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Distance Between Two Points Calculator with Graph

Geometry & Coordinate GeometryFreeStep by stepGraph

The distance between two points on a coordinate grid is the length of the straight line joining them. This calculator uses the distance formula, which comes from Pythagoras: square the horizontal and vertical gaps, add them, and take the square root. Answers are exact where possible, and the midpoint is shown too.

Try:

How to use the distance between two points calculator

  1. Enter the first point (x₁, y₁).
  2. Enter the second point (x₂, y₂).
  3. Press Calculate to see the distance and the steps.

Formula

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Worked example: (1, 2) and (4, 6)

  • x₁: 1
  • y₁: 2
  • x₂: 4
  • y₂: 6

✓ Answer checked

d=5d = 5
Midpoint
(52,  4)\left(\frac{5}{2},\; 4\right)
−4−2246812345678(1, 2)(4, 6)
The distance is the hypotenuse of a right triangle with sides 3 and 4.
Step-by-step working (4 steps)

  1. Use the distance formula Distance formula

    It is Pythagoras: the horizontal and vertical gaps are the two shorter sides.

    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

  2. Find the gaps

    Subtract the coordinates.

    x2−x1=3,y2−y1=4x_2 - x_1 = 3, \quad y_2 - y_1 = 4

  3. Square and add

    Square each gap and add them.

    32+42=9+16=253^2 + 4^2 = 9 + 16 = 25

  4. Take the square root

    The result is a perfect square.

    d=25=5d = \sqrt{25} = 5
Formulas used
d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
How this was checked
  • ✓ An independent hypotenuse calculation gives the same distance.

Frequently asked questions

What is the distance formula?

d = √((x₂ − x₁)² + (y₂ − y₁)²). It is the Pythagorean theorem applied to the horizontal and vertical gaps.

What is the distance between (1, 2) and (4, 6)?

5. The gaps are 3 and 4, and √(9 + 16) = 5.

Does the order of the points matter?

No. The gaps are squared, so swapping the points gives the same distance.

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