Math
Sphere volume and surface area
Find the surface area and volume of a sphere.
Calculators / Math / Spherical triangle area
Spherical triangle area calculator
Find the area of a convex triangle bounded by great-circle arcs on a sphere.
On this page
Spherical excess30degrees
Area52.36units²
Calculator controls
How to calculate
Find the area of a convex triangle bounded by great-circle arcs on a sphere.
Spherical excess =
A+B+C-180 degreesArea =
(A+B+C-180)*pi/180*R^2 units²Worked example
- First interior angle (degrees): 80
- Second interior angle (degrees): 70
- Third interior angle (degrees): 60
- Sphere radius: 10
- Spherical excess: 30 degrees
- Area: 52.36 units²
Assumptions and limits
Use spherical interior angles, not flat-map angles. The sphere is ideal; ellipsoidal Earth models and triangles with major arcs need separate methods.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the area of a convex triangle bounded by great-circle arcs on a sphere. The angular excess above 180 degrees determines the fraction of spherical surface enclosed.
When this tool is useful
The angular excess above 180 degrees determines the fraction of spherical surface enclosed.
Understanding your inputs
| Input | Example |
|---|---|
First interior angle (degrees) A | 80 |
Second interior angle (degrees) B | 70 |
Third interior angle (degrees) C | 60 |
Sphere radius R | 10 |
Frequently asked questions
Which assumptions matter for this result?
Use spherical interior angles, not flat-map angles. The sphere is ideal; ellipsoidal Earth models and triangles with major arcs need separate methods.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.