Distance Between Two Points

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

Your numbers

x₁y₁x₂y₂

Distance

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

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

y₁	Distance	Angle (°) (°)
1	10.8167	56.31
1.5	10.4043	54.78
2	10	53.13
3	9.2195	49.4
4	8.4853	45

What each result means

Result	At 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

QHow 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.

QCan you walk through an example?

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

QWhat do I need to enter?

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

QHow 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.

QHow 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.

QAnything 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

Pythagorean TheoremFind the hypotenuse from the two legs of a right triangle.Missing Leg of a Right TriangleFind the remaining side from the hypotenuse and one leg.Angle from Two SidesGet the angle of a slope from its rise and run.Trig Function ValuesEnter an angle and see sine, cosine and tangent at once.

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