How this calculation works
Find the radius of the circle where two sphere surfaces cross.
THE FORMULA
x=(d²+r₁²−r₂²)/(2d), ρ=√(r₁²−x²)A worked example
Two radius-five spheres six units apart meet on a circle of radius four.
Good to know
A tangent contact gives radius zero.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the radius of the circle where two sphere surfaces cross.
The primary result is labeled “Intersection circle radius”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A tangent contact gives radius zero.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Two radius-five spheres six units apart meet on a circle of radius four.
Which rule does this calculator apply?
x=(d²+r₁²−r₂²)/(2d), ρ=√(r₁²−x²)