Tank Volume Calculator
Enter your tank dimensions to find the total capacity and the filled volume at any liquid level. Choose from eight common tank shapes, switch between metric and imperial dimensions, and pick your preferred volume unit. Results update instantly as you type, and the "show your work" panel walks through every step of the geometry.
How to use this calculator
Select the tank shape that matches your vessel. Enter the inner dimensions using the unit selector (metres, centimetres, millimetres, feet, inches or yards). If you want to know how much liquid is in the tank right now, enter the current liquid depth in the "liquid level" field. Pick your preferred volume unit and the results update instantly. The "show your work" panel below the results walks through every step of the geometry so you can verify the calculation by hand.
Tank shape formulas explained
A vertical or horizontal cylinder uses V = pi x r^2 x h, the most common formula for round tanks. A rectangular tank is simply width x length x height. A capsule tank adds a full sphere to a cylinder: the two hemispherical end caps together equal one sphere, so V = pi x r^2 x h_cylinder + (4/3) x pi x r^3. Oval (elliptical) tanks replace r^2 with the product of the two semi-axes a x b. A cone-bottom tank combines a cylinder on top with a cone on the bottom: V = pi x r^2 x h_cyl + (1/3) x pi x r^2 x h_cone. A frustum (truncated cone) uses V = (pi x h / 3)(r1^2 + r1 x r2 + r2^2), where r1 and r2 are the top and bottom radii.
Partial fill and the circular segment
For a horizontal cylinder lying on its side, the cross-section filled at height h is a circular segment. Its area is r^2 x (arccos((r - h) / r) - (1 - h / r) x sqrt(2hr - h^2) / r), multiplied by the tank length to give volume. This non-linear relationship means the tank fills slowly near the bottom and top but quickly in the middle, which is why horizontal tank gauges often display non-linear scales. This calculator applies the exact segment integral rather than a linear approximation.
Choosing the right volume unit
Litres are the standard for water treatment and domestic tanks in metric countries. US gallons are common in North America for fuel and water storage. Cubic metres are preferred in civil engineering and large industrial applications. Cubic feet appear in HVAC and American construction documentation. Oil barrels (42 US gallons, 158.987 litres) are used for petroleum storage and pipeline capacity. This calculator converts between all five units from the same computed cubic-metre base value.
Tank volume formulas by shape
| Shape | Formula | Notes |
|---|---|---|
| Vertical cylinder | V = pi x r^2 x h | Most common water and chemical tank shape |
| Horizontal cylinder | V = pi x r^2 x L (segment for fill) | Use the circular segment formula for partial fill |
| Rectangular (box) | V = w x l x h | Simplest shape; used for storage pits and IBC totes |
| Vertical capsule | V = pi x r^2 x h + (4/3) x pi x r^3 | Cylinder plus a full sphere for the two end caps |
| Horizontal capsule | Same as vertical; barrel + sphere | Common for propane and compressed-gas tanks |
| Vertical oval | V = pi x a x b x h | Replace r^2 with a x b for elliptical cross-section |
| Cone-bottom | V = pi x r^2 x h_cyl + (1/3) x pi x r^2 x h_cone | Settling tanks; cone empties completely |
| Frustum | V = (pi x h / 3)(r1^2 + r1*r2 + r2^2) | Tapered hopper or silo shape |
Standard formulas used to compute total capacity. r = radius, h = height, a/b = semi-axes, L = length.
Frequently asked questions
How do I calculate the volume of a cylinder tank?
Multiply pi (approximately 3.14159) by the square of the inner radius (half the diameter) by the height: V = pi x r^2 x h. For example, a vertical cylinder with an inner diameter of 2 m and a height of 3 m has a radius of 1 m and a volume of 3.14159 x 1^2 x 3 = 9.425 cubic metres, or 9,425 litres.
How do I find the volume of liquid in a horizontal tank that is not completely full?
Use the circular segment formula. For a horizontal cylinder of radius r and length L filled to height h, the filled volume is V = L x r^2 x (arccos((r - h) / r) - ((r - h) / r) x sqrt(1 - ((r - h) / r)^2)). This calculator performs the full integral automatically when you enter a fill height.
What is freeboard and why does it matter?
Freeboard is the vertical distance between the maximum liquid level and the top of the tank. Water tanks typically keep 10-15% of capacity as freeboard to allow for thermal expansion (water expands about 0.02% per degree Celsius), wave action in open tanks, and foam or vapour space in chemical or fuel tanks. Never fill a closed tank to 100% capacity without confirming the design allows it.
How many litres are in a cubic metre?
Exactly 1,000 litres equal one cubic metre. A cubic metre is a cube 1 m on each side, and a litre is a cube 10 cm (0.1 m) on each side, so 10 x 10 x 10 = 1,000 of them fit inside. For US gallons, one cubic metre equals approximately 264.17 gallons.
Can I use this calculator for a septic tank or rainwater tank?
Yes. Most domestic septic tanks and rainwater tanks are rectangular or vertical cylinders. Select the matching shape, enter the inner dimensions (not the outer shell dimensions, which include wall thickness), and add the fill height if you want to check the current level. For septic tanks, the usable volume is typically 75-80% of the total capacity, as solids accumulate at the bottom.
What is a frustum tank and where is it used?
A frustum is a truncated cone: a shape with a circular cross-section that tapers from one diameter at the bottom to a different diameter at the top. Grain silos, settling hoppers, and some industrial process tanks use this shape to encourage material to flow toward the centre. The volume formula is V = (pi x h / 3)(r1^2 + r1 x r2 + r2^2), where r1 and r2 are the bottom and top radii and h is the height.