Great Circle Calculator

Calculator Inputs

Start label

Optional label for the first location.

End label

Optional label for the second location.

Sphere preset

This updates the radius and unit fields.

Start latitude (degrees)

Allowed range: -90 to 90.

Start longitude (degrees)

Allowed range: -180 to 180.

End latitude (degrees)

Enter the second point latitude.

End longitude (degrees)

Enter the second point longitude.

Sphere radius

Distance output uses this same unit.

Distance unit label

Used for distance, chord, and speed labels.

Travel speed (optional)

Interpreted as unit per hour.

Decimal precision

Controls displayed decimal places.

Graph route points

Higher values make the curve smoother.

Reset

Example Data Table

Route	Start Coordinates	End Coordinates	Radius	Speed	Use Case
New York to London	40.7128, -74.0060	51.5074, -0.1278	6371 km	900 km/h	Flight planning example
Tokyo to Sydney	35.6762, 139.6503	-33.8688, 151.2093	6371 km	850 km/h	Long-distance route study
Moon rover path	12.5000, 18.2000	-4.1000, 45.9000	1737.4 km	12 km/h	Spherical surface modeling

Formula Used

This calculator uses spherical geometry. A great circle is the shortest path between two points on a sphere. It is useful in navigation, geophysics, astronomy, and route analysis.

1) Central angle with the haversine form

a = sin²(Δφ / 2) + cos(φ₁) · cos(φ₂) · sin²(Δλ / 2)
c = 2 · asin(√a)

2) Great circle distance

d = R · c

3) Chord length through the sphere

chord = 2R · sin(c / 2)

4) Initial bearing

θ = atan2[sin(Δλ) · cos(φ₂), cos(φ₁) · sin(φ₂) − sin(φ₁) · cos(φ₂) · cos(Δλ)]

5) Midpoint on the great circle

The midpoint is computed from spherical vector relationships using both coordinates and the longitudinal difference.

Here, φ is latitude in radians, λ is longitude in radians, Δ means difference, and R is the chosen sphere radius.

How to Use This Calculator

Enter optional labels for the two locations.
Type the start and end latitude and longitude values.
Choose a sphere preset or enter a custom radius manually.
Select the output unit label that matches your radius value.
Add travel speed if you also want estimated travel time.
Set decimal precision and the number of route points for plotting.
Press Calculate Great Circle to show results above the form.
Use the CSV or PDF buttons to export the current result.

FAQs

1) What does a great circle represent?

A great circle is any circle on a sphere whose center matches the sphere’s center. It gives the shortest surface route between two points on that sphere.

2) Why is the result different from a flat map distance?

Flat maps distort the curved surface of a sphere. Great circle distance follows spherical geometry, so it is usually more accurate for global travel and physics-based surface calculations.

3) Can I use planets other than Earth?

Yes. Enter the proper mean radius for any spherical body, such as Mars or the Moon. The calculator then returns distance and chord values for that chosen sphere.

4) What unit should I use for radius?

Use any consistent unit for radius, such as kilometers, miles, meters, or nautical miles. The returned distance and chord length will match that same unit.

5) What does the initial bearing mean?

The initial bearing is the starting direction you would follow from the first point along the great circle path. It is measured clockwise from geographic north.

6) Why can the final bearing differ from the initial bearing?

On a sphere, the route curves relative to latitude and longitude lines. Because of that curvature, the arrival direction at the destination often differs from the starting direction.

7) What is chord length used for?

Chord length is the straight line through the sphere between two surface points. It helps compare surface travel distance with internal straight-line separation.

8) Is this calculator suitable for precise geodesy?

It is excellent for spherical modeling and education. For highest Earth accuracy, professional geodesy usually uses an ellipsoidal model instead of a perfect sphere.