Free · Coordinate geometry calculators

Distance Between Two Cartesian Points

Calculate straight-line distance between two points on a plane, with a documented single-branch inverse for missing coordinates.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

The points (−1, 2) and (2, 6) are 5 units apart: their horizontal and vertical differences are 3 and 4.

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Worked example

Enter these known values and leave the other values blank.

First point x-coordinate
-1
First point y-coordinate
2
Second point x-coordinate
2
Second point y-coordinate
6
Nonnegative straight-line distance
5

Assumptions and limitations

  • Use a Cartesian plane with the same length scale on both perpendicular axes. This is straight-line Euclidean distance, not travel distance or a latitude/longitude calculation.
  • Distance is nonnegative. Coincident points give zero. Signed coordinates remain valid in any quadrant.
  • An inverse coordinate calculation can have two solutions. The retained source rule returns the other point’s corresponding coordinate plus the nonnegative square root; it does not enumerate the minus branch.
  • For an inverse, distance must be at least the known perpendicular separation. Otherwise no real coordinate satisfies the inputs. Enter all four coordinates for an unambiguous forward distance.

Common questions

Why can a missing coordinate have two answers?

A circle of possible points can intersect a horizontal or vertical line twice. This tool retains one plus-root branch; the reflected coordinate may be a second valid answer.

Can I use map latitude and longitude?

Not directly. Degrees of latitude and longitude do not form equal Cartesian distance scales over Earth. Use an appropriate geographic distance model.

References

Bookify rejects negative Euclidean distance while retaining signed coordinates and the documented plus-root inverse branch.

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