Distance Between Two Coordinates Calculator and Formula

A distance between two coordinates calculator finds the straight-line separation of two points from their coordinate values. Enter both points in the same coordinate system and units to get the distance; for latitude and longitude, use a geodesic or great-circle calculation rather than the flat-plane formula.

Formula

For two points in a two-dimensional Cartesian plane, subtract the first point’s coordinates from the second point’s coordinates, square both differences, add them, and take the square root:

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

• (x₁, y₁) are the coordinates of the first point.
• (x₂, y₂) are the coordinates of the second point.
• d is the straight-line distance, in the same units used for both coordinate axes.

The calculator accepts any real coordinate values, including negative values. Coordinates do not need to be positive: a point’s position relative to the origin determines its sign. The output is nonnegative because it represents a length.

Worked Example

Using the calculator’s defaults, the points are (0, 0) and (3, 4). The horizontal difference is |3 − 0| = 3 coordinate units, and the vertical difference is |4 − 0| = 4 coordinate units.

d = √[(3 − 0)² + (4 − 0)²] = √(9 + 16) = √25 = 5 coordinate units.

The displayed distance is 5.00 coordinate units. The right-triangle legs are 3 and 4, and the distance is the hypotenuse. The example uses the exact defaults shown in the calculator block.

When to Use a Coordinate Distance

This formula applies when coordinates describe positions on a flat, Cartesian grid. It is useful in geometry, school exercises, diagrams, maps or plans that use a local grid, and software calculations where points are represented by x and y values. It measures direct separation, not the route someone would travel between the points.

Coordinate units might be metres, feet, kilometres, or another consistent unit. If x and y are measured in metres, the answer is in metres. If the axes are measured in feet, the answer is in feet. The formula does not convert units automatically, so convert one coordinate system before calculating if the units differ. For example, do not combine an x difference of 3 metres with a y difference of 4 feet as if both numbers represented the same unit.

The same idea extends to three dimensions by adding a third squared difference: d = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]. This page’s calculator is for two coordinates, meaning two points with x and y values, not a three-dimensional calculation.

Flat Coordinates vs. Latitude and Longitude

A frequent source of error is treating latitude and longitude as ordinary x and y distances. Their values are angles, usually written in degrees, not lengths. One degree of longitude does not represent a fixed ground distance: its east–west span changes with latitude, and longitude lines meet at the poles. Simply putting latitude and longitude degree values into the Cartesian formula therefore does not give a reliable distance on Earth.

For two locations on Earth, use a great-circle or geodesic distance method. A great-circle calculation estimates the shortest path over a spherical Earth; a geodesic calculation can account for the Earth’s ellipsoidal shape. These methods require latitude and longitude in a consistent format, and results depend on the model and units selected. A map’s route distance may be longer because roads, trails, terrain, and access points do not follow the direct surface path.

For a small area, a local projected coordinate system can represent locations in linear units such as metres or feet, making a planar distance formula appropriate within the projection’s intended area. Projection choice matters: map projections can distort distances, especially far from the region for which they are designed.

How to Enter Coordinates and Read the Result

1. Identify the first point’s x and y values, then enter them as x1 and y1.
2. Enter the second point’s values as x2 and y2.
3. Check that both points use the same axis order, coordinate system, and units.
4. Read the distance as the direct straight-line separation. Use the horizontal and vertical differences as intermediate checks.

Swapping the two points does not change the distance because the differences are squared. Reversing the point order changes the signs of the coordinate differences, but not the final length. The separate dx and dy outputs show the absolute size of each axis difference; they are not additional distances to add together.

Common Mistakes and Limitations

• Adding differences instead of using the formula: |x₂ − x₁| + |y₂ − y₁| gives a grid or Manhattan distance, not the straight-line distance.
• Mixing units: Convert feet and metres, or other mismatched units, before calculating.
• Confusing coordinates with differences: The formula uses the change between corresponding coordinates, not the coordinate values as independent side lengths.
• Using rounded coordinates: Rounding inputs early can affect the final answer. Keep suitable precision through the calculation and round the displayed result to the precision the task needs.
• Applying a flat formula to Earth coordinates: Latitude and longitude require a geographic distance method, not a direct Cartesian calculation in degrees.

The result is mathematically exact for the supplied planar coordinates, apart from display rounding. It cannot correct inaccurate measurements, a wrongly chosen coordinate reference system, or projection distortion. It also does not account for barriers or travel routes. If you need walking, driving, or flight distance, calculate a route or use an appropriate geographic method instead.

Frequently Asked Questions

How do I calculate the distance between two points?
Subtract their x-coordinates and their y-coordinates, square each difference, add the squares, and take the square root: d = √[(x₂ − x₁)² + (y₂ − y₁)²].

Does the order of the coordinates matter?
No, provided you keep each point’s x and y values together. Reversing the two points changes the signs of the differences but leaves the distance unchanged.

Can I use negative coordinates?
Yes. Negative coordinates locate points on the other side of an axis or origin. Enter them with their signs; the distance formula works with positive and negative values.

Can I use this for latitude and longitude?
Not directly. Latitude and longitude are angular measurements, so use a great-circle or geodesic calculator designed for geographic coordinates.

What units will the answer use?
The result uses the same linear unit as the coordinate axes, as long as both axes use that unit. The formula does not perform unit conversion.

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in x1 | First point x-coordinate | - | 0 | -
in y1 | First point y-coordinate | - | 0 | -
in x2 | Second point x-coordinate | - | 3 | -
in y2 | Second point y-coordinate | - | 4 | -
out distance | Distance | coordinate units | sqrt((x2 - x1)^2 + (y2 - y1)^2) | 2
out dx | Horizontal difference | coordinate units | abs(x2 - x1) | 2
out dy | Vertical difference | coordinate units | abs(y2 - y1) | 2