Distance Between Points Calculator - Free 2D & 3D Distance Calculator
Distance Between Points Calculator
Calculate the distance between two points in 2D or 3D space. Also find the midpoint and slope (for 2D).
Point 1 (Pā)
Point 2 (Pā)
How to use this calculator
š How to Use the Distance Calculator
- Choose between 2D (x, y) or 3D (x, y, z) distance calculation
- Enter the coordinates for Point 1 (Pā)
- Enter the coordinates for Point 2 (Pā)
- Click Calculate to find the distance
- View the visual graph, midpoint, and slope (for 2D)
š Distance Formulas
2D Distance Formula:
d = ā[(xā-xā)Ā² + (yā-yā)Ā²]
For points in a plane (x, y coordinates)
3D Distance Formula:
d = ā[(xā-xā)Ā² + (yā-yā)Ā² + (zā-zā)Ā²]
For points in space (x, y, z coordinates)
Related Formulas:
- Midpoint = ((xā+xā)/2, (yā+yā)/2)
- Slope = (yā-yā)/(xā-xā)
š Real-World Examples
Example 1: Map Distance
Find the straight-line distance between two cities with coordinates (30, 40) and (90, 120). Distance = 100 units.
Example 2: 3D Space
Distance between points (1, 2, 3) and (4, 6, 8) in 3D space is ā50 ā 7.07 units.
Example 3: Screen Pixels
Distance between pixels at (100, 200) and (400, 500) on a screen is 424.26 pixels.
š” Pro Tips
- ā¢ The distance formula comes from the Pythagorean theorem
- ā¢ Distance is always positive (it's a magnitude)
- ā¢ The midpoint is exactly halfway between the two points
- ā¢ Slope tells you the steepness and direction of the line
- ā¢ Undefined slope means a vertical line
- ā¢ Zero slope means a horizontal line
- ā¢ For GPS coordinates, use specialized formulas that account for Earth's curvature
ā ļø Common Mistakes to Avoid
- ā¢ Don't forget to subtract in the correct order: (xā - xā), not (xā - xā)
- ā¢ Remember to square the differences before adding them
- ā¢ Take the square root at the end, not of each term separately
- ā¢ Check that you're using the same units for all coordinates
- ā¢ For slope, remember that division by zero gives undefined (vertical line)
About this calculator
Calculate the distance between two points in 2D or 3D space. Find distance, midpoint, and slope with visual representation and step-by-step solutions.
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