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Great-Circle Distance — result sheet
Calculate the shortest spherical-surface distance and central angle between two latitude-longitude points on a sphere.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: a = sin^2((phi2 - phi1)/2) + cos(phi1) cos(phi2) sin^2((lambda2 - lambda1)/2); central angle = 2 atan2(sqrt(a), sqrt(1-a)); distance = R central angle.
Convert latitude and longitude differences from degrees to radians, evaluate the haversine central angle, and multiply that angle by the sphere radius to obtain the shorter great-circle arc distance.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sphere radius — distance units; Positive sphere radius in the same distance unit desired for the result.; minimum 1.0E-6; maximum 1000000000
- Point 1 latitude — degrees; Latitude of point 1 from -90 to 90 degrees.; minimum -90; maximum 90
- Point 1 longitude — degrees; Longitude of point 1 from -180 to 180 degrees.; minimum -180; maximum 180
- Point 2 latitude — degrees; Latitude of point 2 from -90 to 90 degrees.; minimum -90; maximum 90
- Point 2 longitude — degrees; Longitude of point 2 from -180 to 180 degrees.; minimum -180; maximum 180
Worked example
| Input | Value |
|---|---|
| Sphere radius | 6371 |
| Point 1 latitude | 0 |
| Point 1 longitude | 0 |
| Point 2 latitude | 0 |
| Point 2 longitude | 90 |
The central angle is pi/2 radians and the quarter-sphere distance is 6371 x pi/2 = about 10007.543 distance units.
Assumptions and limits
- The surface is an ideal sphere with the entered positive radius.
- Latitude is geodetic-style angular latitude in degrees and longitude is angular longitude in degrees within the displayed ranges.
- The output follows the shorter great-circle arc and does not model ellipsoidal flattening, terrain, altitude, or route restrictions.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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