Horizontal cylinder volume, at any depth.

A full horizontal cylinder holds π × r² × L, where r is the inside radius and L the length. A part full one holds the length times the area of the circular slice the liquid fills: V = L × [r² × acos((r − h) ÷ r) − (r − h) × √(2rh − h²)], with h the depth of the liquid measured from the bottom. For a tank 1.2 m across and 3 m long, filled to 0.4 m, r is 0.6, the slice is 0.3300 m² and V = 0.9900 m³, which is 990.0 L. The full tank holds 3.3929 m³, so it is 29.2 percent full though the liquid is a third of the diameter deep. The formula is plain geometry, so there is no outside source to check; the tool and the numbers on this page were compared with a numerical integration.

This page is for tanks on their side where the reading is the depth, such as a fuel or oil tank with a dipstick, a septic or water tank, a pipe or a drum. It handles flat, elliptical and hemispherical ends, and it draws a depth chart you can save. For other tank shapes, a usable volume between an outlet and an overflow, or the time to fill, use the tank volume calculator.

How to use the calculator

1. Choose Volume from depth, or Depth from volume if you know how much liquid is in the tank.
2. Type the inside Size as a diameter or a radius, and the Straight length, which is the part between the two ends. Pick the Length unit.
3. Pick the Ends of the tank: flat, 2:1 elliptical, hemispherical, or an elliptical end whose depth you type.
4. Type the Liquid depth, measured from the bottom inside the tank, or the Volume of liquid.
5. Pick the Volume unit. The big card shows the answer. The cards below show the space left, liters, gallons, cubic meters and the full tank. The end view draws the level.
6. Choose the Dipstick chart steps. The chart lists the depth and volume at every 10, 5 or 2 percent of the diameter, or at every inch, centimeter or foot. Save chart as CSV and Copy chart take it to a spreadsheet. Copy result and Copy link keep the answer.

The depth is not the volume

Because the tank is round, the middle band of depth holds the most liquid per inch. The first 10 percent of the diameter holds only 5.2 percent of the volume, and half the diameter is exactly half. For a tank with flat ends, this table does not depend on the size of the tank:

To read a dipstick, multiply the percentage by the full volume. A quarter of the diameter is 19.6 percent of the volume, not 25.

Dished and domed ends

Many real tanks have rounded ends, called heads. A 2:1 elliptical head is one whose depth is a quarter of the diameter. A hemispherical head is half a ball, so its depth is half the diameter. Both ends together form an ellipsoid, and the liquid in the two ends is (a ÷ r) × π × h² × (3r − h) ÷ 3, where a is the depth of one head, r the radius and h the liquid depth. The straight length you type is the part between the heads, not the overall length. For the same tank as above, 1.2 m across and 3 m straight, filled to 0.4 m:

Half the diameter is still exactly half the volume, because the tank is the same top and bottom. Torispherical (dished and flanged) heads are not a pure ellipse. For those, type the depth of one head in the custom box to get an estimate, and check it against the chart from the tank maker.

Worked examples

• Half depth. Any horizontal cylinder is half full at half the diameter. 1.2 m × 3 m: 1,696.5 L.
• Full tank. π × 0.6² × 3 = 3.3929 m³, 3,392.9 L, or 896.3 US gallons (a US gallon is 231 cubic inches, as in NIST Handbook 44 (2026), Appendix C, checked 24 Oct 2026).
• Depth from volume. For 1,000 L (1 m³) in the same tank with flat ends, choose Depth from volume, type 1000 and keep Liters. The liquid stands 37.2 cm deep.
• A dipstick chart in inches. A tank 48 in across and 120 in long, flat ends, holds 940.0 US gallons. Choose inches and Every 1 length unit to get a line for every inch. At 12 in it shows 183.8 gallons, at 24 in 470.0 and at 36 in 756.3.
• Feet and gallons. A pipe 2 ft across and 10 ft long, filled 6 in deep (r = 1 ft = 12 in): 45.9 US gallons.
• Pipe filled to the brim. Depth equal to the diameter gives the full volume, with no formula needed.

Measuring the tank

Use the inside diameter, not the outside. Subtract the wall twice from the outside across. Measure the straight length between the two ends on the inside, where the heads begin. Read the depth from the lowest point of the inside, with a rod or dipstick that goes straight down through the top. Liquids climb the stick a little at the edge, so read the flat surface. If the tank sits on a slope, the tool is not exact, since it needs a level tank.

What is not counted

Fittings, a dome on top, baffles, a sump and the wall thickness are not counted. For a tank with such parts use the volume the maker prints on it for the full tank, and treat this page as an estimate. A pipe, a drum or a boiler shell with flat ends works as is.

Mistakes to avoid

The first is taking the depth as a straight percent of volume. The second is mixing inches with feet, so check the length unit. The third is typing the radius into the diameter box, which gives a quarter of the volume, so check the Diameter or Radius choice. The fourth is typing the overall length when the tank has dished heads. For a vertical tank the volume is simply the base area times the liquid height. For other shapes see area and volume calculator, and for unit changes see liters to gallons.