Distance Calculator
Input Coordinates
Results
| Distance (d) | — |
|---|---|
| Formula Used | — |
How to Use This Distance Calculator
Measuring the straight-line gap between two plotted points sounds simple until you are squaring differences on a cramped homework sheet or checking a 3D CAD offset. Pick 2D or 3D mode, enter both coordinate sets, and let the tool handle the root.
- Choose dimension mode. 2D Space uses x and y only. 3D Space reveals z fields for height or depth.
- Enter Point 1 and Point 2. Decimals and negative coordinates are fine. Leave no field blank in the active mode.
- Press Calculate Distance. The results table shows d and the formula string used for that mode.
- Review the step block. Differences, squares, and the final root are listed line by line for hand-checking.
For slope and line equations from the same two points, open the Slope Calculator.
Distance Formulas and Practical Applications
Euclidean distance is the shortest straight segment between two points—think of a string pulled tight between two nails, not a path that follows walls or roads.
Two-dimensional distance
d = √((x₂ − x₁)² + (y₂ − y₁)²)
From (1, 2) to (4, 6): Δx = 3, Δy = 4, so d = √(9 + 16) = 5. That is the same 3-4-5 right triangle the Pythagorean Theorem Calculator solves directly.
Three-dimensional distance
d = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²)
Add a floor-to-ceiling z separation when both points sit at different elevations—useful for conduit runs, drone waypoints, or multivariable calculus drills.
Where straight-line distance matters
- Checking whether two survey pins fall within a tolerance radius.
- Computing segment length before slope in analytic geometry.
- Validating a diagonal brace length against horizontal and vertical offsets.
Standard Units and Conversion Tables
Distance inherits whatever unit your coordinates use. All axes in one calculation should share that unit.
| Coordinate unit | Distance unit |
|---|---|
| Meters (m) | Meters (m) |
| Feet (ft) | Feet (ft) |
| Inches (in) | Inches (in) |
| Abstract grid units | Same grid units |
This is not driving or walking distance. For full triangle solving when you know sides and angles, use the Triangle Calculator. See all math calculators.
Frequently Asked Questions
What is the 2D distance formula?
d = √((x₂ − x₁)² + (y₂ − y₁)²). Square the axis differences, add, then take the square root.
How do you calculate 3D distance?
Include (z₂ − z₁)² under the root. Select 3D mode and fill all six coordinate fields.
Is this the same as driving distance?
No—this is straight-line Euclidean length. Road mileage follows curves and turns and needs a mapping tool, not this formula.
Can I use negative coordinates?
Yes. Signed values are normal on Cartesian graphs. Only the differences between points affect d.
Does the calculator show step-by-step work?
Yes—the step block below the table walks through Δx, Δy, (and Δz in 3D), the squared terms, and the final root.
Disclaimer. RapidRatio is informational only—not surveying, navigation, or professional engineering advice. Confirm measurements in the field with qualified methods.