How to Calculate Tank Volume at Any Fill Level (Horizontal, Vertical and Round Tanks)
Knowing how much a tank holds, and how much is in it right now, matters for fuel deliveries, water storage, farm tanks, aquariums and swimming-pool balance tanks. The maths depends on the shape. Vertical tanks and boxes are simple. A tank lying on its side is the tricky one, because the liquid volume does not rise in step with the depth.
Step 1: measure the inside, not the outside
Use the inside diameter or width, and the inside length or height. Steel, plastic and concrete walls take up space, and a few centimetres of wall on every side can change the capacity by several percent. For the liquid level, measure the depth from the lowest inside point of the tank to the liquid surface, with a dipstick or a sight gauge.
Step 2: total capacity
| Tank shape | Capacity formula |
|---|---|
| Vertical cylinder | π × r² × height |
| Horizontal cylinder | π × r² × length |
| Rectangular tank | length × width × height |
| Sphere | (4/3) × π × r³ |
Here r is the inside radius, which is half the inside diameter. The result comes out in cubic units: cubic metres, cubic feet and so on. One cubic metre is 1,000 litres, and one US gallon is about 3.785 litres.
Step 3: the liquid volume at a given depth
In a vertical cylinder or a box the cross-section is the same at every height, so liquid volume is the base area times the depth. A box 2 m long and 1 m wide with 0.6 m of liquid holds 2 × 1 × 0.6 = 1.2 m³, which is 1,200 litres.
A horizontal cylinder is different. The liquid surface is a chord across a circle, and the circle is narrow near the bottom, wide in the middle and narrow again near the top. The volume of liquid at depth h is
with the arccos in radians. Take a heating-oil tank that is 1.2 m across and 3 m long. Its capacity is π × 0.6² × 3 ≈ 3.393 m³, or 3,393 litres. With 0.5 m of oil the formula gives 1.338 m³, which is 1,338 litres, or 39.4% full. The oil depth is about 42% of the tank’s diameter, but the volume is only about 39% of the capacity.
Why depth and volume do not match in a round tank
The table shows what share of a horizontal cylinder is full at different depths, measured as a share of the diameter.
| Depth as % of diameter | Volume as % of capacity |
|---|---|
| 10% | 5.2% |
| 25% | 19.6% |
| 50% | 50.0% |
| 75% | 80.4% |
| 90% | 94.8% |
A tank that looks one quarter full by depth is only about one fifth full by volume. This is why a dipstick for a horizontal tank has uneven markings, and why reading a gauge as a simple percentage of height misleads.
Spherical tanks
Liquid in a sphere takes the shape of a spherical cap, so the volume at depth h is π × h² × (3r − h) / 3. In a sphere with a 2 m diameter (r = 1 m), 0.8 m of liquid is π × 0.64 × 2.2 / 3 ≈ 1.474 m³, or about 1,474 litres.
Common mistakes
- Using outside dimensions. This overstates the capacity.
- Ignoring domed ends. Many fuel and propane tanks have curved heads that add capacity. Estimate each head as a spherical cap and add it.
- Mixing units. Diameter in centimetres and length in metres gives nonsense. Convert first.
- Forgetting tilt. A tank that is not level will read differently at each end, so measure on level ground.
The Tank Volume Calculator applies all of these formulas, draws the liquid level and gives litres, gallons and weight. For the volume and surface area of the tank itself, see the Cylinder Volume Calculator and the 3D Shape Calculator.
Frequently asked questions
How do I calculate the volume of a cylindrical tank? Multiply π by the inside radius squared and by the length (horizontal tank) or height (vertical tank). Convert the cubic result to litres or gallons.
How do I find how much liquid is in a horizontal tank? Use the partial-volume formula with the radius, the length and the liquid depth, or enter these in the Tank Volume Calculator. A tank filled to half its diameter is exactly half full, but at other depths the percentages differ.
How many gallons are in one cubic metre? One cubic metre equals 1,000 litres, which is about 264.2 US gallons.
Does the calculator allow for dished tank ends? No. It assumes flat ends, so a tank with domed heads holds slightly more than the result.
Want the answer without the algebra?
Try the Tank Volume Calculator →