By Wu Peng, Senior Process Instrumentation Engineer · Last reviewed July 23, 2026
Home › Tools › Horizontal tank volume
This calculator gives the fill volume and total capacity of a horizontal cylindrical tank from three numbers: diameter, straight shell length, and liquid depth. It handles flat, 2:1 elliptical, and hemispherical heads, and reports the result in liters, US gallons, and cubic meters. The math is the circular-segment volume, V = L × [r² × arccos((r − h)/r) − (r − h) × sqrt(2rh − h²)], plus the head volumes.
A horizontal tank fills on a curve, not a straight line, so a depth reading does not convert to volume by simple proportion. You need a depth first: that comes from a dip or from a bottom-referenced level transmitter, which reads the hydrostatic pressure of the liquid and turns it into a depth. This tool takes that depth and does the geometry.
Calculator
Horizontal tank volume
Results update as you type. Straight length L is the cylindrical shell only; heads add to it. Depth h is measured from the tank bottom, 0 up to the diameter. Results are geometric estimates, not a strapping table.
Method and formula
The volume of liquid in a horizontal cylinder is the area of the wetted circular segment times the shell length. For a tank of radius r filled to depth h, the segment area comes from the arccosine of the dry portion, and the volume is that area times L.
V = L × [r² × arccos((r − h)/r) − (r − h) × sqrt(2rh − h²)]
Rounded heads add a bit more. Each 2:1 elliptical head holds pi·D³/24, and each hemispherical head holds pi·D³/12, so both heads together add pi·D³/12 or pi·D³/6. Filled to depth h, the two heads combined hold (pi/6)·h²·(3D/2 − h) for elliptical or (pi/3)·h²·(3D/2 − h) for hemispherical. Flat heads add nothing, so the straight cylinder is the whole tank.
A cylinder capped with a hemisphere at each end is also called a capsule tank, so the hemispherical setting covers that shape. ASME torispherical heads, also called flanged and dished, are shallower than 2:1 elliptical, so their volume falls between flat and elliptical ends; use the elliptical mode as an upper bound, or ask us for the exact head volume.
A quick check: a 2 m diameter, 5 m tank with flat ends holds pi × 1² × 5 = 15.71 m³, which is 15,708 L or 4,150 US gallons. At 1 m depth (half the diameter) it is exactly half full, because a horizontal cylinder is symmetric about its centerline.
Worked example
A horizontal diesel tank is 2.5 m in diameter and 6 m long with flat ends. A dip stick reads 1.0 m of diesel.
- Radius r = 1.25 m, depth h = 1.0 m, so the dry height r − h = 0.25 m.
- Segment area = 1.25² × arccos(0.25/1.25) − 0.25 × sqrt(2×1.25×1.0 − 1.0²) = 1.834 m²
- Fill volume = 1.834 × 6 = 11.00 m³ = 11,001 L = 2,906 US gallons
- Total capacity = pi × 1.25² × 6 = 29.45 m³, so the tank is 37.4% full at 40% of the diameter.
The calculator above returns the same numbers, and the 37.4% against 40% depth is the nonlinearity in one line: the tank is a little less than 40% full because the widest part of the circle sits above the liquid.
Application example
Oil and gas, El Salvador. A fuel distributor wanted volume, not just level, from a diesel storage tank. A submersible level transmitter read the depth, and a volume recorder applied the tank geometry to report the contents in liters and gallons rather than a bare height. The geometry step the recorder did on site is exactly what this calculator does.
Nonlinear fill
Half depth is half volume in a horizontal cylinder, by symmetry, but every other point is off a straight line. Reading depth as if it were proportional to volume is worst around the quarter points, where it misses by roughly five percentage points.
| Depth (% of diameter) | Volume (% of capacity) | Linear-gauge error |
|---|---|---|
| 10% | 5.2% | −4.8 pts |
| 25% | 19.6% | −5.4 pts |
| 50% | 50.0% | 0 |
| 75% | 80.4% | +5.4 pts |
| 90% | 94.8% | +4.8 pts |
Flat ends; symmetric heads give the same curve shape. This is why a bottom-referenced transmitter reads level, and the recorder or the calculator turns it into volume.
Related guides and tools
To get the depth in the first place, a submersible pressure transducer or a bottom-mounted hydrostatic level transmitter reads the liquid head and outputs 4-20 mA. If you have a pressure reading and want the depth first, the hydrostatic pressure calculator does that step. The hydrostatic pressure guide explains the density that goes with it. To compare hydrostatic level against radar or ultrasonic for your tank, see the level transmitter types guide or browse our level instruments.
For upright tanks the geometry is simpler: our tank volume calculator for vertical cylindrical and rectangular tanks covers those shapes, with a dip chart and weight output.
FAQ
How do you calculate the volume of a horizontal cylindrical tank?
Find the wetted circular-segment area, then multiply by the shell length. Segment area = r² × arccos((r − h)/r) − (r − h) × sqrt(2rh − h²), where r is the radius and h is the liquid depth. Multiply by length L for the cylinder, then add the head volumes for elliptical or hemispherical ends.
Why isn’t a horizontal tank’s volume linear with the liquid level?
Because the cross-section is a circle. Near the bottom and top a small level change adds little volume; near the middle the same change adds much more. Half depth is exactly half volume, but 25% depth is only about 19.6% of volume and 75% depth is about 80.4%. Use the segment formula, not a straight-line estimate.
How do I measure the fill level of a horizontal tank accurately?
Use a calibrated dip stick or a bottom-referenced level transmitter. A submersible or bottom-port transmitter reads the hydrostatic pressure of the liquid and converts it to depth; feed that depth into this calculator or a strapping table to get volume. For custody accuracy, measure at working temperature and account for tank tilt.
How accurate is a calculated tank volume?
A geometric calculation is an estimate. It assumes exact inside dimensions, a level tank, and a perfect cylinder. Real tanks deform slightly and heads vary, so a strapping table built by physical calibration is more accurate, typically within about 0.5%. Temperature also changes both the steel and the liquid volume.
Request a quote
Tell us the tank size, the liquid, and the accuracy you need, and we will recommend the level transmitter that feeds this volume calculation and provide a quote. Reach our application engineers or use the form below.
Written and technically reviewed by Wu Peng and the Instranova engineering team.