📏 Geometry Tool

Distance Calculator

Calculate distance between two points in 2D or 3D, GPS coordinates using the Haversine formula, or city-grid (Manhattan) distance — with full step-by-step working.

Point A (x₁, y₁)

x₁

y₁

Point B (x₂, y₂)

x₂

y₂

Examples:

📏 Distance

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—Euclidean (d)

—Manhattan

—d² (squared)

—Midpoint

📐 Euclidean √(Δx²+Δy²)

🏙️ Manhattan |Δx|+|Δy|

♟️ Chebyshev max(|Δx|,|Δy|)

📝 Step-by-step solution

Coordinate graph

💡

Key insight

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Distance formulas

Different applications use different distance formulas. Euclidean is the straight-line ("as the crow flies") distance. Manhattan is the city-block distance. Haversine accounts for Earth's curvature for GPS coordinates.

Euclidean (2D): d = √((x₂−x₁)² + (y₂−y₁)²)
Euclidean (3D): d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)
Manhattan: d = |x₂−x₁| + |y₂−y₁|
Chebyshev: d = max(|x₂−x₁|, |y₂−y₁|)
Haversine: d = 2R·arcsin(√(sin²(Δφ/2) + cos(φ₁)·cos(φ₂)·sin²(Δλ/2)))
Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)

Frequently asked questions

What is the distance formula?

The 2D distance formula is d = √((x₂−x₁)² + (y₂−y₁)²). It comes from the Pythagorean theorem — the distance is the hypotenuse of a right triangle formed by the horizontal and vertical differences between the two points.

What is Manhattan distance?

Manhattan distance (also called taxicab or city-block distance) is |x₂−x₁| + |y₂−y₁|. It represents the distance when you can only travel horizontally or vertically — like navigating a grid of city streets. It is always ≥ Euclidean distance.

What is the Haversine formula?

The Haversine formula calculates the great-circle distance between two GPS coordinates on a sphere (Earth). It accounts for Earth's curvature, giving the "as the crow flies" distance between two geographic locations.

How do I find the midpoint between two coordinates?

The midpoint formula is M = ((x₁+x₂)/2, (y₁+y₂)/2). It gives the exact centre point between two coordinates. This calculator shows the midpoint alongside the distance in all modes.