Distance Calculator

Calculate the distance and midpoint between two points in a 2D plane using the distance formula.

Enter Two Points

Distance & Midpoint Results

0
units between points
(0, 0)
center coordinate
0
horizontal distance
0
vertical distance
💡 How it works: The distance formula is derived from the Pythagorean theorem. Imagine a right triangle where the distance between the points is the hypotenuse.

The Distance Formula

The distance between two points (x₁, y₁) and (x₂, y₂) in a Cartesian plane is calculated using:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The Midpoint Formula

The midpoint is the exact center point between two coordinates:

Midpoint = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

Step-by-Step Example

Find the distance between (3, 4) and (7, 1):

  1. Find ΔX: 7 - 3 = 4
  2. Find ΔY: 1 - 4 = -3
  3. Square both: 4² = 16 and (-3)² = 9
  4. Add them: 16 + 9 = 25
  5. Take the square root: √25 = 5

The distance is 5 units.

Real-World Applications

  • GPS & Navigation: Calculating the straight-line distance between two locations on a map.
  • Architecture: Measuring distances between structural points in blueprints.
  • Video Games: Determining if two objects are close enough to collide (collision detection).
  • Aviation: Calculating flight paths and distances between airports.

References

  • Khan Academy. "Distance Formula." 2026.
  • Math is Fun. "Distance Between Two Points." 2026.