Frustum Calculator

A frustum is a cone with its pointed top sliced off parallel to the base, leaving a tapered shape with a wide circular bottom and a smaller circular top. You see frustums everywhere once you start looking: buckets, plant pots, drinking cups, lampshades, hoppers, funnels, cooling towers and countless tapered containers and transitions in engineering and construction. This calculator gives you the full geometry of a conical frustum from three measurements, the bottom radius, the top radius and the vertical height. Enter those and it returns the volume, the slant height up the sloping side, the lateral (curved) surface area and the total surface area including both circular ends, all in matching units and updating instantly as you change a value. The volume is usually the main goal, because it tells you the capacity of a bucket, pot or hopper, and it comes from an elegant formula that blends the two radii so the taper is handled correctly. The slant height is needed before you can find the curved surface, and it is just Pythagoras applied to the height and the difference between the radii. The lateral surface area matters when you are cutting sheet material to wrap a tapered form, lining a hopper or working out the material in a lampshade, while the total surface area adds the two circular faces for problems where they count. Doing all this by hand means combining several formulas without dropping a term, which is exactly the kind of careful arithmetic a calculator handles best. It is a practical tool for makers, engineers, tradespeople and students alike. The formulas and a worked example are below.

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