Distance Formula Calculator – Guide & Formulas
Find the exact straight-line distance between two points using the Pythagorean-derived distance formula. Includes radical solvers.
Calculate the straight-line distance between any two coordinates. It automatically applies the algebraic distance formula and simplifies radicals.
Key Takeaway
Use the free Distance Formula Calculator to find the exact straight-line distance between two points using the pythagorean-derived distance formula. includes radical solvers. Get instant results with step-by-step explanations.
How to Use the Distance Formula Calculator
- Enter the coordinates of Point 1 (x₁, y₁).
- Enter the coordinates of Point 2 (x₂, y₂).
- View the distance in exact radical form and rounded decimal format.
The Formula
Variable Definitions
- d: Straight-line Euclidean distance
- x1, x2: Horizontal coordinate positions
- y1, y2: Vertical coordinate positions
Distance Between Two City Coordinates
Find the direct straight-line distance between coordinate (3, 5) and coordinate (9, 13) on a map grid.
- Step 1: Input coordinates: (3, 5) and (9, 13).
- Step 2: Subtract X-values and Y-values: (9 - 3) = 6, (13 - 5) = 8.
- Step 3: Square the differences: 6² = 36, 8² = 64.
- Step 4: Sum and take the square root: d = √(36 + 64) = √100 = 10 units.
Frequently Asked Questions
Why can distance never be negative?
Because the differences are squared before being summed, the values under the square root are always positive, resulting in a positive distance.
Is the distance formula just the Pythagorean theorem?
Yes. The horizontal difference represents side A, the vertical difference represents side B, and the distance is the hypotenuse C.
What is Manhattan distance versus Euclidean distance?
Euclidean distance is the diagonal "as the crow flies" straight line. Manhattan distance is the grid-like path (sum of horizontal and vertical changes).