Mapping Calculator
Mapping calculator works out Distance and Distance unit from Latitude 1, Longitude 1 and Latitude 2. The default figures on this page give distance of 10,007.5572; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- a = sin²(Δφ/2) + cos φ₁·cos φ₂·sin²(Δλ/2)
- a = 0.5, σ = 2·arcsin(√a) = 1.570796326795 rad
- d = R·σ = 6371.0088 km × 1.570796326795 = 10007.55722102 km
- Initial bearing = 90° (E); final bearing = 90°
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the mapping calculator calculates
Computes the shortest surface distance and the initial and final bearings between two latitude/longitude points using the haversine formula, the spherical law of cosines, an equirectangular approximation or Vincenty’s inverse solution on the WGS84 ellipsoid.
How to use this mapping calculator
Enter Latitude 1, Longitude 1, Latitude 2 and Longitude 2. Distance updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Distance, Distance unit and Initial bearing.
The method follows R. W. Sinnott, "Virtues of the Haversine", Sky and Telescope 68(2), 159, T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations", Survey Review XXIII(176), 88–93, Chris Veness, "Calculate distance, bearing and more between latitude/longitude points", Movable Type Scripts and NGA, Department of Defense World Geodetic System 1984 (WGS 84), NGA.STND.0036 — a = 6378137 m, 1/f = 298.257224.
Quarter of the equator: (0,0) to (0,90) with R = 6371 km example
With Latitude 1: 0, Longitude 1: 0, Latitude 2: 0, Longitude 2: 90, the calculator returns Distance: 10007.5434, Initial bearing: 90, Midpoint longitude: 45. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Distance, Distance unit and Initial bearing. The inputs you can vary are Latitude 1, Longitude 1, Latitude 2, Longitude 2, Model and Distance unit.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How can I map my distance?
Computes the shortest surface distance and the initial and final bearings between two latitude/longitude points using the haversine formula, the spherical law of cosines. Open “How this is worked out” beside the result to see each step for your own figures.
What information do I need for the mapping calculator?
You need Latitude 1, Longitude 1, Latitude 2, Longitude 2, Model, Distance unit and Sphere radius. The page opens with default figures that give distance of 10,007.5572, so you can see the scale before entering your own.
What does this mapping calculator show?
It shows Distance, Distance unit, Initial bearing, Final bearing, Compass direction, Angular separation, Midpoint latitude and Midpoint longitude, with the working and any warnings for your entries.
Can I check how the mapping calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.