How full is my tank, really?

You stick a dipstick into your heating oil tank, it comes out wet at 50 cm on a tank that is 100 cm tall, and you conclude: half full. For a rectangular tank, correct. For the far more common horizontal cylindrical tank, also correct — but only at exactly the halfway point, and wildly wrong everywhere else. At 25 cm you don't have 25% left; you have about 19.6%.

Why isn't the level proportional to the volume?

Because the cross-section of a lying cylinder is a circle. Near the bottom and the top the circle is narrow, in the middle it is at its widest. Each extra centimetre of liquid level therefore adds a different amount of volume: little at the bottom, a lot around the middle, little again near the top.

The circular segment formula

The liquid in a horizontal cylinder forms a circular segment. For a tank with radius r, length L and liquid height h:

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

The first term is the pie-slice area swept by the liquid, the second subtracts the dry triangle above the chord. Not the kind of thing you want to punch into a phone calculator at the bottom of the basement stairs.

An example

Tank: Ø 1.0 m (r = 0.5 m), length 2.5 m, so a full volume of π × 0.5² × 2.5 ≈ 1,963 litres.

Dipstick reading	Naive "percent"	Actual volume	Actual percent
10 cm	10%	≈ 103 L	5.2%
25 cm	25%	≈ 384 L	19.6%
50 cm	50%	≈ 982 L	50%
75 cm	75%	≈ 1,579 L	80.4%
90 cm	90%	≈ 1,860 L	94.8%

The error is largest exactly where it matters: when the tank is getting empty and you're deciding whether to order oil this week or next month.

What about vertical or rectangular tanks?

A vertical cylinder and a rectangular tank are linear: percentage of height equals percentage of volume. The trap is purely the lying cylinder — which, of course, is what most buried and basement fuel tanks are.

Skip the math

The steefware Tank Level Calculator does the segment math for you: enter the tank shape, its dimensions and your measurement, and get litres remaining. It runs entirely in your browser — free, no cookies.