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Horizontal Tank Partial Volume Calculator

A horizontal cylindrical tank does not fill linearly with depth — the liquid surface is a circular segment, so the volume at a given depth needs the segment-area formula rather than a simple proportion. This calculator estimates the liquid volume from the inside diameter, the straight cylindrical length, and the liquid depth, and reports the total cylindrical volume, fill fraction, and ullage. It is a preliminary geometric estimate for a level horizontal cylinder with flat ends — it is not a tank calibration (strapping) table, not a custody-transfer tool, and not a mechanical or pressure-vessel design.

TypeInteractive engineering calculator

Calculator

m
m
m
Result
Total cylindrical volume15.708 m³
Liquid volume at depth7.85398 m³
Fill fraction50 %
Empty volume (ullage)7.85398 m³

Preliminary geometric estimate for a level horizontal cylinder with flat ends. Not a tank calibration table, custody transfer, or mechanical design.

Formulas

Segment area
A = r²·arccos((r − h)/r) − (r − h)·√(2rh − h²)
Liquid volume
V_liquid = A × L
Total cylindrical volume
V_total = π·r²·L
Fill fraction
fill = V_liquid / V_total

Diagram

Horizontal tank partial volume: V = A_segment × LDhend viewL (length)side viewV = A_segment × L

Worked example

A horizontal cylindrical tank has an inside diameter of 2.0 m (radius 1.0 m) and a straight length of 5.0 m. The liquid depth is 1.0 m — exactly half full. What is the liquid volume?

  1. 01r = D/2 = 1.0 m, h = 1.0 m (so h = r, half full)
  2. 02A = r²·arccos((r − h)/r) − (r − h)·√(2rh − h²)
  3. 03A = 1²·arccos(0) − 0·√(…) = π/2 = 1.5708 m²
  4. 04V_liquid = A × L = 1.5708 × 5.0 = 7.854 m³
  5. 05V_total = π·r²·L = π × 1² × 5 = 15.708 m³
  6. 06fill = 7.854 / 15.708 = 50.0%
Result

Liquid volume ≈ 7.854 m³; total volume ≈ 15.708 m³; fill fraction = 50.0%.

FAQ

Why is the volume not just proportional to depth?
In a horizontal cylinder the cross-section is a circle, so the liquid surface is a circular segment whose width changes with depth. The volume rises slowly near the bottom and top and fastest at the half-full level. A straight depth-proportion would be wrong everywhere except exactly half full.
Does this include dished or elliptical ends?
No. The estimate is for the straight cylinder with flat ends. Real horizontal tanks often have dished or elliptical heads that add volume at each end; those are not included here.
Can I use this as a tank gauging or inventory chart?
No. This is a preliminary geometric estimate, not a calibrated strapping table or custody-transfer calculation. For inventory or custody work, use the verified tank calibration data and drawings.
What depth range is valid?
The liquid depth must be between 0 and the inside diameter D. At h = 0 the tank is empty, at h = D it is full, and at h = D/2 it is exactly half full.

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