The Area of a Triangle on a Sphere calculator computes the surface area of a triangle on a sphere based on the angle of the three corners and the radius of the sphere.
INSTRUCTIONS: Choose units and enter the following:
- (α) Angle opposite of Side A
- (β) Angle opposite of Side B
- (γ) Angle opposite of Side C
- (r) Radius of the Sphere (Earth Mean Radius: 6371.009 km)
Area of Triangle on a Sphere (A): The calculator returns the area in square kilometers. However this can be automatically converted to compatible units via the pull-down menu.
The Math / Science
The formula for the area of a spherical triangle on the surface of a sphere of radius ( r) formed by three great circle arc is:
A = (α + β + γ - π)⋅r2
where:
- A = area of triangle on surface of a sphere
- α = first angle
- β = second angle
- γ = third angle
- r = radius of the sphere
The triangle is defined by three angles (α,β,γ) at the vertices of the triangle.
Constraints:
- The three angles must have a sum greater than π.
- Each angle must be greater than zero and less than π.
Triangle Calculators
- Area of a triangle base on the base and height
- Area of a triangle using two sides and the interior angle.
- Area of a triangle using two angles and the interior side.
- Area of a triangle using three known sides.
- Area of a triangle defined by three points (x,y) in a plane.
- Height of a triangle based on the area and base
- Interior Angle of a triangle based on the length of three sides
- Semi-perimeter of a triangle
- Area between two vectors
- Area of Triangle on a Sphere
Sphere Calculators
- Sphere Surface Area based radius (r)
- Sphere Surface Area from Volume
- Sphere Volume from Radius
- Sphere Volume from Circumference
- Sphere Volume from Surface Area
- Sphere Volume from Mass and Density
- Sphere Radius from Volume
- Sphere Radius from Surface Area
- Sphere Weight (Mass) from volume and density
- Sphere Density
- Area of Triangle on a Sphere
- Distance between Two Points on a Sphere
- Sphere Cap Surface Area
- Sphere Cap Volume
- Sphere Cap Weight (Mass)
- Sphere Segment Volume
- Sphere Segment Weight (Mass)
- Sphere Segment Wall Surface Area (without the circular top and bottom ends)
- Sphere Segment Full Surface Area (with the top and bottom circles, aka ends)
- Volume of Spherical Shell
- Mass of Spherical Shell
