Mathematics · Geometry
Great-Circle Distance Calculator
Calculate spherical surface distance between two latitude-longitude points.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Haversine term=0.00007615242180438042.
- Central angle=0.017453292519943295; distance=6371×0.017453292519943295=111.19492664455873.
Problem → model → reason → result
What problem does this model solve?
Calculate spherical surface distance between two latitude-longitude points.
Why does the model apply?
The haversine formula measures the central angle between points on a sphere.
What assumptions does it make?
Lengths use one consistent unit, the named shape is ideal, and dimensions refer to the perpendicular or straight-line measurements specified by the model.
Formula
d=R·2asin√[sin²(Δφ/2)+cosφ₁cosφ₂sin²(Δλ/2)]
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
Along the equator, one degree of longitude is about 111.2 km on Earth.
Common mistake
Earth is not a perfect sphere; high-precision geodesy uses an ellipsoid.
When does this model not apply?
Irregular shapes, measurement error and non-ideal surfaces require a more detailed model or measured uncertainty.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Great-circle distance do?
Calculate spherical surface distance between two latitude-longitude points.
How does the Great-circle distance work?
The calculator applies d=R·2asin√[sin²(Δφ/2)+cosφ₁cosφ₂sin²(Δλ/2)]. The haversine formula measures the central angle between points on a sphere.
What can I learn from the Great-circle distance?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.