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Tank Volume Calculator

Please select a tank shape.

Volume

1. What is a Tank Volume Calculator?

Definition: This calculator computes the total and filled volume of a tank based on its shape (Vertical Cylinder, Horizontal Cylinder, Rectangular Tank, Elliptical Tank, Frustum, or Cone Bottom Tank) using specific formulas.

Purpose: Useful for determining the total or filled volume of tanks for storage, industrial use, or aquarium management.

2. How Does the Calculator Work?

The volume calculations are based on the following formulas:

Vertical Cylinder: \( V_{total} = \pi \times (d/2)^2 \times h \) or \( V_{filled} = \pi \times (d/2)^2 \times f \) (partial)
Horizontal Cylinder: \( V_{total} = \pi \times (d/2)^2 \times l \) or \( V_{filled} = 0.5 \times (d/2)^2 \times (\theta - \sin(\theta)) \times l \), where \( \theta = 2 \times \arccos((r - f)/r) \), \( r = d/2 \)
Rectangular Tank: \( V_{total} = h \times w \times l \) or \( V_{filled} = f \times w \times l \) (partial)
Elliptical Tank: \( V_{total} = \pi \times w \times l \times h / 4 \) or \( V_{filled} = l \times h \times w/4 \times [\arccos(1 - 2f/h) - (1 - 2f/h) \times \sqrt{4f/h - 4(f/h)^2}] \) (partial)
Frustum: \( V_{total} = (1/3) \times \pi \times h \times ((d_{top}/2)^2 + (d_{top}/2) \times (d_{bot}/2) + (d_{bot}/2)^2) \) or \( V_{filled} = (1/3) \times \pi \times f \times R^2 \), where \( R = (d_{top}/2) \times (f + z)/(h + z^2) \), \( z = h \times (d_{bot}/d_{top} - d_{bot}) \)
Cone Bottom Tank: \( V_{total} = (1/3) \times \pi \times h_{cone} \times ((d_{top}/2)^2 + (d_{top}/2) \times (d_{bot}/2) + (d_{bot}/2)^2) + \pi \times (d_{top}/2)^2 \times h_{cylinder} \) (partial fill based on frustum and cylinder portions)

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 total and filled volumes are calculated in cm³, and then converted to liters and gallons. Fill height is optional and adjusts the filled volume accordingly.

3. Importance of Tank Volume Calculation

Details: Calculating the total and filled volume of a tank is essential for storage capacity planning, liquid management, and ensuring proper equipment sizing in industrial or domestic applications.

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). Optionally, enter the fill height for partial volume calculations. The result shows the total volume and, if a fill height is provided, the filled volume in cm³, liters, and gallons.

5. Example

Given (Horizontal Cylinder): Diameter = 1 m, Length = 2 m, Fill Height = 0.5 m.
Volume Calculation: After converting units: Diameter = 100 cm, \( r = 50 \, \text{cm} \), Length = 200 cm, Fill Height = 50 cm.
- \( V_{total} = \pi \times 50^2 \times 200 \approx 15,708,000 \, \text{cm}^3 \)
- \( \theta = 2 \times \arccos((50 - 50)/50) = 0 \) (but for fill height 50 cm): \( \theta = 2 \times \arccos(0) = \pi \)
- \( V_{filled} = 0.5 \times 50^2 \times (\pi - 0) \times 200 \approx 7,854,000 \, \text{cm}^3 \)
Conversions:
- Total: \( \text{cm}^3 \approx 15,708,000 \), \( \text{liters} \approx 15,708 \), \( \text{gallons} \approx 4,150 \)
- Filled: \( \text{cm}^3 \approx 7,854,000 \), \( \text{liters} \approx 7,854 \), \( \text{gallons} \approx 2,075 \).

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