Frustum Volume Calculator
A frustum is a cone (or pyramid) with the top sliced off by a cut parallel to the base, leaving a tapered shape with a circular top and a circular bottom — think of a bucket, plant pot or lampshade.
Enter Values
How to use this calculator
- Enter the bottom radius R, the top radius r, and the vertical height h.
- Press Calculate to get the volume in cubic metres and litres.
- For a full cone, set the top radius to 0; for a cylinder, make both radii equal.
How it works
A frustum is a cone (or pyramid) with the top sliced off by a cut parallel to the base, leaving a tapered shape with a circular top and a circular bottom — think of a bucket, plant pot or lampshade. This tool handles the conical frustum, where both ends are circles of radius R (bottom) and r (top).
The volume is V = (1/3) × π × h × (R² + R×r + r²), where h is the perpendicular height between the two circular faces. When r equals R the formula collapses to the cylinder volume πR²h, and when r is 0 it collapses to the cone volume (1/3)πR²h — the frustum sits neatly between those two extremes.
Worked example
Bottom radius 3 m, top radius 2 m, height 6 m. V = (1/3) × π × 6 × (3² + 3×2 + 2²) = (1/3) × π × 6 × 19 = 38π = 119.3805 m³ (119380.52 L).
Common mistakes
- Using the slant height (the sloped distance along the side) instead of the perpendicular height h between the two flat faces — always use the straight vertical height.
- Entering diameters instead of radii. Both R and r are radii (half the width across each circular face), so halve any diameter first.
- Mixing up which radius is which. Swapping R and r actually gives the same volume, so order doesn't matter — but both must be the radii of the parallel circular ends, not any middle width.
Frequently asked questions
What is a frustum?
A frustum is what's left when you slice the top off a cone or pyramid with a cut parallel to the base. This calculator covers the conical frustum — a truncated cone with a circular top and bottom, like a bucket or a plant pot.
Do I use the slant height or the vertical height?
Use the vertical (perpendicular) height h — the straight-up distance between the top and bottom circles. The slant height runs along the sloped side and is longer, so using it would overstate the volume.
How do I get a plain cone or a cylinder from this tool?
Set the top radius to 0 to compute a full cone ((1/3)πR²h), or make the top and bottom radii equal to compute a cylinder (πR²h). The frustum formula covers both as special cases.
Related tools
- Cone Volume Calculator
- Pyramid Volume Calculator
- Trapezoid Area Calculator
- Bin and Hopper Volume Calculator
- Stockpile Shape Volume Calculator
- Trench Volume Calculator
Explore more in Geometry, Shape, Area & Volume.
Tip: Enter any known values to calculate the remaining results.
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