Tank Volume (Dipstick)
Partial liquid volume of a horizontal or vertical cylindrical tank from a depth (dipstick) reading: horizontal uses the circular-segment area R^2 x acos((R-h)/R) - (R-h) x sqrt(2Rh-h^2) times length, vertical uses pi x R^2 x depth, reported in US gallons, liters, and cubic feet with percent full (first-principles geometry, flat ends).
Formula and source
Horizontal cylinder partial volume = [R^2 x acos((R-h)/R) - (R-h) x sqrt(2Rh - h^2)] x length (circular-segment area times length); vertical cylinder = pi x R^2 x depth. US gallons = in^3 / 231.
Partial volume of a cylindrical tank from a depth reading - first-principles circular-segment geometry; public domain.
Audience
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