Distance Formula Calculator
Find the straight-line distance between two coordinate points using the distance formula. The calculator shows delta x, delta y, squared distance, final distance, and length-unit conversions.
Formula
sqrt(dx^2 + dy^2)
Outputs
Distance + Deltas
Base Idea
Pythagorean Theorem
Live calculator
Distance between two points
Distance
5 cm
Delta x
3 cm
Delta y
4 cm
Squared distance
25 cm²
Distance in other units
| Unit | Converted value | Meaning |
|---|---|---|
| nm | 50,000,000 | Nanometers |
| um | 50,000 | Micrometers |
| mm | 50 | Millimeters |
| cm | 5 | Centimeters |
| dm | 0.5 | Decimeters |
| m | 0.05 | Meters |
| dam | 0.005 | Decameters |
| hm | 0.0005 | Hectometers |
| km | 0.0001 | Kilometers |
| mil | 1,968.5039 | Mils |
| in | 1.9685 | Inches |
| ft | 0.164 | Feet |
| yd | 0.0547 | Yards |
| mi | 0 | Miles |
| nmi | 0 | Nautical miles |
| pt | 141.7323 | Points |
| pc | 11.811 | Picas |
Formula substitution
d = sqrt((4 - 1)^2 + (6 - 2)^2)
The formula uses the horizontal and vertical change as the two legs of a right triangle, then takes the square root of the sum of their squares.
Measure straight-line distance on the coordinate plane
Distance value
Calculate the direct distance between two points instead of counting grid steps manually.
Delta breakdown
Show horizontal and vertical change before applying the square-root step.
Squared distance
Keep the squared sum visible for exact checks and Pythagorean theorem lessons.
Distance formula used on this page
The distance formula comes from the Pythagorean theorem applied to horizontal and vertical coordinate changes.
Working formulas
Distance formula
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Subtract x values and y values, square both changes, add them, and take the square root.
Horizontal change
dx = x2 - x1
This is the run or horizontal leg of the right triangle.
Vertical change
dy = y2 - y1
This is the rise or vertical leg of the right triangle.
Symbols
- d - distance
- The straight-line distance between the two coordinate points.
- dx - horizontal change
- The difference between the second x value and the first x value.
- dy - vertical change
- The difference between the second y value and the first y value.
- sqrt - square root
- The operation that converts the squared distance back to distance units.
Distance results with every formula component visible
Step-aware distance checks
- The calculator shows delta x, delta y, squared distance, and final distance together.
- Formula substitution keeps the Pythagorean relationship visible for students.
- The result updates as coordinates change, which makes comparing nearby examples fast.
- Copy and print controls support homework, worksheets, and graphing notes.
Coordinate geometry context
- FAQ answers explain why the formula squares coordinate differences before adding them.
- Related links connect distance to midpoint and slope, the other major two-point formulas.
- The page supports decimal, negative, horizontal, vertical, and diagonal point pairs.
- Squared distance is shown before the square root so exact-answer checks stay possible.
Distance formula support for graphing and geometry
Students
Check distance formula homework with deltas and squared distance shown.
Coordinate geometry
Measure line segments, diagonals, and plotted coordinate gaps quickly.
Teachers
Print examples that connect coordinate differences to the Pythagorean theorem.
How it works in three quick steps.
Enter the first coordinate
Add x1 and y1 for the first point.
Enter the second coordinate
Add x2 and y2 so the calculator can compute horizontal and vertical changes.
Read the distance
Square each change, add the squares, and take the square root to get the straight-line distance.
Save or print a distance formula result
Copy the distance
Copy coordinates, deltas, squared distance, and final distance in one summary.
Print the formula page
Print the calculator state, formula notes, FAQ answers, and related geometry links.
Compare point pairs
Adjust coordinates to compare horizontal, vertical, diagonal, and decimal examples.
Why the distance formula belongs beside slope and midpoint
The distance formula is a coordinate-plane version of the Pythagorean theorem. Instead of measuring a segment directly, users calculate horizontal change and vertical change from the coordinates, square those changes, add them, and take the square root. Toolarithm's Distance Formula Calculator keeps each part visible because most mistakes happen before the final square root. Users may reverse a subtraction, forget to square a value, or add coordinates instead of subtracting them. Showing delta x, delta y, squared distance, and final distance makes the calculation easier to audit.
This page completes a useful coordinate geometry cluster with slope and midpoint. The same pair of points can describe how steep a line is, where the segment center sits, and how long the segment is. The supporting content focuses on the calculation itself: why coordinate differences become triangle legs, why squaring removes direction, how units carry through the final distance, and how distance differs from midpoint and slope even when the input points are identical.
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