Distance Formula Calculator for Two Points

The distance formula is the Pythagorean theorem in coordinate clothing. For points (1,2) and (4,6), the horizontal leg is Δx = 4−1 = 3 and the vertical leg is Δy = 6−2 = 4, so the straight-line distance is √(3²+4²) = √25 = 5. The calculator prints both legs, squares them, sums and roots — every intermediate value. It also returns the midpoint ((1+4)/2, (2+6)/2) = (2.5, 4), handy for geometry proofs and for locating the center between two locations. The same computation generalizes to 3D by adding (z₂−z₁)² under the root, and to map coordinates once you know the scale. Because it reduces to a²+b²=c², any 3-4-5 or 5-12-13 triangle can be recognized instantly from its coordinates.

1. 1

   Enter both points

   Type (x₁,y₁) and (x₂,y₂) for the two endpoints

2. 2

   Compute the legs

   Δx = x₂−x₁ and Δy = y₂−y₁ are displayed

3. 3

   Apply Pythagoras

   Square, sum and take the square root for d

4. 4

   Read the midpoint

   Average the coordinates: ((x₁+x₂)/2, (y₁+y₂)/2)

• 1

  Squaring kills the sign of Δx and Δy, so point order never matters

• 2

  A 3-4-5 coordinate pair like (1,2)→(4,6) signals a right angle

• 3

  Distance is symmetric: d(P,Q) = d(Q,P)

• Subtracting mixed directions, e.g. x₂−x₁ for one leg and y₁−y₂ for the other

• Forgetting to square before adding, computing √3+4 instead of √(9+16)

• Mixing up distance with slope — slope is Δy/Δx, distance is the hypotenuse

• Averning coordinates without dividing by 2 when finding the midpoint