Frustum Volume Calculator (Truncated Cone)
By Santaji GadepatilinUpdated November 6, 2026
A frustum is a cone with its top cut off parallel to the base — the shape of buckets, flower pots, lampshades and many hoppers. This frustum volume calculator gives the volume, slant height, lateral area and total surface area of a conical frustum from the bottom and top radii and the height.
How to use the frustum volume calculator
Enter the large radius, the small radius and the height between the two parallel faces. For a bucket or pot measured by diameter, halve each diameter first. The calculator gives the volume, the slant height and the surface areas.
Frustum formulas
V = (π h / 3)(R² + R r + r²) · s = √(h² + (R − r)²)
Lateral area = π (R + r) s · Total area = π (R + r) s + π R² + π r²
Worked example
R = 5 cm, r = 3 cm, h = 4 cm:
- V = (π × 4 ÷ 3)(25 + 15 + 9) = 205.25 cm³
- Slant height = √(16 + 4) = 4.472 cm
- Lateral area = π × 8 × 4.472 = 112.40 cm²; total area = 219.21 cm²
Bucket and tub volumes
| Top diameter | Bottom diameter | Depth | Volume |
|---|---|---|---|
| 30 cm | 25 cm | 30 cm | 17.87 L |
| 28 cm | 24 cm | 26 cm | 13.83 L |
| 32 cm | 26 cm | 35 cm | 23.20 L |
| 40 cm | 30 cm | 40 cm | 38.75 L |
| 60 cm | 45 cm | 70 cm | 152.56 L |
Notes
- If r = 0 the formula becomes the cone volume πR²h/3; if r = R it becomes the cylinder πR²h.
- For a partly filled bucket, use the radius at the liquid surface as the top radius and the liquid depth as h.
Frequently asked questions
What is the formula for the volume of a frustum?
V = (πh/3)(R² + Rr + r²), where R and r are the radii of the two circular ends and h is the perpendicular height.
How do I find the slant height of a frustum?
s = √(h² + (R − r)²). The lateral surface area is then π(R + r)s.
How do I calculate the volume of a bucket?
Measure the top and bottom diameters and the depth, halve the diameters to get radii, and use the frustum formula. Divide cm³ by 1,000 for litres.
What about a square or rectangular frustum?
For any frustum with similar parallel ends of areas A₁ and A₂, V = (h/3)(A₁ + A₂ + √(A₁A₂)). For a square frustum with sides a and b that is (h/3)(a² + ab + b²).