Pool volume calculator: cubic metres and litres for any shape

A pool's volume is its water surface area times the average water depth: an 8 × 4 m pool with 1.50 m of water holds 48 m³, or 48,000 litres, and a round pool uses π × diameter² ÷ 4.

Water surface area × average depth

A pool's volume is worked out in two steps: the area of the water surface, then the average depth of the water. A rectangular pool of 8 × 4 m has 32 m² of water surface. At a depth of 1.50 m, the volume is 32 × 1.50 = 48 m³. As a cubic metre holds 1,000 litres, that is 48,000 litres.

Measure inside the pool, and use the depth of the water rather than the height of the wall: the water stops below the coping or at the skimmer. In the same pool, every 10 cm of water is 32 × 0.10 = 3.2 m³, or 3,200 litres.

Volume of a rectangular pool, from 6 × 3 m to 12 × 6 m

Water volume at an average depth of 1.20 m and 1.50 m. Example: an 8 × 4 m pool has 32 m² of water surface; at an average depth of 1.50 m it holds 48 m³, or 48,000 litres.

Round, oval or octagonal: the right formula

A round pool has a surface area of π × diameter² ÷ 4. For an above-ground pool with a 4.57 m inside diameter, π × 4.57² ÷ 4 = 16.40 m². With 1.22 m of water it would hold 20.01 m³, but that is an upper limit: a 1.22 m wall is never filled to the brim.

An oval pool with straight sides breaks down into a rectangle and two semicircles. For an overall length of 8 m and a width of 4 m, the rectangle is (8 − 4) × 4 = 16 m² and the two semicircles make a 4 m circle of 12.57 m²: 28.57 m² in all, and 42.85 m³ with 1.50 m of water. A regular octagonal pool 4 m across the flats has an area of 2 × (√2 − 1) × 4² = 13.25 m².

The multipliers quoted online vary from one site to the next. The calculator does not use any of them: geometry is enough for these shapes.

Sloping floor: the average depth

When the floor slopes evenly from the shallow end to the deep end, the average depth is halfway between the two: from 1.00 m to 1.80 m it is 1.40 m. The 8 × 4 m pool then holds 32 × 1.40 = 44.8 m³. This is only exact for a flat, sloping floor. A hopper bottom, a diving pit or built-in steps have to be worked out in parts and added together.

Kidney and freeform pools

A freeform pool has no exact formula. The reliable method is to split the water surface into rectangles, triangles and semicircles, add up their areas and enter the total in the Freeform tab. If the manufacturer gives the water surface area or the capacity, use their figure: it allows for the real curves.

How long it takes to fill

The filling time is the volume divided by the flow rate. Flow depends on the mains pressure and on the bore and length of the hose, so measure it. Time how long a 10-litre bucket takes to fill from the tap you will use: if it takes 20 seconds, the flow is 10 ÷ 20 × 60 = 30 litres per minute. The 44,800 litres of the sloping pool then take 44,800 ÷ 30 = 1,493 minutes, or 1 day and 53 minutes.

Mistakes that throw the volume out

• Using the wall height instead of the water depth: in the 8 × 4 m pool, 15 cm makes a difference of 4.8 m³, or 4,800 litres.
• Measuring the outside diameter of an above-ground pool, frame included.
• Putting the radius instead of the diameter into π × D² ÷ 4: the volume comes out four times too small.
• Forgetting the conversions: 1 m³ = 1,000 litres, and 1 m³/h = 16.67 litres per minute.

For the work around the pool, the area calculator helps with the paving, the cubic metres to tonnes converter with the spoil to take away, and the slope calculator with the fall of the surround.