Truncated Cone Volume Calculator

A truncated cone, frequently called a conical frustum, is generated by slicing the top off a standard cone parallel to its base. To find its exact volume, the calculator uses the standard geometric formula: V = (π × h / 3) × (R² + r×R + r²), where h represents the perpendicular cone height, R is the base radius, and r is the top radius. Additionally, if you need the slant height, the calculator determines it using the Pythagorean theorem variant: s = √((R - r)² + h²), accounting for the diagonal outer boundary of the frustum.

Imagine you are designing a custom storage hopper shaped like a truncated cone. The perpendicular height (h) is 5 cm, the bottom base radius (R) is 2 cm, and the top radius (r) is 1 cm. First, square the radii: R² = 4 and r² = 1. Next, multiply the bottom and top radii together: 2 × 1 = 2. Sum these three values inside the parenthesis: 4 + 2 + 1 = 7. Multiply this sum by the height (5) and pi (π ≈ 3.14159), then divide the product by 3. This gives you a total truncated cone volume of approximately 36.65 cubic centimeters (cm³).

Always double-check whether your input specifications are given in radii or diameters. If a blueprint provides diameter measurements, divide them by two before entering them into the calculator. Additionally, ensure that all units of measurement—whether inches, centimeters, or meters—are consistent across both radii and the height to prevent unit mismatch errors in your volumetric results.