Find the liquid volume in a level horizontal cylinder with flat ends. The internal diameter is 6 ft, internal length is 12 ft, and liquid depth measured vertically from the bottom is 2 ft.
1. Calculator Inputs
Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.
| Calculator field | Value | Unit / setting |
|---|---|---|
| Tank shape | Horizontal cylinder · flat ends | |
| Dimension unit | ft | |
| Internal diameter, D | 6 | ft |
| Internal length, L | 12 | ft |
| Liquid level from bottom, h | 2 | ft |
| Volume unit | US gal |
2. Step-by-step Math
Calculate the liquid cross-sectional area
r = D/2 = 3 ft A = r² arccos[(r−h)/r] − (r−h)√(2rh−h²) A = 9 arccos(1/3) − 1 × √8 A ≈ 8.25 ft²
Evaluate arccos in radians. The segment formula accounts for the curved walls; depth fraction is not volume fraction in a horizontal cylinder.
Multiply area by tank length
Vliquid = A L Vliquid = 8.25020763132 × 12 Vliquid ≈ 99 ft³ Vliquid = 99.00249157585 × 1728/231 Vliquid ≈ 741 US gal
Use internal dimensions. One US gallon is 231 cubic inches, and one cubic foot is 1,728 cubic inches.
Calculate capacity and percent full
Vtotal = πr²L = π × 3² × 12 ≈ 339 ft³ Vtotal ≈ 2,540 US gal Percent full = 100 × Vliquid/Vtotal ≈ 29.2% Remaining volume ≈ 2,540 − 741 Remaining volume ≈ 1,800 US gal
A 2 ft depth is one third of the tank diameter, but only about 29.18% of its volume.
3. Compare Your Answers
Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Liquid volume | 741 US gal | __________ |
| Total capacity | 2,540 US gal | __________ |
| Remaining geometric volume | 1,800 US gal | __________ |
| Percent full | 29.2% | __________ |
Second check
At 3 ft liquid depth, the tank is exactly half full: 1,270 US gal. At 4 ft depth, symmetry gives 2,540 − 741 = 1,800 US gal.
4. Assumptions and Method
The cylinder is level, with flat end plates and constant internal diameter. No allowance is made for internals, tilt, thermal expansion or operating freeboard. A tank with elliptical or hemispherical heads needs the corresponding tank shape.
Equation definitions and implementation: Horizontal Tank Volume Calculator. See also calculation methodology and other worked examples.