Truncated Cone Calculator

A truncated cone (frustum) is a cone with its tip sliced off parallel to the base.

How the Math Works

The Truncated Cone Calculator uses the formula V = ⅓πh(R² + Rr + r²) to compute the volume of a frustum. This formula extends the volume calculation for a full cone by accounting for the difference between the larger base radius (R) and smaller top radius (r). The term (R² + Rr + r²) effectively averages the areas of the two circular bases and their transitional zone, while h represents the vertical height. The calculator also determines slant height using the Pythagorean theorem: l = √(h² + (R-r)²), and lateral surface area as πl(R+r).

Practical Applications

To use this calculator, measure the height of your truncated cone-shaped object and both the top and bottom radii. Enter these values into their respective fields, and the calculator instantly provides the volume, slant height, and lateral area. This is particularly useful for architects calculating material requirements for tapered columns, or engineers determining fluid capacity in truncated cylindrical tanks. The tool eliminates manual calculations and potential errors in applying the complex frustum formula.

Day-to-Day Use

You can apply this calculation when designing decorative planters, measuring the capacity of drinking cups or buckets, or planning materials for DIY projects involving tapered structures. For instance, if you're buying coffee and want to know the exact volume of a conical cup, or determining how much concrete you need for a truncated concrete pillar, this calculator provides precise measurements that help with purchasing and planning. It's also handy for cooking recipes scaled to unusual container shapes.

Worked example

R = 5, r = 3, h = 8 → volume ≈ 410.5.

FAQ