Curved corner aquarium
This is a relatively simple case as far as calculating area and volume of curved tanks. The curve-corner is simply one quarter of a circle, therefore, you can calculate it's area simply by having the measurement for length of one side (L) which is the circles radius. The surface area is then given by:

Area = Pi. L.L/4

Where Pi is approximately equal to 3.14 (Scientific calculators and spreadsheet programs will give a more precise value of Pi, but this approximation is accurate enough for this purpose)

ie: Multiply the length of the straight side by itself, then multiply by 3.14, then divide by four.

Calculation form

Curve-front aquaria
To calculate the surface area of a curve front aquarium, it is best to consider it as two parts: ie, as a rectangle joined to a curved section. This curved section can be considered as a segment of a circle, and its area can be calculated by knowning the length of the curved section (L) and the width of the curved section at its maximum (X). This area can then be added to the area of the rectangle, which is given by the length multiplied by the width (W).

In order to calculate the area of a circle segment, you need to first calculate the radius of the circle (r) & the angle theta:

r = (L.L + 4.X.X)/(8.X) and then,

theta = 2arcsin(X/2r)

The formula for surface area is then:

Area(circle segment) =r.r.(theta - sin(theta))/2

This should then be added to the area of the rectangle which is given by:

Area(rectangle) = L.W

You will need a calculator or spreadsheet program in order to calculate the arcsine and sine functions. If you are not comfortable with this, use our calculation form.

Wave front
As with the curve front, the wave front shape can be treated as a rectangle plus a circle segment. This is somewhat of an approximation, but is accurate enough for our needs. To calculate the area of the rectagular part you need its width (W) and length (L). For the protruding curve you need the length of the protusion (Y) and the maximum width off the curve (X).

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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