Home·Geometry

Distance Between Two Points

Square the x-difference and the y-difference, add, take the root — the Pythagorean theorem applied to coordinates.

Your numbers

Distance

10

Angle (°)

53.13°

Formula

Distance = √((x₂−x₁)² + (y₂−y₁)²)

From (1,2) to (7,10) the distance is exactly 10. The angle is measured counter-clockwise from the x-axis.

What to enter

InputDefaultAccepted range
x₁The horizontal coordinate of the first point.1No limit
y₁The vertical coordinate of the first point.2No limit
x₂The horizontal coordinate of the second point.7No limit
y₂The vertical coordinate of the second point.10No limit

Step by step

FormulaDistance = √((x₂−x₁)² + (y₂−y₁)²)
With the default numbersDistance = √((7−1)² + (10−2)²)
AnswerDistance = 10

Quick reference table

Results when only y₁ changes and everything else stays put.

y₁DistanceAngle (°) (°)
110.816756.31
1.510.404354.78
21053.13
39.219549.4
48.485345

What each result means

ResultAt default values
DistanceThe straight-line distance between two points.10
Angle (°) (°)An angle in degrees; a full turn is 360°.53.13

Common mistakes

From (1,2) to (7,10) the distance is exactly 10. The angle is measured counter-clockwise from the x-axis.

Glossary

x₁
The horizontal coordinate of the first point.
y₁
The vertical coordinate of the first point.
x₂
The horizontal coordinate of the second point.
y₂
The vertical coordinate of the second point.
Distance
The straight-line distance between two points.
Angle (°)
An angle in degrees; a full turn is 360°.

Frequently asked questions

Q. How is Distance Between Two Points calculated?

Distance = √((x₂−x₁)² + (y₂−y₁)²) — Square the x-difference and the y-difference, add, take the root — the Pythagorean theorem applied to coordinates.

Q. Can you walk through an example?

With x₁ 1, y₁ 2, x₂ 7, y₂ 10, the answer is Distance 10.

Q. What do I need to enter?

Enter x₁, y₁, x₂, y₂. The result recalculates as you type, and an empty box counts as zero.

Q. How much does the answer move if I change a number?

Changing only y₁ moves the answer to y₁ 1 → Distance 10.8167 and y₁ 4 → Distance 8.4853. The table below lays out five steps.

Q. How are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

Q. Anything to watch out for?

From (1,2) to (7,10) the distance is exactly 10. The angle is measured counter-clockwise from the x-axis.

Related calculators

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.