Tank Volume Calculator
Calculate the total and filled volume of cylindrical, capsule, oval, rectangular and cone-bottom tanks. Enter the tank dimensions and the measured liquid depth to get the volume in liters, gallons, ft³ and m³, plus the fill percentage.
Calculate Total and Filled Tank Volume
Tank Volume Formula
Where:
- \(D\) — inside diameter of the tank (m)
- \(L\) — length of the cylindrical section (m)
- \(r\) — radius, equal to half the diameter
- \(h\) — fill height, i.e. the depth of liquid measured from the bottom of the tank (m)
- \(A(h)\) — area of the circular segment covered by liquid at depth \(h\)
The formulas above describe a horizontal cylinder with flat ends, the default shape. The total volume is simply the cross-section area times the length, while the filled volume multiplies the length by the circular segment area wetted by the liquid. For every other supported shape the calculator applies the analogous exact formula — an elliptical segment scaled by \(a/b\) for oval tanks, spherical-cap volumes for capsule ends, and a cubic term for the cone section of cone-bottom tanks.
Tank Volume – Calculation Example
Example: a horizontal cylindrical tank with an inside diameter of \(D = 48\) in (4 ft) and a length of \(L = 120\) in (10 ft), containing liquid to a depth of \(h = 12\) in (1 ft).
\[ V_{total} = \pi \times \left(\frac{4\ \text{ft}}{2}\right)^{2} \times 10\ \text{ft} = 125.66\ \text{ft}^{3} \approx 3558\ \text{L} \approx 940\ \text{US gal} \]
The liquid depth of 1 ft equals half the radius (\(r = 2\) ft, so \(h = r\)), meaning the circular segment is exactly half of the circle:
\[ V_{filled} = \frac{V_{total}}{2} = 62.83\ \text{ft}^{3} \approx 1779\ \text{L} \approx 470\ \text{US gal} \]
Result: the tank holds about 3.558 m³ (3558 L, 940 US gal, 125.66 ft³) in total, and the liquid fills 1.779 m³ (1779 L, 470 US gal, 62.83 ft³) — the tank is exactly 50% full.
How to Use the Calculator
- Select the Tank shape from the dropdown: horizontal or vertical cylinder, rectangular box, horizontal or vertical capsule, horizontal oval, or a cone-bottom vertical cylinder.
- Enter the tank dimensions — Diameter (D), Length (L), Height (H), Width (W), Cylinder height (Hc) and/or Cone height (Hk) — using the unit dropdown next to each field. Only the fields used by the selected shape are shown, so you never have to guess what to leave blank.
- Enter the Fill height (h): the vertical depth of liquid measured from the very bottom of the tank. Use 0 for an empty tank. For horizontal shapes it must not exceed the diameter; for vertical shapes it must not exceed the total height.
- Read the Volume Results: total and filled volume in liters, US gallons, cubic feet and cubic meters, the fill level in percent, a to-scale diagram with the liquid level, and a step-by-step calculation detail showing the exact formula used.
What the Results Mean and Why They Matter
Knowing a tank's total volume tells you its capacity — what it can hold when completely full. The filled volume tells you how much liquid is actually inside right now. Together they answer everyday questions: how much fuel is left, how much a delivery truck must bring to top the tank off, how much chemical to add to reach a target concentration, or whether rainwater storage is sufficient for a dry spell.
An important subtlety: for horizontal tanks (horizontal cylinders, capsules and ovals), the relationship between fill height and volume is non-linear. Because the tank is wider in the middle than near the top and bottom, a dipstick reading of 25% of the diameter corresponds to only about 19.5% of the volume, and the half-full mark sits exactly at the centerline. This is why gauge charts and this calculator must use the segment formulas rather than simple proportions. For vertical tanks the math is linear — fill percentage equals depth percentage.
The fill level result makes interpretation easy: 100% means the liquid reaches the very top, 50% means half the capacity is used. If you need the weight of the contents rather than the volume, multiply the filled volume by the liquid's density with our density unit converter.
Total Volume Formulas for Each Shape
| Tank shape | Total volume formula |
|---|---|
| Horizontal cylinder (flat ends) | \(V = \pi\left(\frac{D}{2}\right)^{2} L\) |
| Vertical cylinder | \(V = \pi\left(\frac{D}{2}\right)^{2} H\) |
| Rectangular (box) | \(V = L \times W \times H\) |
| Horizontal capsule | \(V = \pi\left(\frac{D}{2}\right)^{2} L + \frac{4}{3}\pi\left(\frac{D}{2}\right)^{3}\) |
| Vertical capsule | \(V = \pi\left(\frac{D}{2}\right)^{2} H_c + \frac{4}{3}\pi\left(\frac{D}{2}\right)^{3}\) |
| Horizontal oval (elliptical) | \(V = \pi \left(\frac{W}{2}\right)\left(\frac{H}{2}\right) L\) |
| Cone-bottom vertical cylinder | \(V = \pi\left(\frac{D}{2}\right)^{2} H_c + \frac{1}{3}\pi\left(\frac{D}{2}\right)^{2} H_k\) |
For the horizontal capsule, the two hemispherical ends together hold exactly as much liquid as one full sphere of the same radius filled to the same depth — a useful shortcut the calculator exploits. For the cone-bottom tank, the filled volume inside the cone grows with the cube of the depth, because the liquid radius grows linearly as the cone widens.
Assumptions, Limitations and Practical Tips
- Enter inside (internal) dimensions. If you can only measure the outside, subtract twice the wall thickness from each dimension to avoid overestimating capacity.
- Capsule ends are assumed to be perfect hemispheres with radius equal to half the diameter. Real pressure vessels often have shallower dished or ASME heads, so their true capacity is somewhat lower.
- The horizontal cylinder assumes flat end caps; the cone-bottom tank assumes a sharp conical tip. Real tanks may include rounded transitions, outlet sumps or internal fittings that shift volumes slightly.
- Tanks are assumed to be level and symmetric. Tilting a horizontal tank noticeably changes the height-to-volume relationship.
- When measuring in mixed imperial units, the feet and inches calculator helps convert readings such as 4' 6" into a single decimal unit before entering them.
- Results are in US gallons; for imperial (UK) gallons, divide the liters figure by 4.54609. Quick metric conversions are also available with the meters to feet converter.
Frequently Asked Questions
How can I make a dipstick or gauge chart for my tank?
Run the calculator several times with increasing fill heights — for example every inch or every 5% of the diameter — and write down the filled volume for each depth. Glue or print the table onto your dipstick. For horizontal tanks this is essential, because the volume per inch varies a lot: near the bottom and top a whole inch adds very little, while at the centerline it adds the most.
How do I calculate tank volume by hand with a shortcut formula?
For a vertical cylinder in US gallons: \(V = 0.0034 \times D^2 \times H\), with D and H in inches. For a rectangle: length × width × height in feet, then multiply by 7.4805 to get gallons (or by 28.317 for liters). These shortcuts come from \(1\ \text{ft}^3 = 7.4805\ \text{US gal} = 28.317\ \text{L}\), so they are exact for vertical shapes but only work for a full horizontal cylinder, not a partially filled one.
How much does the liquid in my tank weigh?
Multiply the filled volume by the liquid's density. Fresh water weighs about 1000 kg (2205 lb) per cubic meter or 8.34 lb per US gallon; gasoline is about 0.74 kg/L and diesel about 0.85 kg/L. A 1000-liter water tank therefore holds roughly one metric ton, not one tonne-force of thrust — make sure the floor or stand is rated for the full weight, and note that using imperial gallons instead of US gallons changes the result by about 20%.
How do I calculate how much liquid to add to reach a target level?
Calculate the filled volume at your current depth, then run the calculator again with the target depth (or target percentage) and subtract the first result from the second. For vertical cylinders you can also do it by proportion: the difference between the two depths divided by the height, times the total volume. For horizontal tanks always use the two depths method — never a simple proportion, since volume is non-linear with depth.
What are the most common mistakes when measuring a tank?
The biggest one is using outside dimensions — wall thickness can add several percent to the apparent capacity. Also make sure you enter the diameter, not the radius, and for capsules measure only the straight cylindrical section, not the total length including the rounded ends. Finally, keep all inputs in one unit system: mixed feet and inches first need conversion into a single decimal value.
Can this calculator be used for propane or pressure vessels with dished heads?
Only approximately. Dished, ellipsoidal or ASME heads hold less than the perfect hemispheres assumed here, and 2:1 elliptical heads hold noticeably less than hemispheres of the same diameter. The capsule shape will therefore overestimate a real pressure vessel's total volume, typically by a few percent. Check the manufacturer's data sheet for exact wetted volume or capacity of ASME vessels.
How do I convert the results to imperial (UK) gallons, oil barrels or cubic inches?
One m³ equals 219.97 UK gallons, 6.2898 oil barrels and 61,024 cubic inches. A quicker route: 1 US gallon = 0.83267 UK gallons = 231 cubic inches, and 1 oil barrel = 42 US gallons. So divide the US gallon result by 1.2009 to get UK gallons, or take liters ÷ 4.54609. Mixing US and imperial gallons is a very common source of wrong fuel estimates.