About the conical frustum calculator
A frustum is what remains of a cone after slicing off its tip parallel to the base. Buckets, paper cups, flower pots and lampshades are frustums. Its volume formula πh(R² + Rr + r²)/3 reduces to the cone formula when r = 0 and to the cylinder when r = R.
Formulas
| Volume | V = πh(R² + Rr + r²)/3 |
| Slant height | l = √(h² + (R − r)²) |
| Lateral area | L = π(R + r)l |
| Total surface | S = L + πR² + πr² |
Frequently asked questions
How much does a bucket hold?
Measure the bottom and top radii and the height, then V = πh(R² + Rr + r²)/3. The result is converted to litres and gallons for you.