Horizontal Tank Volume Calculator
Liquid volume in a partially filled horizontal cylinder, sphere, or cylinder with 2:1 elliptical heads, from diameter, length, and liquid height.
When to use this calculator
Use whenever a dip reading has to become a volume on a horizontal vessel — inventory reconciliation, batch make-up, spill containment, or checking how much is left before a transfer. Volume does not vary linearly with level on a horizontal tank, so reading a percentage off the dip and multiplying by capacity is wrong everywhere except exactly half full. Three geometries are covered: a plain horizontal cylinder with flat ends, a sphere, and a horizontal cylinder closed by two 2:1 elliptical heads, which is the usual bullet or receiver.
Required inputs
- Shape — horizontal cylinder, sphere, or cylinder with 2:1 elliptical heads
- Diameter D and length L (length is not used for a sphere)
- Liquid height h, measured from the lowest point of the shell
- Liquid density, for the mass equivalent
Expected outputs
- Liquid volume, in m³ and litres or ft³ and US gallons
- Total capacity, fill percentage, and remaining ullage
- Liquid mass at the entered density
- Fill curve of volume against level, with the current point marked
Formula overview
Dimensions accepted in m, mm, ft, or in. SI output is m³ with litres; imperial output is ft³ with US gallons. Liquid height is clamped to the range 0 ≤ h ≤ D.
Horizontal cylinder — circular segment area × length:
A = R²·acos((R−h)/R) − (R−h)·√(2Rh − h²)
V = A · L
Sphere — spherical cap:
V = (π/3) · h² · (3D/2 − h)
2:1 elliptical head, each end:
V = D³ · 0.5 · (π/12) · (3r² − 2r³), r = h/D
V_total = V_cylinder + 2 · V_headWorked example
Horizontal cylinder, D = 2.0 m, L = 5.0 m, dip h = 1.0 m (half full):
R = 1.0 m, (R − h) = 0
A = 1.0² × acos(0) − 0 × √(2×1×1 − 1²)
= 1.0 × 1.5708 = 1.5708 m²
V = 1.5708 × 5.0 = 7.854 m³ (7 854 L)
Capacity = π × 1.0² × 5.0 = 15.708 m³ → 50.0% full,
ullage 7.854 m³. At h = 0.5 m the volume is only 3.08 m³ — 19.6%,
not the 25% a linear reading would suggest.Common mistakes
- Interpolating volume linearly from the dip. A horizontal tank fills slowly at the bottom, quickly through the middle, and slowly again at the top — linear interpolation over-reads near the bottom and under-reads near the top by a wide margin.
- Ignoring the heads. Two 2:1 elliptical heads on a 2 m tank add about 2.1 m³ of capacity, which is a large fraction of a short vessel and shows up directly as a reconciliation error.
- Using the outside diameter. Wall thickness and any internal lining come off the capacity, so work from the inside diameter — and remember a real tank also has deadwood such as internal piping and heating coils.
FAQ
Learn
Related articles
Pressure Vessel Design & Calculation: คู่มือออกแบบตาม ASME Sec VIII Div 1
คู่มือออกแบบ pressure vessel และความหนา shell/head ตาม ASME Sec VIII Div 1 พร้อมสูตรและตัวอย่างคำนวณ
NPSHa vs NPSHr ต่างกันอย่างไร
เข้าใจความแตกต่างระหว่าง NPSH available และ NPSH required เพื่อป้องกัน cavitation ในปั๊ม