Math & Science
Tank Area Calculator
Capacity and surface area for the three common tank shapes — including how much a partly-filled horizontal tank actually holds.
Tank Area Calculator
About the Tank Area Calculator
Three tank shapes, with capacity and surface area for each: rectangular, vertical cylindrical and horizontal cylindrical. Enter the dimensions in metres and you get the full capacity in litres, the surface area for coating or insulation, and the volume actually held at a given fill level.
That last figure is the one worth having. For a rectangular or upright tank, a half-full reading means half the capacity. For a horizontal cylinder it does not — the cross-section is a circle, so the relationship between depth and volume is a curve, not a straight line. The tool uses the circular segment formula to get it right.
Capacity comes out in litres, with cubic metres alongside. One cubic metre is exactly 1,000 litres, which makes metres the convenient unit to measure in.
How to use the Tank Area Calculator
- Choose the tank shape.
- Enter the dimensions in metres.
- Optionally enter the fill level as a depth of liquid.
- Select Calculate capacity.
- The paint estimate assumes a typical 10 m² per litre spreading rate.
The formulas
Rectangular V = l × w × h S = 2(lw + lh + wh)
Vertical cyl. V = πr²h S = 2πr(r + h)
Horizontal cyl. V = πr²L S = 2πr(r + L)
Dimensions in metres give cubic metres. Multiply by 1,000 for litres.
Worked example
A vertical cylindrical water tank, 0.6 m radius and 1.5 m tall.
V = π × 0.6² × 1.5 = π × 0.36 × 1.5 = 1.696 m³
1,696 litres — about 373 UK gallons
Surface area: 2π × 0.6 × (0.6 + 1.5) = 7.92 m² for painting or lagging.
Why a half-full horizontal tank is not half full
Actually, at exactly half depth it is half full — a circle is symmetric about its centre line. Everywhere else the relationship breaks down badly, because the circle is widest in the middle and narrows toward top and bottom.
| Depth (% of diameter) | Volume (% of capacity) | Difference |
|---|---|---|
| 10% | 5.2% | −4.8 |
| 20% | 14.2% | −5.8 |
| 25% | 19.6% | −5.4 |
| 40% | 37.4% | −2.6 |
| 50% | 50.0% | 0 |
| 60% | 62.6% | +2.6 |
| 75% | 80.4% | +5.4 |
| 90% | 94.8% | +4.8 |
A dipstick reading a quarter of the depth means the tank holds under 20% of its capacity, not 25%. On a 5,000 litre heating oil tank that is a 270 litre error — enough to run dry a good deal earlier than expected.
Filled area = r² × [ arccos((r − d) ÷ r) − (r − d) × √(2rd − d²) ÷ r² ]
d = fill depth, r = radius. Multiply the area by the tank length for volume. This is the circular segment formula, and it is why a calculator earns its keep here.
Working out paint or insulation
Surface area drives coating quantities. Decide first which surfaces you actually need:
- Full external area — the tool's figure, covering ends and sides.
- Subtract the base if the tank stands on a plinth. For a vertical cylinder that is πr².
- Subtract fittings — manways, nozzles and brackets. Usually a small correction.
- Add 10–15% for overspray, wastage and touching in.
Typical coverage runs 8–12 m² per litre for a smooth-surface coat. Our 7.92 m² tank needs about one litre per coat, so two litres for two coats plus wastage. Always check the coverage on the tin — primers and textured finishes go considerably further or less far.
Capacity conversions
| From | To | Relationship |
|---|---|---|
| 1 cubic metre | Litres | 1,000 (exact) |
| 1 cubic metre | UK gallons | 219.969 |
| 1 cubic metre | US gallons | 264.172 |
| 1 litre | Cubic centimetres | 1,000 (exact) |
| 1 cubic foot | Litres | 28.3168 |
UK and US gallons differ by about 20% — a UK gallon is 4.546 litres, a US gallon 3.785. Tank capacities quoted in gallons are ambiguous without knowing which. When it matters, work in litres.
How to find the volume of a fish tank (aquarium gallons)
Aquariums are usually rectangular, so length × width × height gives the volume. Two adjustments make the number realistic:
- Use the water depth, not the tank height. Most aquariums run 3–5 cm below the rim.
- Subtract about 10% for substrate, rocks and decoration.
A tank 120 × 40 × 50 cm has a nominal 240 litres, but filled to 45 cm and with gravel in, the actual water volume is nearer 195 litres. Dosing treatments on the nominal figure overdoses the tank by around 20%.
For shipment volume rather than storage, see the CBM calculator. For other shapes, the volume calculator covers seven solids.
Related guides
Other ways to use this calculator
- Tank calculator and tank volume calculator — tank volume litres and gallons for cylinders and boxes.
- Water tank capacity and tank capacity calculator — capacity is the volume when full.
- Tank surface area — for paint or insulation, see the section above.
- Horizontal tank fill — a half-height fill is not always half the volume; see the section above.
- Tank size calculator — work backwards: try sizes until the volume matches what you need.
- How to find volume of a fish tank — length × width × height in inches ÷ 231 tells you how many gallons in a tank.
Frequently asked questions
Multiply the internal dimensions in metres, then multiply by 1,000. A vertical cylindrical tank 0.6 m in radius and 1.5 m tall holds π × 0.6² × 1.5 = 1.696 m³, or 1,696 litres. For a rectangular tank use length × width × height. Measure inside the walls rather than outside, since wall thickness does not hold water.
Because the cross-section is a circle, so depth and volume are not proportional. The tank is widest at the middle and narrows toward top and bottom. At exactly half depth it genuinely is half full, but at a quarter of the depth it holds under 20% of capacity, not 25%. Working that out needs the circular segment formula, which this calculator applies.
Take the surface area, subtract any face you are not coating such as a base on a plinth, and divide by the paint's coverage — typically 8–12 m² per litre. Add 10–15% for wastage and overspray, then multiply by the number of coats. A tank with 7.92 m² of surface needs roughly two litres for two coats. Check the coverage figure on the tin.
Exactly 1,000 litres. That is why measuring tanks in metres is convenient — the volume in cubic metres converts to litres by moving the decimal point three places. One litre is also exactly 1,000 cubic centimetres. In imperial terms, a cubic metre is about 220 UK gallons or 264 US gallons, which differ by roughly 20%.
Multiply length × width × height in inches, then divide by 231 for US gallons. A 30 × 12 × 18 inch tank holds 6,480 ÷ 231 = 28 gallons. In centimetres, divide by 1,000 to get litres.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — volume and capacity units and conversions
- NIST — Units of volume and capacity — the exact litre to cubic metre relationship
- Circular segment — the formula for a partly filled horizontal cylinder