Calculate the distance between two points using Euclidean, Manhattan, or Haversine formulas. Supports 2D, 3D, and geographic coordinates.
Distance
5.0000
units
Formula
d = √[(x₂-x₁)² + (y₂-y₁)²]
Distance
5.000000
units
"As the crow flies" - straight-line distance. Uses Pythagorean theorem. Most common for geometric calculations.
Sum of absolute differences in each dimension. Used in grid-based pathfinding, machine learning, and urban navigation.
Great-circle distance on a sphere. Accounts for Earth's curvature. Essential for GPS/navigation applications.
Extended Euclidean formula for 3D space. Used in 3D graphics, physics simulations, and spatial analysis.
Distance
5.0000
units
Quick-start with common scenarios
Test your skills with practice problems
Practice with 3 problems to test your understanding.
The distance formula finds the straight-line distance between two points. In 2D: d = sqrt((x2-x1)^2 + (y2-y1)^2). In 3D: d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). This is derived from the Pythagorean theorem. For points (1,2) and (4,6), distance = sqrt(9+16) = sqrt(25) = 5.
Distance in coordinate geometry is the length of the straight line connecting two points. The distance formula, derived from the Pythagorean theorem, calculates this Euclidean distance using the differences in coordinates. It is fundamental to geometry, physics, navigation, computer graphics, and many scientific applications.
The distance formula finds the straight-line distance between two points. In 2D: d = sqrt((x2-x1)^2 + (y2-y1)^2). In 3D: d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). This is derived from the Pythagorean theorem. For points (1,2) and (4,6), distance = sqrt(9+16) = sqrt(25) = 5.
The distance formula finds the length between two points. In 2D: d = √[(x₂-x₁)² + (y₂-y₁)²]. This is derived from the Pythagorean theorem. In 3D, add (z₂-z₁)² under the square root.
Manhattan distance (also called taxicab or L1 distance) measures distance along grid lines, like walking city blocks. It's |x₂-x₁| + |y₂-y₁|. Named after Manhattan's grid street layout where you can't travel diagonally.
Use the Haversine formula for great-circle distance on a sphere. It accounts for Earth's curvature. For short distances (<10km), the simple formula works well. For accuracy, use WGS84 ellipsoid calculations.
Use 2D Euclidean for flat surfaces and direct "as the crow flies" distance. Use 3D for points in space. Use Manhattan for grid-based movement (game AI, urban navigation). Use Haversine for geographic coordinates on Earth.
Distance is the total length traveled along any path (scalar, always positive). Displacement is the shortest straight-line distance between start and end points with direction (vector). Distance ≥ |Displacement|.
Last updated: 2025-01-15
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Distance
5.0000
units