Your Actual Tank Volume: A Quick Lesson in Geometry

Okie, so you’ve bought your brand spankin’ new fish tank and are all excited about how big it is, right? Right!? But is it really as big as was advertised? The United States stubbornly refuses to adopt metric, which has kept the aquarium industry in North America bouncing back and forth between S.I. and Imperial units, causing round-off errors when units are converted between systems. Unfortunately, there is also a small amount of exaggeration that happens if the wrong measurements are taken or rounded up improperly. Also, there is a big difference between how much volume a tank occupies in space and how large a volume of water it can hold, a discrepancy that increases the larger your tank is. Tanks should be measured from the insides of the glass (not the outsides, not the frame) for an accurate measurement of the capacity. Lastly, since anything solid in your tank will displace some of this water and reduce the total water volume in the tank, some of your tank (roughly 10%) will be taken up by rocks, gravel, decorations and even the fish themselves. If you don’t believe me, sit down in a full bathtub and watch what happens.

On a side note, something similar happens when you buy a new iPod or a hard drive. Manufacturers typically define a “gigabyte” as a billion bytes, rather than as  2^30 (or 1,073,741,824) bytes – the standard definition of a gigabyte. Further, another chunk of space (~7%) is taken by the filesystem to format your drive, so in reality, an iPod that is sold as “160 GB” actually has only about 138 GB of usable space! But I digress…

Some important things to realise when calculating your tank’s actual volume:

  • Take measurements between the insides of the glass, not the outsides.
  • 1 US gallon = 231 cubic inches = 3.785412 litres
  • 1 Imperial gallon (deprecated) = 4.546092 litres
  • 1 litre = 1 cubic decimetre = 1000 cubic cm
  • 1 millilitre = 1 cubic centimetre = 0.001 cubic decimetre
  • 1 L = 1 dm3 = 1000 cm3 = 1000 mL
  • 1 decimetre = 10 centimetres = 0.1 metres
  • 1 inch = 2.54 centimetres

Volume Calculations

Rectangular tanks

To calculate this volume, we’ll need three inside measurements:

  • length (left-to-right)
  • width (front-to-back)
  • height (depth of the water)

Total volume of a rectangular tank in litres using measurements taken in cm:

volume = (length)(width)(height)(1 L / 1000 cm3)
volume = (length)(width)(height)(0.001 cm-3) L

Divide this value by 3.785412 for US gallons.

— OR —

Total volume of a rectangular tank in US gallons using measurements taken in inches:

volume = (length)(width)(height) / (231 in3/gal)
volume = (length)(width)(height)(1 in-3)(/231) gal

Multiply this value by 3.785412 for litres.

For example: [ — COMING SOON — ]

Hexagonal tanks

To calculate this volume in litres, we’ll need two (or three) inside measurements taken in cm:

  • side length (one of the six sides)
  • heighttank (depth of the water)
  • diameter (distance across the tank between two sides (not corners!))

Total volume of a hexagonal tank in litres = area of basetank x heighttank x (1 L / 1000 cm3)

So, what is the area of the basetank? Well, the basetank is just a collection of six equilateral triangles, so we can calculate their six areas from the formula A = (1/2)basetri x heighttri and multiply by six for the area of the whole bottom of the tank. The base of each triangle is the side length of the tank, while the height of each triangle is the found from the Pythagorean Theorem as h = sqrt( side2 – [(1/2)side]2 ). You’ll find that h = ( (√3)/2 )side. Alternatively, this value is the same as half the diameter of the tank (distance between two opposite sides), which you can measure if this is easier for you. So, the area of the basetank = 6 x (1/2) x side x ( (√3)/2 ) x side = 6 x (1/2) x side x (1/2) x diameter

Total volume of a hexagonal tank in litres:

volume = (√3)(3/2)(side2)(heighttank)(1 L / 1000 cm3)
volume = (0.00259808 cm-3)(side2)(heighttank) L

— OR —

volume = (6)(1/2)(side)(1/2)(diameter)(height) (1 L / 1000 cm3)
volume = (1.5)(side)(diameter)(height)(0.001 cm-3) L

Divide this value by 3.785412 for US gallons.

For example: [ — COMING SOON — ]

I will leave it up to you whether or not you take another 10% off the volume of your tank to account for gravel, decorations and occupants.

So, now that you know all of this, how big is your tank really?!

Weight Calculations

Another related topic here is how heavy your tank is. Maybe you just moved into a new apartment and you need to check if the floor is strong enough, or perhaps you want to have a bedroom aquarium and don’t want to find your tank in your living room because your floor isn’t to spec.

To estimate the weight of your tank when full:

  • Water weighs about 1 gram per mL or 1 kg/L
  • Aquarium gravel is typically sold in 2 kg, 5 lb/2.268 kg, 10 kg or 25 lb/11.340 kg bags.
  • Decorations you can easily throw on your bathroom scale for a good estimation.
  • You can usually find the empty weight of your tank on the box or from the manufacturer’s Web site.
  • 1 kilogram = 2.204622 pounds

So, the weight of the tank when full = empty tank + gravel + decorations + water.

It’s just that easy! Think your floor will hold? 😉

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