Cone-Bottom Tank Volume from Dipstick

ScopeFrom a dipstick depth measured up from the apex - a poly, process, or feed tank. Below the cone height the liquid fills a cone whose radius grows with height, so V = (pi R^2/(3 Hc^2)) h^3; above it, the full cone (1/3) pi R^2 Hc plus a straight cylinder pi R^2 (h - Hc). A 6 ft tank with a 3 ft cone and an 8 ft straight side holds 1,904 gallons full, but the cone empties as the CUBE of the depth - 1.5 ft up the tip (half the cone height) is only 3.5 ft^3 (26 gal), an eighth of the full cone - so a low stick reads far less than a straight-side guess. Enter inside dimensions in feet. A right cone concentric with the cylinder, apex down; a flat-bottom tank is gauged separately, and the tank's own chart governs. Reported in cubic feet and US gallons with the percent full.

Formula or tableR = D/2; volume = (pi R^2/(3 Hc^2)) h^3 for h <= Hc, else (1/3) pi R^2 Hc + pi R^2 (h - Hc); full = (1/3) pi R^2 Hc + pi R^2 Hcyl.

Source and editionCone-bottom vertical tank partial gauging - a right cone from the apex plus a straight cylinder; standard solid geometry (cone + cylinder) as in Machinery's Handbook (Industrial Press), by name; public domain.

Free accessPublic-domain solid geometry; the diameter, cone height, cylinder height, and depth are user-supplied.

What governsEstimate. AHJ and licensed professional govern.

API field namesdiameter_ft, cone_height_ft, cylinder_height_ft, depth_ft, volume_gal, percent_full

• Cone region V = (pi R^2/(3 Hc^2)) h^3, a right cone from the apex with r(h) = R h/Hcsolid geometry
• Cylinder region full cone + pi R^2 (h - Hc) above the cone heightsolid geometry
• Scope right cone concentric with the cylinder, apex down; a flat-bottom tank is the tank-volume tilescope of this tile