Rainwater tank cylindrical volume:
formula and worked example

How much water a round tank really holds

A cylindrical tank has a straight, circular wall and a flat base, so its capacity is a simple geometric volume. For rainwater harvesting, that volume is the upper limit on how much roof runoff you can store between rains, which decides how many dry days the tank can cover.

Manufacturers print a nominal litre rating, but a site-built tank, a repurposed drum or a masonry sump has no label. A short calculation from the measured radius and height gives the same figure and lets you check a rating that looks too generous.

The result is the gross internal volume. Not all of it is usable: water below the outlet and the freeboard above the overflow are not available for supply.

The formula and its units

• Radius is half of the inside diameter, in metres. Measure across the inside of the tank, not the outer shell, since wall thickness can be a few centimetres.
• Height is the depth of water the tank can hold, in metres, measured from the floor up to the overflow level.
• Pi is about 3.14159. A calculator constant is enough; rounding it to 3.14 changes the answer by under 0.1%.

If you work in centimetres, convert to metres before squaring, or divide the cm cubic result by 1,000 to get litres.

Worked example: a 1.2 m radius, 2 m high tank

A masonry-ringed tank has an inside radius of 1.2 m, which is a 2.4 m inside diameter, and a water depth of 2 m to the overflow pipe.

1. 1Square the radius: 1.2 x 1.2 = 1.44 m².
2. 2Multiply by pi to get the base area: 1.44 x 3.14159 = 4.524 m².
3. 3Multiply by the height: 4.524 x 2 = 9.048 m3.
4. 4Convert to litres: 9.048 x 1,000 = 9,047.787 L.

About 9,000 litres is a practical figure to quote; the extra decimals imply a precision the measurements do not have.

Turning 9,048 litres into something useful

To judge whether the tank is big enough, compare the volume with expected collection and daily demand. A roof collects an amount that depends on its area and the rainfall, and the tank should hold enough for the stretch between the heavier showers.

Reserve is usually less than capacity. The outlet sits above the floor so sediment does not enter the supply, and the top few centimetres under the overflow are not safe to fill. If the outlet is 20 cm above the bottom and the overflow is 15 cm below the rim, the usable depth is less than the wall height.

• Subtract the unusable depths and recompute with the usable height for a supply plan.
• Keep the figure in litres when comparing with household demand, which is normally quoted per person per day.

Why the radius matters more than the height

Increasing the radius by 10% from 1.2 m to 1.32 m changes the base area by 1.1 squared, or 1.21 times, so the volume rises by 21%, from 9,047.787 to 10,947.82 litres.

A 10% change in height alone would raise the volume by only 10%. When choosing between a taller or a wider tank of the same footprint budget, widening is more effective, subject to site and structural limits.

Mistakes with cylindrical tank volume

• Using the diameter in place of the radius, which overstates the volume by a factor of four.
• Measuring the outside of the tank, or including a thick wall, so the inside radius is overestimated.
• Taking the total wall height rather than the overflow-level depth, which counts litres that will spill and not be stored.
• Leaving the 1000 conversion out, giving the volume in cubic metres but reading it as litres.

The last error is easy to spot: a household tank of 9 litres is clearly wrong, and 9,000 is the sensible magnitude.

Checking a tank before you buy or build

Measure the diameter in two directions, as hand-built tanks are rarely perfectly round, and use the average. Mark the overflow level on the wall and measure its height from the floor.

Write down the usable volume and the nominal volume side by side, so later discussions about demand and roof area start from the number that can actually be drawn.