What This Tool Does
Calculate the straight-line (Euclidean) distance between two coordinate points. Choose 2D or 3D, enter both points, and the result shows the distance, formula, and intermediate values.
The Governing Formula
For two points in 2D, (x1, y1) and (x2, y2), the distance formula is:
d = sqrt((x2 − x1)² + (y2 − y1)²)
This comes directly from the Pythagorean theorem: the difference in x and the difference in y form the two legs of a right triangle, and the distance is the hypotenuse. In 3D, a third coordinate difference is added under the square root:
d = sqrt((x2 − x1)² + (y2 − y1)² + (z2 − z1)²)
Inputs and Unit Label
- Choose 2D (x, y) or 3D (x, y, z). The z fields are hidden in 2D and required in 3D.
- Enter x1, y1, x2, and y2. In 3D, also enter z1 and z2.
- Coordinates may be positive, negative, zero, or decimal values.
- Unit offers Unitless (plain coordinates), Millimeters (mm), Centimeters (cm), Meters (m), Kilometers (km), Inches (in), Feet (ft), Yards (yd), and Miles (mi). The selection labels the result; it does not convert units.
How to Use the Distance Formula Calculator
- Choose 2D (x, y) or 3D (x, y, z).
- Fill in the coordinate fields for Point 1 and Point 2.
- Select a value in Unit if you want a unit label.
- Click Calculate. After a successful calculation, the Result area shows distance statistics and Formula & steps.
- Use Copy result or Download result (.txt) to save the output. If copying fails, select and copy the result manually.
- Click Reset to clear the fields, restore Unitless (plain coordinates), switch to 2D, and hide the result or error.
Validation and Result States
- Leave a field blank and it shows a required-field error. Other invalid input shows an error instead of a result.
- Enter trimmed decimal values with an optional leading minus sign. Leading plus signs and exponent notation are not accepted.
- Coordinates with an absolute value greater than
1e12are rejected as too large to calculate. - Changing between 2D and 3D clears errors and hides the current result.
Limits and Coordinate Assumptions
The calculator uses flat Cartesian geometry for two points in 2D or 3D. Both points must use the same coordinate system and unit. It does not convert units, use latitude/longitude, account for map projections or Earth's curvature, use elevation data, calculate roads or paths, or infer missing coordinates. It is not certified surveying, engineering, or professional advice.
Calculation Privacy
The calculation script processes the coordinates locally in your browser and does not submit those coordinate values as part of generating the result.
Frequently Asked Questions
What is the distance formula?
For two 2D points (x1, y1) and (x2, y2), the distance is d = sqrt((x2 - x1)^2 + (y2 - y1)^2). It is derived directly from the Pythagorean theorem.
How is 3D distance calculated?
For two 3D points (x1, y1, z1) and (x2, y2, z2), the distance is d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2), extending the 2D formula with a third coordinate difference.
Can coordinates be negative?
Yes. Coordinates can be positive, negative, or zero decimal values, provided they match the accepted input format and do not exceed the calculator's 1e12 magnitude limit. The formula uses squared differences, so the sign of each coordinate does not affect validity.
What units does this calculator support?
You can label the result as unitless or in millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. The calculator does not convert between units - it assumes both points are already expressed in the same unit you select.
Does this calculator work for real-world map distances?
No. This tool computes straight-line (Euclidean) distance on a flat plane or in flat 3D space from coordinates you provide. It does not account for Earth's curvature, elevation data, or GPS coordinate systems.