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Distance
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Enter coordinates to calculate
Manhattan Distance
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Midpoint
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Slope (2D)
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Δx, Δy
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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 It Works

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.

Worked Example

See It In Action

For the points (0, 0) and (3, 4) — a classic 3-4-5 right triangle: Δx=3, Δy=4, so Euclidean distance = √(3² + 4²) = √25 = 5. Manhattan distance = |3| + |4| = 7, and the midpoint between the two points is (1.5, 2).
Real-World Use Cases

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.
Common Mistakes

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.
Pro Tips

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.
Troubleshooting

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.

Glossary

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.

FAQ

Frequently Asked Questions

What's the difference between Euclidean and Manhattan distance?
Euclidean distance is the shortest possible straight-line path between two points, while Manhattan distance sums movement along perpendicular axes only — like navigating city blocks where you can't cut diagonally through buildings.
Why is Manhattan distance always greater than or equal to Euclidean distance for the same two points?
The straight-line (Euclidean) path is always the shortest possible route between two points by definition, so any path restricted to horizontal and vertical movement (Manhattan distance) can only be equal to or longer than it, never shorter.
Does the calculator work in 3D too?
Yes — switch to the 3D Distance tab to add a z-coordinate for each point, and the calculator extends the same Pythagorean-based formula to three dimensions.
How accurate are the unit conversions?
They use standard, widely accepted fixed conversion factors (such as 1 meter = 3.28084 feet), accurate to 6 decimal places — more than sufficient precision for virtually any practical use.