Conical Frustum Tank Fill Calculator

Method, example, and limits

Formula: At depth h, r(h) = r₀ + (r₁ − r₀)h/H. Volume to that depth is V = πh[r₀² + r₀r(h) + r(h)²]/3; total capacity uses h = H.

Inputs and units: r₀ and r₁ are bottom and top inside radii; H is the inside height; h is the liquid depth. All lengths use the same unit and volume is in its cube.

Worked example: For bottom radius 2 m, top radius 1 m, height 4 m, and depth 2 m, the fill volume is 19.373155 m³ out of 29.321531 m³ (about 66.0714%).

Assumptions: The tank is vertical, circular at every horizontal section, straight-sided, and has constant internal dimensions. Liquid depth must be between zero and H. This estimates geometric volume, not usable capacity or calibration corrections.

Limits: Does not account for domed ends, fittings, wall thickness, tilt, deformation, or nonlinear shapes. For zero radii at both ends the geometry has no capacity.