Calculate Euclidean distances on a 2D Cartesian plane, 3D coordinate space, and find spherical geodesic (great-circle) flight distances between latitude/longitude points on Earth.
• Tool 1 (2D Distance): Calculates Euclidean distance d = √[(ΔX)² + (ΔY)²] and line slope m.
• Tool 2 (3D Distance): Calculates 3D space diagonal d = √[(ΔX)² + (ΔY)² + (ΔZ)²].
• Tool 3 (Lat/Lon Geodesic): Computes shortest great-circle distance on Earth using the Haversine formula.
• Tool 4 (Interactive Map): Click anywhere on the world map to measure distances and initial bearing.
Use this calculator to find the distance between two points on a 2D coordinate plane.
Enter coordinates for Point 1 and Point 2 on the left and click "Calculate" to view Euclidean distance and line slope.
Understanding Euclidean flat geometry, 3D space vectors, the Haversine great-circle formula, and unit conversions.
In traditional Euclidean geometry, the shortest distance between two points is a straight line segment. However, across large distances on Earth, straight lines through the planet's mantle are physically impossible for travel. Instead, navigation relies on Spherical Geodesics (great-circle routes), which represent the shortest path along the curved surface of a sphere.
Derived from the Pythagorean Theorem (a² + b² = c²).
Calculates true line-of-sight distance in 3D coordinate space.
Computes flight and maritime shortest-path distances on Earth.
| Unit | Equivalent in Kilometers | Equivalent in Miles | Primary Usage |
|---|---|---|---|
| Kilometer (km) | 1.0000 km | 0.62137 mi | Metric road and geographic navigation |
| Statute Mile (mi) | 1.60934 km | 1.0000 mi | US & UK customary road transport |
| Nautical Mile (NM) | 1.85200 km | 1.15078 mi | Aviation flight plans and maritime voyages |
A great circle is any circle that divides the Earth into two equal hemispheres. The shortest distance between any two points on a sphere lies along the arc of a great circle, which is why transatlantic aircraft fly curved flight paths on flat map projections.
A nautical mile is historically defined as one minute of arc (1/60th of a degree) along a meridian of the Earth, equal to exactly 1,852 meters (~1.1508 statute miles). It is universally used in aviation and marine navigation.
2D distance accounts only for horizontal (X) and vertical (Y) coordinates. 3D distance adds altitude or depth (Z) via Pythagoras: d = √[(X₂-X₁)² + (Y₂-Y₁)² + (Z₂-Z₁)²].
Because great circles cross meridians at changing angles, the compass direction needed to start flying directly toward your destination is the initial forward bearing.