Here Is How To Calculate The Volume And Surface Area Of Your Aquarium


The volume and surface area of a tank are both important things to know. It is usually a simple matter, once either surface area or volume is known, to calculate the other, since volume is equal to the surface area multiplied by the depth (and conversely: surface area = volume divided by depth). The rare exception to this is a tank with a sloping front, which is not dealt with here.

The following section explains how to calculate the surface area (and hence volume) for a range of differently shaped tanks: Rectangular, hexagonal, octagonal, D-shaped (also called half octagonal), corner, and curves. There are some maths involved, and formulae are provided for those who are not scared by them, but in most cases, instructions are given in plain English as well. Some of the calculations are lengthy, so once you have determined the surface area and/or volume of your tank, it is a good idea to record it somewhere safe. You can even write the volume onto an inconspicuous part of the tank with a water-proof marker so that it is always there when you need it.

Measure the dimensions of your tank in either cm or inches, apply the necessary formula or calculations, then use this conversion guide to convert to liters or gallons.

Rectangular



This is by far the simplest case. The surface area of a rectangle is simply its length (L) multiplied by its width (W):

Area = L.W

Hexagonal


Do not confuse hexagonal tanks (which are fairly rare) with octagonal (which are more common). A hexagonal tank has six sides (as per the diagram below) while an octagonal has eight.
To determine the surface area of a hexagonal tank you need to know its length (L), its width (W), and the length of the front pane (X).

The formula for surface area is then:

Area = 0.5(W.L + W.X)

ie: Multiply the width of the tank by its length and record the answer. Multiply the width of the tank by the length of the front pane and add this to the first number. Divide by two to get the surface area.

Octagonal


To determine the surface area of an octagonal tank you need to know its length (L), its width (W), the length of the front pane (X), and the length of the side or end pane (Y).

The formula for surface area is then:

Area = 0.5(W.L + W.X + Y.L – X.Y)

ie: Multiply the width of the tank by its length and record the answer. Multiply the width of the tank by the length of the front pane and record. Multiply the length of the tank by the length of the end pane and record. Add these three numbers together, record. Mulitply the length of the front pane by the length of the end pane. Subtract this number from your previous answer, then divide by two to get the surface area.

For a round octagonal the length of the side and front panes will be equal (ie Y=X). However, this does not make the resulting maths much easier! The new equation is:

Area = 0.5(W.L + W.X + X.L – X.X)

Or simply follow the instructions as above.

D-shaped


To determine the surface area of a D-shaped tank you need to know its length (L), its width (W), the length of the front pane (X), and the length of the side or end pane (Y).

The formula for surface area is then:

Area = 0.5(W.L + W.X + Y.L – X.Y)

ie: Multiply the width of the tank by its length and record the answer. Multiply the width of the tank by the length of the front pane and record. Multiply the length of the tank by the length of the end pane and record. Add these three numbers together, record. Mulitply the length of the front pane by the length of the end pane. Subtract this number from your previous answer, then divide by two to get the surface area.

Corner


To determine the surface area of a corner tank you need to know the lengths of the long sides (L), which will be equal, and of the short sides (X). You do not need the length of the front pane. For curve-fronted corner tanks, see the section on curves.

The formula for surface area is then:

Area = 0.5(L.L + 2X.L – X.X)

ie. Multiply the length of the long side by itself, record the answer. Multiply the length of the long side by the length of the short side. Times this answer by two, add to your previous answer, and record. Multiply the length of the short side by itself. Subtract this number from your previous answer, then divide by two to get the surface area.

Converting surface area to volume

As previously mentioned, volume is equal to the surface area of the tank multiplied by the depth, regardless of the shape of the tank.

If you have measured your tank’s dimensions in cm:
Multiply the calculated surface area by depth in cm. This gives you volume in millilitres ( = cubic centimetres). Divide by 1000 to get volume in litres. Then, divide by 3.8 for US Gallons, or by 4.54 for imperial gallons.

If you have measured your tank’s dimensions in inches:
Multiply the calculated surface area by depth in inches. This gives you volume in cubic inches. Multiply by 0.0164 to get volume in litres, by 0.00431 for US Gallons, or 0.00361 for imperial gallons.

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