A cylindrical tank holds π × r² × h cubic metres, multiplied by 1,000 for litres. A tank 2 metres across and 3 metres tall works out to about 9,425 litres (2,490 US gallons or 2,073 imperial gallons). Below you will find the formula, a unit conversion table, five worked examples for common tank sizes, and the awkward case of a partly-filled horizontal tank.
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
- Step-by-step calculation
- US gallons vs imperial gallons
- Vertical vs horizontal tanks
- Worked examples
- 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:
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 |
Step-by-Step Calculation
Here is the method for any upright cylindrical tank. Five steps, about 30 seconds each.
- Find the radius. Measure the full width (diameter) across the top of the tank and halve it. A 2 m wide tank has a radius of 1 m.
- Square the radius. 1² = 1. For a 1.5 m radius: 1.5² = 2.25.
- Multiply by π and the height. Use 3.14159 for π. For r = 1, h = 3: 3.14159 × 1 × 3 = 9.42 m³.
- Convert to your unit. 9.42 × 1,000 = 9,420 litres. Or 9.42 × 264.17 ≈ 2,490 US gallons.
- Sanity-check the result. A rough rule: a tank 1 m in radius and 1 m tall holds about 3,140 litres. Scale up proportionally from there for any other size.
That is the complete method. Every example in the worked examples section below uses these exact five steps.
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.
Worked Examples
Five common tank sizes, each worked through from dimensions to litres and gallons. All measurements are in metres.
Example 1: Standard 2 m Rainwater Tank
Dimensions: diameter 2 m, height 3 m (radius = 1 m).
V = π × 1² × 3 = 9.42 m³. That is 9,425 litres, 2,490 US gallons, or 2,073 imperial gallons. This is one of the most common domestic rainwater tank sizes in Australia and the UK. At 150 litres per person per day, a household of two has about 31 days of supply.
Example 2: Large 3 m Farm Storage Tank
Dimensions: diameter 3 m, height 5 m (radius = 1.5 m).
V = π × 1.5² × 5 = π × 2.25 × 5 = 35.34 m³. That is 35,343 litres (about 9,336 US gallons or 7,775 imperial). A tank this size covers several months of livestock watering or acts as a fire-fighting reserve for a rural property. It also weighs over 35 tonnes when full, so the foundation matters.
Example 3: Compact 1 m Garden Tank
Dimensions: diameter 1 m, height 2 m (radius = 0.5 m).
V = π × 0.25 × 2 = 1.57 m³. That is 1,571 litres or about 415 US gallons (346 imperial). A slim, space-efficient choice for a suburban garden. Fits beside a wall, supplies a vegetable patch through several dry weeks, and weighs just over 1.5 tonnes when full.
Example 4: Horizontal Tank (Full), Radius 1 m, Length 4 m
Dimensions: radius 1 m, length 4 m, lying on its side.
For a full horizontal tank, treat the length as h: V = π × 1² × 4 = 12.57 m³. That is 12,566 litres or about 3,321 US gallons (2,765 imperial). This size is typical for above-ground tanks on farm trailers or truck frames, where a low centre of gravity matters more than footprint.
Example 5: Partly-Filled Vertical Tank
Dimensions: 2 m diameter, 3 m total height, water depth at 1.8 m (60% full).
Substitute the water depth for h: V = π × 1² × 1.8 = 5.65 m³. That is 5,655 litres or 1,494 US gallons (1,244 imperial). Notice that 60% of the height gives exactly 60% of the full capacity. Vertical cylinders fill linearly, which is why a simple dipstick is all you need to read the current volume.
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.
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.
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.