Tank Volume (Dipstick)
Partial liquid volume of a horizontal or vertical cylindrical tank from a depth (dipstick) reading.
Example
You enter
- Tank orientation horizontal
- Dimension unit in
- Tank diameter 24
- Tank length (horizontal) or height (vertical) 48
- Liquid depth (dipstick) 12
You get
- Liquid volume 47.0015
- Full tank 94.00 gal
- Percent full 50%
Checked against published worked examples from: National Bureau of Standards (U.S. Department of Commerce); Highland Tank; Naval Education and Training Professional Development and Technology Center (U.S. Navy).
Details, formula, and sources
ScopeHorizontal 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 or tableHorizontal 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.
Source and editionPartial volume of a cylindrical tank from a depth reading - first-principles circular-segment geometry; public domain.
Free accessPure geometry, public; the tank diameter, length, and dipstick depth are user-supplied.
What governsEstimate. AHJ and licensed professional govern.
API field namesorientation, linear_unit, diameter, length, depth, volume_gal, full_gal, percent_full
- Flat ends the tank ends are flat; dished/hemispherical heads need a separate head-volume correctiontank geometry