness of a 2D line, rise over run (Δy ÷ Δx). Positive slope rises left-to-right, negative falls, zero is horizontal, and a vertical line has undefined slope.

Vertical line A line where both points share the same x-value, so the run (Δx) is zero. Its slope is undefined because division by zero is not allowed.

Quadrant One of the four regions the x- and y-axes divide the plane into. Quadrant I is upper-right (x>0, y>0) and they number counter-clockwise from there.

Endpoint One of the two points that bound a segment. Given the midpoint and one endpoint, the other endpoint is B = 2M − A.

👥

Scenarios

Real-World Examples

3 worked examples

📐

Geometry homework

Midpoint of (2, 3) and (8, 11)

Point A (2, 3) Point B (8, 11)

Average each coordinate: x = (2 + 8)/2 = 5, y = (3 + 11)/2 = 7, so the midpoint is (5, 7). The segment length is √(6² + 8²) = √100 = 10, and the slope is 8 ÷ 6 ≈ 1.3333 — a line rising from left to right.

📏

Vertical segment

Midpoint of (3, 4) and (3, 10)

Point A (3, 4) Point B (3, 10)

The midpoint is (3, 7) and the length is 6. But because both points share x = 3, the run Δx is 0, so the slope is undefined — this is a vertical line. The calculator flags it as 'undefined (vertical line)' instead of dividing by zero.

🧊

Finding a missing endpoint

Midpoint (5, 7), one endpoint (2, 3)

Midpoint M (5, 7) Known endpoint A (2, 3)

Use B = 2M − A: x = 2(5) − 2 = 8, y = 2(7) − 3 = 11, so the other endpoint is (8, 11). That is the reverse of the first example — proof that doubling the midpoint and subtracting the known end recovers the missing point.

📄

Deep Dive

Understanding the Midpoint of a Segment

4 chapters · 4 min read

The midpoint is the point exactly halfway between two others, and it is one of the most useful results in coordinate geometry. This guide explains the midpoint formula, how it connects to distance and slope, what to do in 3D, and how to work backwards to find a missing endpoint.

The midpoint formula and why it is just an average

To find the point halfway between two values on a number line you average them — the number halfway between 2 and 8 is (2 + 8)/2 = 5. The midpoint formula does exactly that, one axis at a time: M = ((x1 + x2)/2, (y1 + y2)/2). In three dimensions you average the z-values too. Because each coordinate is handled independently, the formula extends to any number of dimensions without changing its shape.

The result is always on the straight segment connecting the two points, and it splits that segment into two equal halves — so the distance from A to M equals the distance from M to B.

Distance and slope of the same segment

Once you have two points, two more facts come almost for free. The distance between them is the segment's length, found with d = √(Δx² + Δy²) — the Pythagorean theorem with the coordinate differences as the legs of a right triangle. In 3D you add Δz² under the root.

The slope (a 2D idea) measures steepness as rise over run, m = Δy ÷ Δx. A positive slope rises to the right, a negative one falls, and a horizontal line has slope 0. When the two points share an x-value the run is zero, so the slope is undefined rather than infinite — this calculator says so explicitly instead of dividing by zero.

Working in three dimensions

Switching to 3D adds a z-coordinate to every point. The midpoint and distance formulas simply gain a z-term. Slope, however, has no single value in 3D: a line in space is described by a direction vector, not one rise-over-run number, so the calculator reports slope as 'N/A in 3D'. The coordinate sketch still helps by showing the segment's shadow on the xy-plane.

Reversing the formula to find an endpoint

Sometimes you know where the middle of a segment is and one of its ends, and you need the other end — for example, reflecting a point through a center. Rearranging the midpoint formula gives B = 2M − A: double the midpoint and subtract the known endpoint, coordinate by coordinate. The Find Endpoint tab does this automatically, and you can sanity-check it by feeding the answer back into the Midpoint tab.

❓

Questions

Frequently Asked Questions

7 questions

What is the midpoint formula?+

The midpoint of two points is the average of their coordinates: M = ((x1 + x2)/2, (y1 + y2)/2). In 3D you also average the z-values. The midpoint is always exactly halfway along the straight segment joining the two points.

How do I find the distance between the two points?+

Use the distance formula, d = √((x2 − x1)² + (y2 − y1)²), which is the Pythagorean theorem applied to the differences in x and y. In 3D, add (z2 − z1)² under the square root. This calculator shows the distance right below the midpoint.

What is the slope of a vertical line?+

It is undefined. Slope is Δy ÷ Δx, and a vertical line has two points with the same x-value, so Δx = 0. Dividing by zero is not allowed, so the slope does not exist — the calculator reports 'undefined (vertical line)' rather than a number.

Does the midpoint work in 3D?+

Yes. Switch the dimension toggle to 3D and a z-coordinate appears for each point. The midpoint and distance formulas just gain a z-term. Slope, though, is only defined in 2D — a 3D line needs a direction vector, so slope shows as 'N/A in 3D'.

How do I find a missing endpoint from the midpoint?+

Use the Find Endpoint tab. If you know the midpoint M and one endpoint A, the other endpoint is B = 2M − A — double the midpoint's coordinates and subtract the known endpoint's coordinates. This is just the midpoint formula rearranged.

Is the midpoint the same as the average of the points?+

Yes — that is exactly what it is. The midpoint is the coordinate-by-coordinate average (mean) of the two endpoints. Averaging is why it lands precisely halfway between them and splits the segment into two equal lengths.

How do I share or save a calculation?+

The calculator encodes your points and dimension into the page URL as you work, so copying the link — or using the Share button — sends the exact calculation to someone else. Your last inputs are also saved locally in your browser, and you can export the result as CSV.

Download a one-page PDF of your numbers instantly. Add your email to also get our occasional calculator tips — no spam, unsubscribe anytime. Privacy.

Midpoint Calculator

Two points

Coordinate sketch

Distance and slope of the segment

Midpoint and one endpoint

How to Use This Calculator

Pick 2D or 3D

Enter the two points

Read the midpoint, distance, and slope

Or work backwards with Find Endpoint

Formula & Methodology

Key Terms Explained

Real-World Examples

Geometry homework

Vertical segment

Finding a missing endpoint

Understanding the Midpoint of a Segment

The midpoint formula and why it is just an average

Distance and slope of the same segment

Working in three dimensions

Reversing the formula to find an endpoint

Frequently Asked Questions

Get a branded PDF of your results

Midpoint Calculator

Two points

Coordinate sketch

Distance and slope of the segment

Midpoint and one endpoint

Related Calculators

How to Use This Calculator

Pick 2D or 3D

Enter the two points

Read the midpoint, distance, and slope

Or work backwards with Find Endpoint

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding the Midpoint of a Segment

The midpoint formula and why it is just an average

Distance and slope of the same segment

Working in three dimensions

Reversing the formula to find an endpoint

Frequently Asked Questions

Get a branded PDF of your results

Keep Exploring

Related calculators

Guides & articles