Midpoint calculator

Type two points, such as (1, 2) and (4, 8). Brackets and names are optional, so A(1, 2), B(4, 8) and 1 2 4 8 all work. Coordinates can be whole numbers, decimals, fractions like 3/4 or mixed numbers like 1 1/2.

The midpoint appears as you type, with each coordinate worked out on its own line. Whole numbers and fractions give an exact fraction, with the decimal beside it when it ends. The graph scales itself to fit the points and marks A, B and the midpoint M.

Type six numbers for two points in 3D, such as (1, 2, 3) and (4, 6, 8). The working gains a z line; there's no graph for those.

To work backwards from a midpoint to a missing end, set Find to the other endpoint, or use the endpoint calculator.

The midpoint of the segment from (x₁, y₁) to (x₂, y₂) is M = ((x₁ + x₂)/2, (y₁ + y₂)/2). In words: add the two x values and halve, then add the two y values and halve. It's the average of the two points.

For (1, 2) and (4, 8): the x value is (1 + 4) ÷ 2 = 5/2 and the y value is (2 + 8) ÷ 2 = 5. So M = (5/2, 5), or (2.5, 5).

The midpoint is the same distance from both ends, and it cuts the segment into two equal halves. The calculator lists the length of AB and of each half, so you can see that AM and MB match.

Most slips come from signs. For (−3, 4) and (5, −2), the x value is (−3 + 5) ÷ 2 = 1 and the y value is (4 + (−2)) ÷ 2 = 1, so M = (1, 1). Writing the brackets around negatives keeps the signs straight.

With fractions, add first over a common denominator and then halve. For (1/2, 1) and (3/4, 2): 1/2 + 3/4 = 5/4, and half of that is 5/8. Halving a fraction is the same as doubling its denominator.

The formula carries over to any number of coordinates: average each one. In 3D, M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2). For (1, 2, 3) and (4, 6, 8), that's (5/2, 4, 11/2).