A level transmitter measures distance, but nearly every customer wants volume — litres delivered, litres remaining, or a percentage of the tank. On a vertical tank that is a simple multiplication; on a horizontal one it is a curved relationship that surprises people. This guide gives the formulas, worked examples and ready-made calibration tables for the three tank shapes you will actually meet.
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Volume is level times cross-sectional area. When that area is constant along the whole height — a vertical cylinder or a box — the two are proportional and the maths is trivial. When the area changes with height — a horizontal cylinder, a cone-bottom tank, a spherical tank — volume grows in a curve, and a “50 % full” reading on the transmitter can be a long way from half the tank’s volume.
Vertical cylinder, rectangular tank. Percentage of level equals percentage of volume. Easy to hand to a customer.
Horizontal cylinder, cone or dish bottom, spherical. Needs a table or formula per height — this is what a strapping table is for.
Below the outlet and below the sensor’s dead zone there is liquid you cannot measure. Subtract it from the usable total, not from the reading.
Geometric volume is what you compute; custody-transfer volume needs temperature correction and density. Keep them separate on the report.
The simplest case. With r the tank radius and h the measured liquid height:
Calibration table for a 2.0 m diameter vertical tank (r = 1.0 m, total height 2.0 m, full volume 6,283 L):
| Level h (m) | Volume (m³) | Volume (L) | % of tank |
|---|---|---|---|
| 0.00 | 0.000 | 0 | 0 % |
| 0.25 | 0.785 | 785 | 12.5 % |
| 0.50 | 1.571 | 1,571 | 25.0 % |
| 0.75 | 2.356 | 2,356 | 37.5 % |
| 1.00 | 3.142 | 3,142 | 50.0 % |
| 1.25 | 3.927 | 3,927 | 62.5 % |
| 1.50 | 4.712 | 4,712 | 75.0 % |
| 1.75 | 5.498 | 5,498 | 87.5 % |
| 2.00 | 6.283 | 6,283 | 100 % |
Because the relationship is a straight line through the origin, one point is enough: measure the volume at any single level, then scale it. A 4 mA-to-20 mA span set on level is automatically correct in volume too.
This is where the curve appears. With r the radius, L the tank length and h the liquid height measured from the bottom:
Calibration table for a 2.0 m diameter × 3.0 m long horizontal tank (r = 1.0 m, full volume 9,425 L):
| Level h (m) | Volume (m³) | Volume (L) | % of tank |
|---|---|---|---|
| 0.00 | 0.000 | 0 | 0.0 % |
| 0.25 | 0.680 | 680 | 7.2 % |
| 0.50 | 1.843 | 1,843 | 19.6 % |
| 0.75 | 3.228 | 3,228 | 34.3 % |
| 1.00 | 4.712 | 4,712 | 50.0 % |
| 1.25 | 6.197 | 6,197 | 65.8 % |
| 1.50 | 7.582 | 7,582 | 80.4 % |
| 1.75 | 8.745 | 8,745 | 92.8 % |
| 2.00 | 9.425 | 9,425 | 100 % |
Best for Feeding a PLC or platform with the volume value directly, using the table above as the linearisation curve, rather than reporting raw height.
Watch out Elliptical or dished ends, internal baffles and a sloped installation all break the formula. For billing, dip the tank and build the table from measurement, not geometry.
Box tanks, IBCs and site-built concrete basins follow the same constant-area rule as a vertical cylinder:
A 3.0 × 1.5 × 2.0 m basin holds 9.0 m³ (9,000 L) full; at 0.5 m it holds 2.25 m³ (25 %), at 1.0 m it holds 4.5 m³ (50 %).
Whatever the shape, the deliverable is usually a strapping table — a level-to-volume list at fixed increments that everyone downstream can read:
Use 10 equal steps for reporting and alarms; use 1 % or 10 mm steps if the table feeds a billing or custody calculation.
In the transmitter (if it supports a volume table), in the PLC, or in the cloud platform. Keep one master copy so they cannot drift apart.
Check the table against a tape or flowmeter total at two or three levels before trusting it for deliveries.
Most level transmitters output level (distance or percentage). If the receiving system wants volume, you have three options, in order of preference:
Configure the unit to output volume and load the strapping table. The PLC then reads litres — no maths downstream, and it works for curved tanks.
Output level and hold the table in the controller. Keeps the instrument simple and makes the table easy to revise.
Only valid for constant-section tanks, where volume and level are proportional. Never use it on a horizontal cylinder.
A 2.0 m diameter × 3.0 m long horizontal tank supplies a small works. The safe maximum level is set 200 mm below the top, so the span is 1.8 m. From the formula, 1.8 m holds 8,934 L:
| What | Value | Working |
|---|---|---|
| 4 mA reference | 0 L | Tank empty at the outlet level |
| 20 mA reference | 8,934 L | Volume at 1.80 m (safe maximum) |
| At half height (1.00 m) | 4,712 L → 12.44 mA | 4 + 16 × (4,712 / 8,934) |
| At quarter height (0.50 m) | 1,843 L → 7.30 mA | 4 + 16 × (1,843 / 8,934) |
| High alarm | 8,000 L → 17.3 mA | ~10 % headroom before the safe maximum |
Note the asymmetry: half height is 50 % of volume but quarter height is only 19.6 % — which is why the alarm is set on volume rather than on a level percentage. Configure the zero and span itself with our calibration guide, and send the readings to a cloud platform with the 4G setup guide.
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