How this calculation works
Find the radius and area of the circular section made by a plane through a sphere.
THE FORMULA
ρ=√(R²−d²)A worked example
At offset 3 in a sphere of radius 5, the section radius is 4.
Good to know
A plane farther away than the radius does not cut the sphere.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the radius and area of the circular section made by a plane through a sphere.
The primary result is labeled “Section radius”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A plane farther away than the radius does not cut the sphere.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
At offset 3 in a sphere of radius 5, the section radius is 4.
Which rule does this calculator apply?
ρ=√(R²−d²)