About the Cone Frustum Calculator
A frustum is a cone with its tip cut off by a plane parallel to its base, like a bucket, a flower pot, a lampshade or a paper cup. This calculator takes the bottom radius, the top radius and the height, and gives the volume, the slant height, the area of the sloping side and the total surface area including both ends. Type the bottom radius, the top radius and the height and the frustum volume appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Cone Frustum Calculator
- 1Enter the bottom radius, the top radius and the height.
- 2Pick the units or options from the menus if the frustum volume tool offers them.
- 3Read the frustum volume in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the frustum volume
Designers use it for buckets, cups, planters and lamp shades, where the volume tells how much it holds and the side area how much material forms the wall. Builders use it for tapered concrete pillars and funnels.
A useful check: a frustum whose top radius is zero is a plain cone, and the volume formula becomes one third of π r² h. The tool accepts both radii above zero only, but you can try a very small value to see it.
How the frustum volume is worked out
Volume = π × h × (r1² + r1 × r2 + r2²) ÷ 3. Slant height = √(h² + (r1 − r2)²). Side area = π × (r1 + r2) × slant height. A frustum with radii 5 and 3 and a height of 6 has a volume of 307.88, a slant height of 6.325, a side area of 158.95 and a total surface area of 265.77. If the two radii are equal the shape becomes a cylinder.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Two radii and a height
- Slant, side and total areas
- Symmetric in the radii
Mistakes to avoid with frustum volume
The height is the vertical distance between the two flat faces, not the slant length along the side. Confusing them overstates the volume. The slant height is the one that you need to cut a paper pattern for the side.
On phone and computer
On a phone, type into the boxes one after another and read the frustum volume underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the frustum volume move. The cone frustum calculator works the same on both. A frustum is a cone with its tip removed, so Cone Calculator handles the full cone and Cylinder Calculator handles a straight sided cup. Volume Calculator and Surface Area Calculator cover other solids.
Features
- Height is vertical
- Slant height for patterns
- Equal radii give a cylinder
- Clear messages when the frustum volume inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate frustum volume?
Volume = π × h × (r1² + r1 × r2 + r2²) ÷ 3. Slant height = √(h² + (r1 − r2)²). Side area = π × (r1 + r2) × slant height. A frustum with radii 5 and 3 and a height of 6 has a volume of 307.88, a slant height of 6.325, a side area of 158.95 and a total surface area of 265.77. If the two radii are equal the shape becomes a cylinder.
What is the formula for frustum volume?
Volume = π × h × (r1² + r1 × r2 + r2²) ÷ 3. Slant height = √(h² + (r1 − r2)²). Side area = π × (r1 + r2) × slant height. The cone frustum calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is the slant height used for?
It is the length along the sloping side, needed for cutting a flat pattern or measuring the surface.
How do I find the volume in litres?
If the lengths are in centimetres, divide the cubic centimetres by 1,000.
Can the top be larger than the bottom?
Yes. The formulas are symmetric, so an upside-down bucket gives the same answers.
Is this cone frustum calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.