How this calculation works
Find the area enclosed by three minor great-circle sides using spherical excess.
Area = R²(A+B+C−π) for angles in radiansA worked example
Three 90° angles enclose one eighth of the sphere, giving 9π/2 at radius 3.
Good to know
Use a convex nondegenerate spherical triangle with angles below 180°.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the area enclosed by three minor great-circle sides using spherical excess.
The primary result is labeled “Area”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use a convex nondegenerate spherical triangle with angles below 180°.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Three 90° angles enclose one eighth of the sphere, giving 9π/2 at radius 3.
Which rule does this calculator apply?
Area = R²(A+B+C−π) for angles in radians