A cylindrical tank holds π × r² × h cubic metres, multiplied by 1,000 for litres. The formula is short, but three things bite people in practice: confusing diameter with radius (it quadruples the error), not knowing which gallon a supplier means, and the non-linear fill curve of a horizontal tank. This guide covers all three, plus a dipstick reference table, a capacity planning guide, and the formulas for tanks of other shapes.
Whether you are sizing a rainwater tank, working out how long a water supply will last, or checking a quoted capacity against what your site needs, the cylinder volume formula is the one tool you need. It looks a little intimidating with the π symbol. In reality, the calculation takes under a minute by hand, and a calculator makes it instant.
Here is the key thing to understand before you start. Volume and capacity are the same thing expressed differently. One cubic metre of internal space holds exactly 1,000 litres. That single conversion factor is why the formula is so easy to use in practice.
Table of Contents
- The formula and unit conversions
- How much capacity do you need?
- US gallons vs imperial gallons
- Vertical vs horizontal tanks
- Practical sizing scenarios
- Reading the level (dipstick reference)
- Other tank shapes
- Related calculators
- Frequently asked questions
- References
The Formula
A cylinder's volume is the area of its circular base times its height. The area of a circle is π × r², so the full formula is:
Here, r is the radius in metres (half the diameter) and h is the height in metres. The result lands in cubic metres. If you prefer to work from the full diameter rather than the radius, use this equivalent form. The same πr²h base is also why a cone holds exactly a third of the matching cylinder, if you ever need that comparison instead:
Both give the same answer. The ÷ 4 compensates for squaring the diameter instead of the radius. Pick whichever is easier for the measurement you have.
Once you have cubic metres, one multiplication converts to your preferred unit:
| To get | Multiply m³ by |
|---|---|
| Litres | 1,000 |
| US gallons | 264.17 |
| Imperial (UK) gallons | 219.97 |
| Cubic feet | 35.31 |
| US quarts | 1,056.69 |
How Much Capacity Do You Need?
Before working out what a tank holds, it is worth knowing what you need it to hold. Here are common starting points:
| Use case | Daily volume (approx) | 30-day supply |
|---|---|---|
| One person (drinking, cooking) | 5–10 L | 150–300 L |
| One person (all household use) | 100–200 L | 3,000–6,000 L |
| One dairy cow | 80–120 L | 2,400–3,600 L |
| Garden irrigation (100 m²) | 50–100 L | 1,500–3,000 L |
| Fire fighting reserve (residential) | n/a | 10,000–20,000 L total |
Add a 20–30% buffer for evaporation, leaks, and seasonal shortfalls. Then match that total to a tank size using the formula or the Cylinder Volume Calculator. If the required capacity exceeds about 10,000 litres, check local building codes: tanks over that size often need engineer-approved foundations.
Weight is the other factor most buyers overlook. Water weighs 1 kg per litre. A full 10,000-litre tank weighs 10 tonnes, not counting the tank shell. A standard residential concrete slab is typically rated for 4–5 kPa. That 10,000-litre tank sitting on a 2 m diameter footprint exerts about 32 kPa. Structural review before installation is not optional at that scale.
US Gallons vs Imperial Gallons
This trips up a lot of people, especially when buying tanks online or reading imported spec sheets. The two gallon systems are not the same size:
- 1 US gallon = 3.785 litres
- 1 imperial (UK) gallon = 4.546 litres
An imperial gallon is about 20% bigger. That 9,425-litre tank is 2,490 US gallons on a North American data sheet, but only 2,073 imperial gallons on a British or Australian one. Same water. Different yardstick.
Here is why it matters in practice. A supplier quotes "2,000 gallons" without specifying which type. The tank could be anywhere from 7,570 litres (US) to 9,092 litres (imperial): a 20% gap that changes whether the tank meets your storage requirement. Always check the country of origin, or ask. Do not assume.
Think of it this way: every time you see the word "gallons" on a product listing, treat it as ambiguous until you see "US" or "imperial" written next to it.
Vertical vs Horizontal Tanks
The volume formula works the same way for both orientations, as long as the tank is full. A horizontal tank on its side just swaps "length" for "height" in V = π × r² × h. Two tanks with identical internal dimensions hold the same amount of water regardless of how they sit.
But there is a catch. The difference appears as soon as the tank is not full, which is most of the time in real use.
Vertical tank, partly full: easy. The water still forms a cylinder, just a shorter one. Replace h with the actual water depth. If your 3 m tank has water 2 m deep, use h = 2. The relationship is perfectly linear: 50% depth means 50% capacity.
Horizontal tank, partly full: genuinely harder. The water sits as a curved segment across the circular cross-section. Halfway up the wall does not mean half the volume. The water-filled area at depth d is given by:
Multiply that cross-sectional area by the tank's length to get volume. The formula is correct, but it is awkward to compute by hand. For partly-filled horizontal tanks, the Cylinder Volume Calculator solves the segment geometry directly and is far quicker than working through the inverse cosine yourself.
Practical Sizing Scenarios
These two scenarios show how the formula informs real decisions, rather than just producing a number. For the arithmetic itself, enter your dimensions into the Cylinder Volume Calculator.
Scenario 1: Choosing a rainwater tank for household use
A household of four uses about 150 litres per person per day. A 30-day dry-season reserve means targeting 4 × 150 × 30 = 18,000 litres. The standard domestic tank in Australia and the UK is 2 m in diameter and 3 m tall, which the formula gives as roughly 9,425 litres. That is barely half the reserve target, so you are looking at two of those tanks plumbed in series, or stepping up to a 3 m diameter tank at 3 m tall (about 21,200 litres).
The weight implication: water is 1 kg per litre. An 18,000-litre system weighs 18 tonnes, not counting the shell. A standard domestic concrete slab is typically rated for 4–5 kPa; a single 2 m diameter tank at that depth exerts roughly 30 kPa on its footprint. Structural review is not optional at this scale, and that review should happen before you choose tank dimensions, not after.
Scenario 2: What happens when a horizontal tank reads "half full"
A farm trailer carries a horizontal cylindrical tank, 1 m radius and 4 m long. The driver checks a sight gauge and reads "halfway up the wall." How much water is actually left?
For a vertical tank, "halfway up" means exactly half the volume. For a horizontal tank, it does not. The water-filled cross-section at the midpoint of the wall is not a half-circle in volume terms: the circular geometry means the lower segment fills more slowly at first, then accelerates. At 50% wall height, a horizontal cylinder is actually about 50% full by volume, but the relationship is non-linear at every other depth. At 25% wall height the tank holds only about 19% of its capacity; at 75% wall height it holds about 81%. This asymmetry is why horizontal tanks ship with a calibration chart rather than a simple dipstick scale, and why the Cylinder Volume Calculator has a dedicated horizontal partial-fill mode using the inverse cosine segment formula.
Reading the Level (Dipstick Reference)
For a vertical cylindrical tank, every metre of depth adds a fixed number of litres: π × r² × 1,000. Compute that constant once for your tank and you have a permanent dipstick multiplier. Here it is for the most common diameters:
| Tank diameter | Litres per metre of depth | US gallons per metre |
|---|---|---|
| 0.8 m | 503 L | 133 gal |
| 1.0 m | 785 L | 207 gal |
| 1.2 m | 1,131 L | 299 gal |
| 1.5 m | 1,767 L | 467 gal |
| 2.0 m | 3,142 L | 830 gal |
| 2.5 m | 4,909 L | 1,297 gal |
| 3.0 m | 7,069 L | 1,868 gal |
To use it: find your tank diameter, measure the water depth with a stick or gauge, then multiply. A 2 m diameter tank at 1.4 m depth holds 3,142 × 1.4 ≈ 4,399 litres. Round to the nearest 50 litres and you have a practical field estimate in seconds.
This is the principle behind every commercial tank calibration chart: a lookup table that converts a dipstick reading to a volume. For horizontal tanks the relationship is non-linear (because the cross-section is a curved segment), so a calibration chart is even more valuable there, and harder to build by hand. Most manufacturers of horizontal tanks ship a pre-printed calibration chart with the tank. If yours did not arrive with one, the Cylinder Volume Calculator can generate depth-to-volume values at any increment you need.
Other Tank Shapes
Rectangular or square tanks. No π involved. Volume = length × width × height. A 2 m × 2 m × 3 m rectangular tank holds 12 m³ = 12,000 litres. That is more than the round 2 m × 3 m tank (9,425 L), because a rectangle fills the corners that a circle loses. The Rectangular Tank Calculator handles these in litres and gallons with no extra steps.
Tanks with domed (hemispherical) ends. Also called capsule tanks. Add the straight cylindrical body to the two end caps, which together form one complete sphere:
Where L is the length of the straight section (not including the domes). The Capsule Volume Calculator takes r and L as inputs and returns the full volume in litres and gallons directly.
Tanks with a conical base. Many industrial and food-grade tanks are cylindrical on top with a conical bottom to promote full drainage. Calculate the two sections separately: the cylindrical body uses V = πr²h, and the conical base uses V = ⅓πr²h (where h is just the cone's height). Add the two results for the total capacity. If the cone tapers to a central drain point, the conical section rarely stores usable liquid, so some designers exclude it from the rated capacity and only count the cylinder. Always check which convention the manufacturer uses before comparing capacities across brands.
Unusual or irregular shapes. The Volume Calculators hub covers spheres, cones, frustums, ellipsoids, and pyramids. If your tank has a non-standard cross-section, start there to find the closest matching shape.
Related Calculators
- Cylinder Volume Calculator: enter diameter (or radius) and height, get litres, US gallons, and imperial gallons instantly. Also handles partly-filled horizontal tanks.
- Rectangular Tank Volume Calculator: for square and rectangular tanks with flat sides, including depth-fill calculations.
- Capsule Volume Calculator: for tanks with rounded hemispherical ends, common in industrial, food-grade, and chemical storage vessels.
- Volume Calculators (all shapes): the full collection, covering spheres, cones, frustums, ellipsoids, and more.
Frequently Asked Questions
How do you calculate the volume of a cylindrical tank?
Multiply π (3.14159) by the radius squared by the height: V = π × r² × h. Use metres for the dimensions and multiply the result by 1,000 to get litres, or by 264.17 for US gallons. If you only have the diameter, halve it first, or use V = π × d² × h ÷ 4 directly.
What is the difference between US gallons and imperial gallons?
A US gallon is 3.785 litres; an imperial (UK) gallon is 4.546 litres. Imperial gallons are about 20% larger. A 10,000-litre tank is 2,642 US gallons but only 2,200 imperial gallons. Always check which system a spec sheet or product listing uses before comparing capacities or placing an order.
My tank is listed in gallons but I want litres. How do I convert?
Multiply US gallons by 3.785 to get litres. Multiply imperial gallons by 4.546. So 500 US gallons = 1,893 litres; 500 imperial gallons = 2,273 litres. If the listing does not specify, check the country of manufacture: US-sourced tanks use US gallons, and UK or Australian tanks generally use imperial.
I only know my tank's diameter, not its radius. What do I do?
Halve the diameter. A 2.4 m diameter gives a radius of 1.2 m. Or use the diameter form directly: V = π × d² × h ÷ 4. Both routes give the same answer, so use whichever feels more natural with your measurement.
How do I calculate a partly-filled horizontal cylindrical tank?
You need the liquid depth d and the tank radius r. The filled cross-sectional area is A = r² × cos−1((r − d) ÷ r) − (r − d) × √(2rd − d²). Multiply A by the tank length for volume. In practice, the Cylinder Volume Calculator handles this segment formula directly and is far faster than working through the inverse cosine by hand.
Why does a round tank hold less than a square one of the same width and height?
A circle covers about 78.5% of its bounding square. The four corners are empty space. A 2 m round tank and a 2 m × 2 m square tank of the same height: the round one holds 9,425 litres, the square one 12,000 litres. That is about 27% less capacity from the same footprint, purely because of geometry.
What is a dipstick chart and how do I make one for a vertical tank?
A dipstick chart maps a depth reading to a volume. For a vertical cylindrical tank, each metre of depth adds π × r² × 1,000 litres. Compute that constant for your tank's radius, then multiply by each increment (every 0.1 m or 0.25 m) to build a lookup column. A 2 m diameter tank adds 3,142 litres per metre, so 0.5 m = 1,571 L, 1.0 m = 3,142 L, and so on up to the full height.
How much does a full 9,425-litre tank of water weigh?
Water weighs 1 kg per litre at normal temperatures, so 9,425 litres weighs about 9,425 kg (roughly 9.4 tonnes). That is before the tank itself. Most standard domestic concrete slabs cannot support that load without engineering review, so check foundation ratings before installing a large tank on an existing slab.
What is the formula for a tank with hemispherical (domed) ends?
Capsule-shaped tanks use V = π × r² × L + (4/3) × π × r³, where L is the straight cylindrical section between the domes and r is the radius. The second term is the volume of one full sphere formed by the two half-sphere end caps. The Capsule Volume Calculator takes r and L and returns the result in litres and gallons.
Can I use the same formula for a tank lying on its side?
Yes, for a full tank. Replace h with the horizontal length: V = π × r² × length. The volume is identical to a vertical tank with the same dimensions. The difference only matters when the tank is partially filled, because the cross-section filling a horizontal tank is a curved segment, not a smaller cylinder.
How do I calculate tank capacity in cubic feet?
Measure radius and height in feet and apply the same formula: V = π × r² × h. The result is in cubic feet. One cubic foot holds 7.48 US gallons or 6.23 imperial gallons, and 28.32 litres. Multiply your cubic-feet result by the appropriate factor for the unit you need.
References
- NIST Weights and Measures: authoritative US conversion factors for volume units including US gallons and litres.
- Bureau International des Poids et Mesures: SI Units: international standard definitions for the cubic metre and all derived SI volume units.
- Engineering Toolbox: Volume Unit Converter: practical reference for converting between litres, cubic metres, US gallons, imperial gallons, and cubic feet.