Why a horizontal tank is not linear
Almost every underground fuel tank in India is a horizontal cylinder, and the shape has a consequence that catches people out constantly: the relationship between dip depth and volume is a curve, not a straight line.
The reason is geometry. Near the bottom of a horizontal cylinder the tank is narrow, so a centimetre of depth adds very little volume. Across the middle it is at its widest, so the same centimetre adds a lot. Near the top it narrows again.
The practical effect is largest exactly where it matters most — near empty, when you are deciding whether you can trade until the tanker arrives. On a two-metre tank, a dip at a quarter of the diameter holds under a fifth of the tank, not a quarter. Reading it linearly overstates what you have.
The one depth where the intuition is right
Exactly half. By symmetry of the circle, a horizontal tank dipped at half its diameter really is half full. Every other depth is off, and the further from the middle, the more so.
The arithmetic
The wetted cross-section of a horizontal cylinder at depth h, for a tank of radius r, is a circular segment:
segment area = r² · arccos((r − h) / r) − (r − h) · √(2rh − h²)
Multiply by the tank's length and you have the volume. A vertical tank needs none of this — the wetted cross-section is the full circle at every depth, so volume is simply the circle's area times the dip.
What this does not model, and why it says so
A plain cylinder is not quite a real tank. Most underground tanks have dished or hemispherical end caps, which hold extra volume beyond the straight barrel — which is why a tank rated at 20,000 litres usually measures a little short of that as a plain cylinder.
This calculator does not model the end caps, and rather than quietly absorbing the difference it asks for your tank's rated capacity and reports the gap. A few percent is the end caps. A large gap means either the dimensions entered are external rather than internal, or the rated capacity belongs to a different tank.
For anything you are signing — a delivery, a stock statement, a shortage claim — your tank's own calibration chart is the authority. It was produced for that specific tank, end caps and all, and no formula substitutes for it.
Where it is genuinely useful
Three cases, none of which needs settlement-grade precision.
- Ullage before a delivery — will the tanker's load actually fit, or will you be turning a compartment away?
- Sanity-checking a chart reading that looks wrong, particularly near the bottom of the tank where linear estimates go furthest astray.
- Sizing a tank you are specifying, where the question is what a given diameter and length actually hold.
Frequently asked questions
Why does my calibration chart disagree with this?
Almost certainly the end caps. This models a plain cylinder; your chart was produced for your specific tank including its dished ends, and it is the correct figure. The gap should be a few percent and consistent — if it is large or varies with depth, check that the dimensions you entered are internal rather than external.
Should I use internal or external dimensions?
Internal. Steel wall thickness on a 20,000-litre tank is small but not nothing, and external dimensions overstate the volume systematically at every depth.
How do I measure the dip correctly?
Same point on the tank every time, when nothing is dispensing, and after a delivery has had time to settle — fuel that is still moving reads high. Record water separately: it sits under the fuel and reads as product on a plain dip, hiding a real loss underneath an apparently healthy figure.
Can I use this for a delivery shortage claim?
No. Use your tank's calibration chart and correct both quantities to 15 °C. A claim resting on a formula from a web page rather than on the chart produced for that tank is one you will lose, and correctly so.