Midpoint Calculator: Midpoint of Two Points
Find the midpoint of a line segment from its two end points with the midpoint formula ((x₁ + x₂) / 2, (y₁ + y₂) / 2), with the steps shown, free in your browser.
Midpoint
- Midpoint (M)
- (2.5, 5)
M = ((1 + 4) / 2, (2 + 8) / 2) = (2.5, 5)
Slope
- Slope (m)
- 2
- Δx and Δy
- 3 and 6
m = (y₂ − y₁) / (x₂ − x₁) = (8 − 2) / (4 − 1) = 6 / 3 = 2
Equation of the line
- Slope-intercept form
- y = 2x
- y-intercept (b)
- 0
- Point-slope form
- y − 2 = 2(x − 1)
- Standard form
- 2x − y = 0
b = y₁ − m × x₁ = 2 − 2 × 1 = 0
Distance
- Distance (d)
- 6.7082039325
- Exact distance
- √45 = 3√5
d = √((4 − 1)² + (8 − 2)²) = √(9 + 36) = √45 = 3√5 = 6.7082039325
Angle
- Angle with the x-axis
- 63.4349488229°
θ = atan(m) = atan(2) = 63.4349488229°
Midpoint Calculator
This page opens with the midpoint first. Enter the two end points of a line segment and the calculator finds the point exactly halfway between them, with the working laid out as ((x₁ + x₂) / 2, (y₁ + y₂) / 2). Below it you also get the slope, the equation of the line, the distance between the points and the angle of the line. The points (1, 2) and (4, 8) are filled in, so the midpoint (2.5, 5) shows straight away.
The midpoint formula
The midpoint's x-coordinate is the average of the two x-coordinates, and its y-coordinate is the average of the two y-coordinates. It splits the segment into two equal halves, so its distance to each end point is half the length of the segment.
How to use it
Steps
- Type the first end point into x₁ and y₁ and the second into x₂ and y₂.
- Read the midpoint at the top of the results.
- Check the step line, which adds each pair of coordinates and halves them.
Worked examples
(1, 2) and (4, 8)
M = ((1 + 4) / 2, (2 + 8) / 2) = (5 / 2, 10 / 2) = (2.5, 5).
(−2, 3) and (4, −1)
M = ((−2 + 4) / 2, (3 + (−1)) / 2) = (2 / 2, 2 / 2) = (1, 1).
Finding a missing end point
If you know the midpoint M and one end point, the other end is (2Mₓ − x₁, 2Mᵧ − y₁). With M = (2.5, 5) and the end point (1, 2), the other end is (5 − 1, 10 − 2) = (4, 8).
Where it is used
Midpoints find the centre of a circle from the ends of a diameter, the point where the diagonals of a parallelogram cross, and the perpendicular bisector of a segment, which passes through the midpoint at right angles to the line. In everyday terms, the midpoint of two places on a grid map is a fair meeting point. Coordinates may be negative or decimal and must lie between −1e150 and 1e150.
Midpoint and distance
The midpoint is halfway along the segment, so its distance to each end point is half the full length. For (1, 2) and (4, 8) the full distance is √45 = 6.7082039325, so the midpoint (2.5, 5) lies 3.35410196625 from each end. You can check that with the distance formula, and the results on this page show the full distance below the midpoint.
Common mistakes
Add the coordinates, do not subtract them, and halve each sum separately. Keep the signs of negative coordinates: the midpoint of −2 and 4 is 1, not 3. Working with fractions is fine too; the midpoint of 1/2 and 3/2 is 1.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
The full Slope Calculator puts the slope and the equation of the line first, and the Distance Formula Calculator puts the length of the segment first.
Frequently asked questions
What is the midpoint formula?
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2). Each coordinate of the midpoint is the average of the two end points' coordinates. For (1, 2) and (4, 8) the midpoint is (2.5, 5).
Can the midpoint have decimal coordinates?
Yes. When the sum of two coordinates is odd, its half ends in .5, as in (1 + 4) / 2 = 2.5.
How do I find an end point from the midpoint?
Double the midpoint and subtract the known end point: x₂ = 2Mₓ − x₁ and y₂ = 2Mᵧ − y₁. For a midpoint (2.5, 5) and an end point (1, 2) the other end is (4, 8).
Does the order of the points matter?
No. Addition does not depend on order, so (x₁ + x₂) / 2 is the same whichever point comes first.
What else does the page show?
The slope, the equation of the line in three forms, the distance between the points and the angle of the line, each with its working.