Tank Level to Volume Conversion: A Worked Strapping-Table Guide

The short answer. Tank level to volume conversion is a geometry problem before it is an instrumentation problem. A radar may report level within a few millimetres while the inventory is wrong because the zero point, tank heads, tilt or strapping table is wrong. Linear volume scaling is valid for a vertical cylinder with constant cross-section; it is not valid for a horizontal cylinder, spherical tank or vessel with changing internals.

Establish the zero and the units first

Define whether the reported level is above the tank bottom, above the lower tangent line, below a datum, or below the transmitter. Confirm whether the required result is gross volume, volume below the current level, free space, or saleable working volume. These are different quantities.

Record the tank’s actual inside dimensions and the drawing revision. Nominal “10,000 litre” capacity is not a calibration table. Also identify deadwood such as coils and supports, internal linings, tilt, and whether dished heads are included in the stated cylindrical length.

Vertical cylinder: the simple case

For a vertical cylinder with inside radius r and level h above its flat bottom:

V = πr²h

A 3.0 m inside diameter has a cross-sectional area of 7.069 m². Therefore, a 10 mm level change represents:

7.069 × 0.010 = 0.0707 m³ = 70.7 litres

That number is useful during acceptance. If a 10 mm independent level change produces a 120 litre indicated change, investigate scaling before blaming the radar.

Horizontal cylinder: height-to-volume scaling is nonlinear

For a horizontal cylinder of radius r, cylindrical length L and liquid depth h measured from the bottom, with 0 ≤ h ≤ 2r, the filled volume is:

V = L × [r² acos((r − h) ÷ r) − (r − h) × √(2rh − h²)]

Use radians for the inverse cosine and keep units consistent. Add the two heads separately using their real geometry; do not silently treat them as extra cylindrical length.

Worked example. Take a horizontal cylinder with inside diameter 2.0 m, so r = 1.0 m, and cylindrical length L = 5.0 m. At liquid depth h = 1.25 m:

r − h = −0.25 m;

acos(−0.25) = 1.8235 radians;

√(2rh − h²) = √0.9375 = 0.9682 m;

cross-sectional liquid area = approximately 2.0655 m²;

cylindrical-section volume = 5 × 2.0655 = 10.33 m³.

The tank is 62.5% full by height, but the cylindrical section is about 65.7% full by volume. That difference is exactly why a PLC’s linear 4–20 mA-to-volume scaling is wrong for this tank.

For the cylindrical section alone, the calculation produces this short table. A production strapping table would use closer spacing and add the real heads and deadwood.

The rounded values explain why the worked result can differ slightly in the last digit. Keep full precision in the calculation and round only the published table.

Convert millimetres into inventory uncertainty

Near the middle of a horizontal cylinder, small level errors have a large volume effect because the surface is wide. The local volume sensitivity is:

dV/dh = 2L√(2rh − h²)

At the example point, dV/dh is approximately 9.68 m². A 10 mm level difference therefore corresponds to about 0.0968 m³, or 97 litres, before head effects. This does not mean the radar error is 97 litres; it means any level error—including datum or tilt error—must be multiplied by this local sensitivity.

Calculate this sensitivity at low, mid and high level. A single “±X litres” statement across the whole tank is misleading when the cross-section changes.

Build the strapping table from geometry, then verify it

Interpolation error depends on breakpoint spacing and curvature. Use more points around knuckles, dished heads, conical bottoms and changes in diameter. A table with 20 evenly spaced points may still be poor at the transitions.

Do not hide density inside a volume table

Level-to-volume gives volume. Converting that volume to mass requires product density at a defined condition, and inventory at standard conditions may require temperature and pressure corrections. Keep these steps separate in the calculation and in the audit trail. Otherwise a density change looks like a level fault and operators lose confidence in a healthy transmitter.

What to send with an inquiry

A useful request includes the tank GA drawing, inside dimensions, head type, nozzle datum, required volume units, tilt, internal attachments, operating level range and whether the result is for process indication, inventory or custody transfer. Custody-transfer and legal-metrology applications require the applicable approved methods and equipment; a general control-system calculation is not automatically sufficient.

Practical questions

Q1. Can a radar transmitter calculate volume directly?

Many systems can store a linearization table, but the table is only as good as the geometry and datum. Confirm whether calculation occurs in the transmitter, PLC or inventory software so it is not applied twice.

Q2. How many points should a strapping table have?

Enough to keep interpolation error below the project’s inventory tolerance. Determine that by calculation; do not use a universal point count.

Q3. Does a tilted tank need a new table?

Often yes, especially when tilt is significant relative to the required accuracy or the level changes across heads and transitions. The measurement location also matters because level is not uniform relative to a tilted datum.

Q4. Why does total volume disagree at low level but agree when full?

Check bottom geometry, deadwood, zero offset and interpolation near the bottom. Matching only the full point does not validate the rest of the curve.

Related technical guides

• How to Specify a Radar Level Transmitter: The 14 Fields That Decide the Quote
• Radar Level Transmitter Output Signals: Choosing the Right One

Discuss your measurement application with METRAVON