Horizontal Tank Volume Calculator: Partial Fill Formula and Dip Chart
Keywords: horizontal tank volume calculator, tank dip chart, tank level to volume, fuel tank calculator, how to calculate volume of a partially filled tank
If you manage a diesel tank on a farm, a water tank on a job site or an oil tank at a plant, you know the problem: the stick says the level is some number of inches, and you need gallons or liters. In a horizontal cylinder the relationship is not linear.
The partial-fill formula
For a horizontal cylinder of length L and radius r filled to depth h:
V = L x [ r^2 x arccos((r - h) / r) - (r - h) x sqrt(2rh - h^2) ]
(arccos in radians.) This covers the cylindrical shell only.
Worked example
A tank with a diameter of 2 m (r = 1 m) and a length of 5 m, filled to 0.5 m:
- arccos((1 - 0.5) / 1) = arccos(0.5) = 1.0472
- r^2 x 1.0472 = 1.0472
- (r - h) x sqrt(2rh - h^2) = 0.5 x sqrt(0.75) = 0.4330
- V = 5 x (1.0472 - 0.4330) = 3.07 m3, about 3,070 liters or 811 US gallons
A full tank holds pi x 1^2 x 5 = 15.71 m3, so the tank is 19.6% full by volume at 25% of the depth. A quarter on the stick is not a quarter in the tank. For diesel at roughly 0.84 kg/L, that is about 2,580 kg of fuel.
Why heads matter
Real tanks have heads (ends), and they add volume: flat, elliptical, hemispherical or dished (torispherical). In a partially filled horizontal tank the head contribution changes with level, so a rule of thumb can give errors of a few percent, which matters when you are ordering fuel or reconciling inventory. The accurate way is to integrate the real head profile numerically.
What a dip chart is
A dip chart (or strapping table) lists the volume for each dipstick reading, for example every inch or every centimeter. Once you have one for a tank, anyone on site can read the volume straight off the stick. Printing it and keeping it near the tank is a simple fix for guesswork.
How Tank Volume Calc helps
Tank Volume Calc: Dip Chart is built for fuel, water, oil and chemical tanks:
- Horizontal cylinders, vertical cylinders and rectangular tanks, with flat, elliptical, hemispherical and dished heads and conical bottoms
- Level to volume and volume to level
- Density presets (diesel, gasoline, water, oil) and weight in kg, lb or tons
- On-screen dip chart in 1 mm to 1 in steps
- Liters, gallons, barrels, cubic meters; metric, US and Imperial
- Works fully offline
Head volumes use numerical integration of the real head profile. Free includes the calculator and one saved tank. Pro (one-time purchase, no subscription) adds unlimited tanks with location and serial number, PDF dip charts, CSV export and inspection history with notes and photos. Buyers of the original paid version keep Pro.
