Excesso esférico
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The spherical excess calculator determines the difference between the sum of internal angles of a spherical triangle and π radians (180°). In spherical geometry, triangle angles sum to more than π radians, and this excess reflects the curvature of the spherical surface. The formula is (A + B + C) − π, where A, B, and C are the triangle's angles in radians.
This measure is critical in navigation, astronomy, and geodesy, where Earth's or celestial curvature affects precise calculations. For instance, when plotting air routes or calculating distances on a globe, spherical excess corrects deviations caused by the planet's round shape.
Important: angles must be provided in radians to ensure calculation accuracy. Additionally, spherical triangles do not follow flat geometry rules; results below π radians indicate input errors or incorrect formula application.
Frequently asked questions
What is spherical excess used for?
Spherical excess measures the curvature of a spherical triangle, used in air navigation, cartography, and astronomy to adjust calculations on curved surfaces like Earth.
How to convert degrees to radians before calculation?
Multiply degrees by π/180. Example: 90° = 1.5708 radians.
Why use radians instead of degrees?
The spherical excess formula requires radians for mathematical precision and consistency with spherical geometry.
What does a negative spherical excess mean?
A negative result means the input angles do not form a valid spherical triangle, as their sum is less than π radians.