Reading a tank
Heating oil, propane, water and rainwater tanks are usually measured with a stick or a gauge, which gives a height, not a volume. For a vertical tank, the volume is proportional to the height. For a horizontal cylinder, it is not: the tank is widest in the middle. This calculator converts a liquid level into gallons for vertical cylinders, horizontal cylinders and rectangular tanks.
The formulas
- Vertical cylinder: volume = 3.14 × r² × height, and the liquid is 3.14 × r² × level.
- Rectangular tank: volume = length × width × height, and the liquid is length × width × level.
- Horizontal cylinder: the liquid fills a circular segment. Its area is r² × θ − (r − h) × √(2rh − h²), where θ = arccos((r − h) ÷ r) in radians and h is the level. Multiply by the tank length.
- Gallons = cubic inches ÷ 231.
Worked example: a horizontal tank
The tank is 48 in in diameter and 96 in long. A stick shows 30 in of liquid.
- Full capacity: 3.14 × 24² × 96 = 173,718 cu in, or 752 gallons.
- Segment at 30 in: θ = arccos(−6 ÷ 24) = 1.82 radians, area = 576 × 1.82 + 6 × 23.2 = 1,190 sq in.
- Liquid: 1,190 × 96 ÷ 231 = 494 gallons, or 65.7% full.
- Room left: 258 gallons.
Gallons by liquid level (same tank)
| Level | Gallons | Fill |
|---|---|---|
| 6 in | 54 | 7.2% |
| 12 in | 147 | 19.6% |
| 24 in | 376 | 50.0% |
| 36 in | 605 | 80.4% |
| 42 in | 698 | 92.8% |
Near the bottom and top of a horizontal tank, each inch holds little liquid. Around the middle, each inch holds the most: between 24 and 36 in, the tank gains 229 gallons.
Measuring correctly
- Diameter: measure the outside circumference with a tape and divide by 3.14, then subtract twice the wall thickness for the inside diameter if it is significant.
- Level: lower a clean stick straight down to the bottom through the fill opening, and read the wet mark. For oil, a paste that changes color on contact with water also shows any water at the bottom.
- Length: for a tank with domed ends, the calculator treats them as flat. Use the straight length plus about two thirds of the depth of each dome for a closer estimate.
Tank shapes it does not cover
Common 275 and 330 gallon indoor oil tanks are oval (obround), not round, so their readings follow a different curve: use the manufacturer’s tank chart. Spheres and tanks with cone bottoms also need their own formulas.
Safe filling
Propane tanks are filled to about 80% and heating oil tanks to about 90% of capacity, to leave room for expansion. Water weighs about 8.34 lb per gallon, so a full 752 gallon tank of water weighs over 3 tons: check that the base or floor can carry it.