Principles
- One library, tested. All calculators use the same code for the same sum. Each formula is checked against worked examples: for instance, a 48 × 13 × 21 inch tank must come out at 56.7 US gallons, and the published glass-thickness example for a 3 m × 0.95 m panel must give 25 mm.
- Exact units. 1 US gallon = 231 cubic inches = 3.785411784 litres. 1 UK gallon = 4.54609 litres. 1 inch = 2.54 cm. 1 lb = 0.45359237 kg.
- Cautious rounding. Where a result is something you buy (heater watts, glass thickness, bags), we round up to the next size sold.
- Stated assumptions. Every rule of thumb is named as one, with its source and its limits.
Volume
Footprint area × height. Real water volume subtracts the glass (from outside measurements), the gap above the water line, 60% of the substrate layer (the solid share of a gravel bed; the other 40% is water between the grains) and an allowance for decor: 4% for a lightly decorated tank, 10% for a rock-filled one. Fresh water is taken as 0.998 kg per litre and sea water as 1.025 kg per litre. Volume calculator.
Standard tank sizes
Nominal gallons and outside dimensions as published by the main North American tank makers, and the metric sizes most often stocked in Europe, the UK and Australia. Makers differ by a few millimetres. Dimensions calculator.
Heater wattage
W per gallon is 5 up to 55 gallons, falling in a straight line to 3 at 75 gallons and above. This follows the guidance Aqueon publishes for its heaters (5 W per gallon for aquariums of 55 gallons or smaller, 3 W per gallon over 60 gallons), scaled by the temperature rise. An open-topped tank adds 15% for evaporative heat loss. Two heaters are recommended from 40 gallons or above 300 W. Results round up to the sizes sold: 10, 25, 50, 75, 100, 150, 200, 250, 300, 400, 500 W. Heater calculator.
Filter flow
Tank volume × turnovers per hour: 2–4 for bettas, 3–5 for shrimp, 4–6 community, 4–8 planted, 6–10 for goldfish, cichlids and fish-only marine tanks, 10–20 for reefs (total water movement). Light stocking multiplies the range by 0.85 and heavy stocking by 1.25. These are box ratings, which already allow for the usual one-third to one-half loss of flow in use. Filter calculator.
Substrate
Bed volume × bulk density: gravel 1.5 kg/L, sand 1.6, planted-tank soil 1.0, crushed coral 1.2, aragonite sand 1.45. Sloped beds use the average of the front and back depths. Densities vary by about 10% between products. Substrate calculator.
Water changes
Dilution: nitrate after = before × (1 − f) + tap × f, where f is the fraction changed. Repeated changes compound. A fixed weekly change of fraction f against a weekly rise r settles at a peak of tap + r ÷ f. Water change calculator.
Weight
Water + five glass panels (glass 2,500 kg/m³; acrylic 1,190 kg/m³) + substrate + decor + stand. When the glass thickness is unknown we estimate what a factory-built tank of that size would use. Floor advice is general guidance only; the capacity of a timber floor depends on its joists, and only a structural engineer or builder who has seen it can confirm it. Weight calculator.
Glass thickness
Side panels are treated as plates supported on three edges with the top edge free, under water pressure rising from zero at the surface to p = 9.81 kPa per metre at the bottom. Design strength of float glass is 19.2 N/mm², divided by the chosen safety factor (3.8 by default). The plate constants β (stress) and α (deflection) are interpolated from the standard table by length-to-height ratio, as set out by Warren Stillwell and derived from Roark's Formulas for Stress and Strain. Modulus of elasticity 69,000 N/mm². The edge-supported bottom panel uses Roark's constants for a plate simply supported on four sides. Results round up to stock thicknesses: 4, 5, 6, 8, 10, 12, 15, 19, 25 mm. This is a planning guide, not an engineering certificate. Glass thickness calculator.
Stocking
Build is 0.8 for slim fish, 1 for average and 1.5 for heavy-bodied, high-waste fish. Under 3 inches this is the traditional "one inch per gallon" rule; above it, load rises with the square of length, because body mass and waste rise faster than length. Dwarf shrimp count 0.15 points per inch and snails 0.6.
Tank capacity is 1.25 points per US gallon of real water (equal to one point per gallon of label size for a tank holding 80% of its nominal volume), multiplied by a filtration factor (0.8 below 3 turnovers an hour, 0.9 below 4, 1.0 from 4 to 6, 1.1 up to 9, 1.15 above) and by 1.1 for a heavily planted tank. Up to 60% is light, 60–95% well stocked, 95–110% full, and above 110% overstocked.
Separate checks compare each species' minimum tank, adult length against tank length (at least four body lengths), group size, temperament, fin-nipping against long fins, predation by size, and the overlap of temperature and pH ranges. This index is our own. It is deliberately cautious and it is a planning aid: fish behaviour and water tests have the final say. Stocking calculator.
Sources
- NIST, unit conversion factors.
- Warren Stillwell, "How to calculate the glass thickness for your aquarium".
- Young & Budynas, Roark's Formulas for Stress and Strain.
- Aqueon, aquarium heater sizing guidance.
- Seriously Fish species profiles; FishBase maximum lengths.
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