Frustum Volume Calculator
Calculate truncated cone frustum volume from top & bottom radii or diameters and height. Perfect for buckets, pots, planters, and lampshades.
The frustum volume formula derives from subtracting a smaller imaginary cone from a larger parent cone.
Multiplying by the height and π/3 yields the exact capacity of the truncated cone, bucket, or tapered flower pot.
The volume of a conical frustum (truncated cone) is V = (1/3) × π × h × (R² + r² + R×r). For a 5-gallon bucket with 12" top diameter, 10" bottom diameter, and 14" height, the volume is 1,334.1 cubic inches (5.77 US gallons).
Frustum Volume Calculator Formula
| Variable | Definition | Standard Units |
|---|---|---|
| V | Internal volume of the truncated cone | in³, ft³, gal, L, cm³ |
| R | Larger radius (e.g. top opening or base) | in, ft, cm, or m |
| r | Smaller radius | in, ft, cm, or m |
| h | Vertical perpendicular height between planes | in, ft, cm, or m |
Understanding the Conical Frustum Formula
A frustum is created by slicing off the pointed apex of a cone with a plane parallel to its base. The volume formula derives from taking a large imaginary cone and subtracting the smaller missing top cone. The resulting term (R² + r² + Rr) combines the bottom area, top area, and their geometric mean.
Common Calculation Mistakes to Avoid
- Averaging the top and bottom radii and treating it like a standard cylinder (underestimates volume)
- Using the slant height along the tapered side instead of vertical perpendicular depth
- Entering diameters directly into the radii formula
Frequently Asked Questions
What is the formula for the volume of a frustum?▼
Can you just average the top and bottom diameters of a bucket?▼
How do you calculate the volume of a tapered bucket or flower pot?▼
What is the slant height of a conical frustum?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.