Midpoint Calculator

Quick Answer

Last updated: 3 November 2026 ·How we calculate this: the midpoint formula

How This Midpoint Calculator Works

Enter the coordinates of two points to find the point exactly halfway between them. Or switch the mode, enter one endpoint and the midpoint, and the calculator finds the missing endpoint. It also gives the length of the segment, its slope, and the equation of the perpendicular bisector, the line that cuts the segment in half at a right angle.

How to Use the Midpoint Calculator

1. Choose whether to find a midpoint or a missing endpoint.
2. Enter the x and y of point 1.
3. Enter point 2, or the midpoint.
4. Press Calculate.
5. Read the result, distance, slope and perpendicular bisector.

Core Formulas

• Midpoint: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
• Missing endpoint: (x₂, y₂) = (2x_m − x₁, 2y_m − y₁)
• Distance: d = √((x₂ − x₁)² + (y₂ − y₁)²)
• Slope: m = (y₂ − y₁) ÷ (x₂ − x₁)
• Perpendicular bisector: slope −1/m, through the midpoint

Key Terms

• Midpoint: the point exactly halfway between two points.
• Endpoint: a point at either end of a line segment.
• Line segment: the part of a line between two endpoints.
• Perpendicular bisector: a line that crosses a segment at its midpoint at a right angle.
• Coordinates: the (x, y) numbers that give a point's position.

Worked Example

The midpoint of a segment is (1, −2) and one end is (−3, 4). Find the other end.

• x₂ = 2(1) − (−3) = 5
• y₂ = 2(−2) − 4 = −8
• The other endpoint is (5, −8). Check: ((−3 + 5) ÷ 2, (4 − 8) ÷ 2) = (1, −2).

Real-Life Examples

• Geometry homework: find the center of a circle from the ends of a diameter.
• Construction: find the center point between two posts or marks.
• Graphing: the perpendicular bisector of (2, 3) and (8, 11) is y = −0.75x + 10.75.
• Meeting halfway: on a grid map, average the coordinates of two places.

Midpoint vs Distance

• Midpoint: a point, the average of the two endpoints.
• Distance: a length, from the Pythagorean theorem.
• Together: the midpoint is half the distance from each end.

Midpoint Examples

Tips

• Watch negative signs: −3 + 5 = 2, not −8.
• Keep the order: pair x with x and y with y.
• 3D points: average the z values the same way.
• Maps: for short distances, the midpoint of two map coordinates is close to the halfway point.

The midpoint formula comes from the idea of an average. Moving from the first point to the second, the x value changes by x₂ − x₁, so halfway along it has changed by half that amount. Starting at x₁ and adding half the change gives x₁ + (x₂ − x₁) ÷ 2, which simplifies to (x₁ + x₂) ÷ 2. The same reasoning works for y, and for z in three dimensions. You can also split a segment into other fractions this way: one third of the way from the first point is x₁ + (x₂ − x₁) ÷ 3.

Common Mistakes to Avoid

• Subtracting instead of adding. The midpoint uses (x₁ + x₂) ÷ 2.
• Forgetting to divide by 2.
• Mixing x and y. Average x values together and y values together.
• Using the midpoint formula for an endpoint. Use 2M − P instead.
• Sign errors with negatives. Use brackets when substituting.

Frequently Asked Questions

References & Sources