2D Distance Calculator

Measure straight-line distance between two points and see the horizontal, vertical and diagonal parts on a true-scale coordinate diagram.

Calculation inputs

Precision & interpretation

This is a Euclidean plane calculation, not a latitude/longitude or road-distance model. Exact rational or radical form is retained for decimal inputs; a decimal approximation is shown alongside it.

Calculation results

Distance d5Exact distance 5

Horizontal change Δx3

Vertical change Δy4

Midpoint(3/2, 2)

Step-by-step solution

Choose the formula
$d = √((x₂−x₁)² + (y₂−y₁)²)$
Substitute your inputs
$d = √((3)² + (4)²)$
Calculate in order
$d = \sqrt{25}$
Write the result
$d = 5$

Distance on the coordinate plane

Both axes use the same scale; each coordinate unit has the same geometric size.

Decimal coordinates are interpreted exactly (up to six decimal places). Diagram coordinates and decimal distances use floating point.

Exact value & calculation details

Quantity	Value
Point A	(0, 0)
Point B	(3, 4)
Midpoint	(3/2, 2)
Distance (decimal)	5
Distance (exact)	5

Understand the calculation

Concept & meaning

The straight-line distance is the hypotenuse of the right triangle formed by the coordinate differences. Squaring removes their signs; the final distance is nonnegative.

Formula & special cases

Both coordinates must use the same physical unit and the axes the same scale. The plotted axes use equal geometric scale, so the drawing does not distort angles or distances.

Precision & limitations

This is a Euclidean plane calculation, not a latitude/longitude or road-distance model. Exact rational or radical form is retained for decimal inputs; a decimal approximation is shown alongside it.

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

Worked example from your inputs

Exact distance 5 = 5

Frequently asked questions

Does the order of the points matter?

No. Reversing both coordinate differences leaves their squares, and therefore the distance, unchanged.

Can the distance be negative?

No. It is zero for coincident points and positive for distinct points.

Can I use latitude and longitude?

Not directly. Geographic coordinates need an appropriate spherical or ellipsoidal distance model and unit conversion.

Are the axes drawn to the same scale?

Yes. Both axes share the same units-per-pixel scale, preserving the shape of the right triangle.

Show all questions (5 more)Show fewer questions

What does the 2D Distance calculate?

Measure straight-line distance between two points and see the horizontal, vertical and diagonal parts on a true-scale coordinate diagram.

Which values should I enter?

Use the labeled fields above. Values outside the supported range clear the result and show an explanation.

What formula does this calculator use?

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Inputs and presets update the result, teaching diagram and expandable steps together. Invalid input clears the previous result.

Sources & References

$OpenStax official logo$ OpenStax · CoordinatesDistance, midpoint and Cartesian coordinatesRead the reference $OpenStax official logo$ OpenStax · Complex numbersModulus, argument and polar representationRead the reference

References explain the mathematics; they do not imply institutional endorsement.