Distance Calculator
Calculate 2D and 3D Euclidean distance, Manhattan distance, midpoint, and unit conversions.
Calculate the straight-line (Euclidean) distance between two points in 2D or 3D space, the Manhattan (grid) distance, the midpoint, and convert between length units.
How Distance Calculator Works
2D Euclidean distance applies the Pythagorean theorem: distance = √((x₂−x₁)² + (y₂−y₁)²) — treating the two points as opposite corners of a right triangle, where the horizontal gap (Δx) and vertical gap (Δy) are the two legs, and the direct distance between the points is the hypotenuse.
3D distance extends the same idea by adding a third dimension: distance = √(Δx² + Δy² + Δz²). Manhattan distance, by contrast, sums the absolute differences along each axis separately (|Δx| + |Δy| [+ |Δz|]), representing movement restricted to grid lines (like city blocks) rather than a direct diagonal path.
Midpoint is found by simply averaging the corresponding coordinates of the two points, and the unit conversion mode uses fixed, standard conversion factors (for example, 1 meter ≈ 3.28084 feet) to translate a single length value between metric and imperial units.
See It In Action
Who Uses Distance Calculator and Why
- Computing the straight-line distance between two coordinate points for a geometry or physics problem.
- Estimating grid-based travel distance between two locations, like delivery routing along city blocks, using Manhattan distance.
- Finding the midpoint between two locations for a meeting point or a geometry construction.
- Converting a measured length between metric and imperial units using the built-in conversion factors.
Mistakes to Avoid
- Using Manhattan distance when the actual shortest path (Euclidean distance) is what the situation actually calls for, or the reverse.
- Forgetting to switch to 3D mode when a z-coordinate or elevation genuinely matters for the calculation, understating the true distance.
- Mixing coordinate units between the two points, such as entering one point in meters and the other in feet before calculating.
Tips for Best Results
- Manhattan distance is always greater than or equal to Euclidean distance for the same two points — a quick way to sanity-check which figure you're looking at.
- Use the midpoint result directly rather than manually averaging each coordinate pair by hand.
Fixing Common Problems
The distance seems larger than expected for two coordinates that look close together. — Check whether you're reading the Manhattan distance value instead of the Euclidean one — Manhattan distance sums movement along each axis separately and is always equal to or greater than the direct straight-line distance.
Terms Explained
Euclidean distance: The shortest possible straight-line distance between two points, based on the Pythagorean theorem.
Manhattan distance: The sum of the absolute differences along each axis between two points, representing movement restricted to grid lines rather than a direct diagonal path.