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Midpoint Calculator

The midpoint is the average of the two points: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Between (2, 3) and (8, 11) it is (5, 7). The distance between them is √(6² + 8²) = 10 and the slope is 8 ÷ 6 = 1.33. With site coordinates, use eastings for x and northings for y.

Inputs

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Point 1
Point 2
Two points and their midpointMidpoint (5, 7)1 (2, 3)2 (8, 11)myconstructioncalculator.comNot to scale
Diagram updates as you type.

Results

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Midpoint
(5, 7)
Distance between the points10
Half the distance5
Slope (rise ÷ run)1.3333
Angle from the x axis53.13 °
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Working
  1. Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) = ((2 + 8) ÷ 2, (3 + 11) ÷ 2) = (5, 7)
  2. Distance = √((x₂ − x₁)² + (y₂ − y₁)²) = √(6² + 8²) = 10
  3. Slope = (y₂ − y₁) ÷ (x₂ − x₁) = 8 ÷ 6 = 1.3333
Results are estimates for planning and material ordering only. They are not a substitute for structural design or approval by a qualified engineer. Read the full disclaimer.
Formula


Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
Distance = √((x₂ − x₁)² + (y₂ − y₁)²)
Slope    = (y₂ − y₁) ÷ (x₂ − x₁)


Worked Example


Two setting-out points: E 1,250.0, N 3,420.0 and E 1,310.0, N 3,500.0:


    

  1. Midpoint E = (1,250 + 1,310) ÷ 2 = 1,280.0; N = (3,420 + 3,500) ÷ 2 = 3,460.0
    2. 

  2. Distance = √(60² + 80²) = 100 m
    3. 

  3. The midpoint is 50 m from each point
    4. 



Examples






Point 1
Point 2
Midpoint
Distance






(0, 0)
(6, 8)
(3, 4)
10




(2, 3)
(8, 11)
(5, 7)
10




(−4, 2)
(6, −8)
(1, −3)
14.142




(1, 1)
(4, 5)
(2.5, 3)
5






Frequently Asked Questions
What is the midpoint formula?
Add the two x values and halve them, then do the same with the y values. The midpoint of (2, 3) and (8, 11) is (5, 7).
How do you find the distance between two points?
Use Pythagoras: √((x₂ − x₁)² + (y₂ − y₁)²). From (2, 3) to (8, 11): √(36 + 64) = 10.
How do I find the centre between two setting-out points?
Enter the eastings as x and the northings as y. Points at E 1,250.0, N 3,420.0 and E 1,310.0, N 3,500.0 have their midpoint at E 1,280.0, N 3,460.0, 50 m from each.
Can coordinates be negative?
Yes. The formulas work the same way: the midpoint of (−4, 2) and (6, −8) is (1, −3).
What if the two x values are the same?
The line between the points is vertical, so its slope is undefined. The midpoint and distance still work normally.
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