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Aquarium Calculator - Fish Tank Volume Calculator

Please select a tank shape.

Volume

1. What is a Fish Tank Volume Calculator?

Definition: This calculator computes the volume of an aquarium based on its shape (Rectangular Prism, Cube, Cylinder, Half Cylinder, Quarter Cylinder, or Bow Front) using specific formulas for each shape.

Purpose: Useful for aquarists to determine the water volume for tank maintenance, fish stocking, and equipment sizing.

2. How Does the Calculator Work?

The volume calculations are based on the following formulas:

Rectangular Prism: \( V = height \times width \times length \)
Cube: \( V = length^3 \)
Cylinder: \( V = \pi \times (diameter / 2)^2 \times height \)
Half Cylinder: \( V = \pi \times (diameter / 2)^2 \times height / 2 \)
Quarter Cylinder: \( V = \pi \times radius^2 \times height / 4 \)
Bow Front: \( V = height \times width \times length + \text{bow segment area} \times height \), where \( \text{bow segment area} = \frac{r^2 \times (\alpha - \sin(\alpha))}{2} \), \( r = \frac{length^2 + 4 \times (full_width - width)^2}{8 \times (full_width - width)} \), \( \alpha = 2 \times \arcsin(\frac{length}{2r}) \)

Unit Conversions:

  • Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
  • Volume (from cm³): liters (×0.001), gallons (×0.000264172)
Explanation: All dimensions are converted to cm, the volume is calculated in cm³, and then converted to liters and gallons.

3. Importance of Fish Tank Volume Calculation

Details: Calculating the volume of a fish tank is crucial for proper fish care, water treatment, and equipment sizing. Note that spherical tanks are discouraged due to unnatural fish movement and filtering difficulties.

4. Using the Calculator

Tips: Select the tank shape, then enter the required dimensions in mm, cm, m, in, or ft (all must be >0, with appropriate constraints for bow front shapes). The result shows the volume in cm³, liters, and gallons.

5. Example

Given (Bow Front): Length = 12 m, Full Width = 8 m, Width = 7 ft, Height = 12 m.
Volume Calculation: After converting units: Length = 1200 cm, Full Width = 800 cm, Width ≈ 213.36 cm, Height = 1200 cm.
- \( diff_width = 800 - 213.36 = 586.64 \, \text{cm} \)
- \( r = \frac{1200^2 + 4 \times 586.64^2}{8 \times 586.64} \approx 591.84 \, \text{cm} \)
- \( \alpha = 2 \times \arcsin(1200 / (2 \times 591.84)) \approx \pi \)
- \( bow_area = \frac{591.84^2 \times (\pi - 0)}{2} \approx 550,220 \, \text{cm}^2 \)
- \( bow_volume = 550,220 \times 1200 \approx 660,264,000 \, \text{cm}^3 \)
- \( rectangular = 1200 \times 213.36 \times 1200 \approx 307,443,200 \, \text{cm}^3 \)
- Total ≈ 967,707,200 cm³ ≈ 967,707 liters.
Conversions:
- \( \text{cm}^3 \approx 967,707,200 \),
- \( \text{liters} \approx 967,707 \),
- \( \text{gallons} \approx 255,683 \).

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