How this calculation works
When the slant equals the difference of radii, the vertical height vanishes. A positive-height frustum requires a larger slant.
THE FORMULA
ℓ = A/[π(R+r)]A worked example
Radii 5 and 2 with lateral area 35π give slant height 5 and height 4.
Good to know
Use lateral area only. It excludes both circular ends.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Recover the slant height and vertical height of a cone frustum from its lateral area.
The primary result is labeled “Slant height”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use lateral area only. It excludes both circular ends.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Radii 5 and 2 with lateral area 35π give slant height 5 and height 4.
Which rule does this calculator apply?
ℓ = A/[π(R+r)]