Distance between two points calculator (x, y)

How to use the distance calculator

1. Enter the first point in x₁ and y₁.
2. Enter the second point in x₂ and y₂.
3. Read the Distance. Below it you get Δx, Δy and the Manhattan distance.
4. Copy the Working box if you need to show your method.

What it does and when to use it

Plot two points on graph paper and join them with a ruler: this tool measures that line. Students use it for coordinate-geometry homework, such as checking whether a triangle is isosceles or finding the radius of a circle from its centre and a point on it. It also helps in game design, CAD drawings and any grid where you need “how far apart” in a straight line.

If you also want the midpoint and the slope, the coordinate line properties tool gives all of them at once. For points with a z value, use the 3D distance calculator.

How it works

The tool uses the distance formula:

d = √((x₂ − x₁)² + (y₂ − y₁)²)

It first finds the change in each direction, Δx = x₂ − x₁ and Δy = y₂ − y₁. Those are the legs of a right triangle, so the Pythagorean theorem gives the hypotenuse. The Manhattan distance is |Δx| + |Δy|.

Worked examples

Step by step. From (−3, 2) to (5, −4).

1. Δx = 5 − (−3) = 8.
2. Δy = −4 − 2 = −6.
3. Square them: 8² = 64 and (−6)² = 36.
4. Add and take the root: the working ends √(64 + 36) = √100 = 10.

The tool also reports Manhattan distance: 14, because a grid path would go 8 across and 6 down.

A distance that is not whole. From (2, 3) to (7, 5): Δx = 5 and Δy = 2, so d = √29, shown as Distance: 5.385164807. In an exam you may be asked to leave it as √29; the working line shows that form.

Limits and tips

• Watch the signs when subtracting a negative number. The working writes it as “5 − -3”, which means 5 + 3.
• The tool has no units. The answer is in the same unit as your coordinates.
• Results are shown to up to 10 significant figures.
• Nothing is sent anywhere; the sums run in your browser.