Tank Capacity Calculator: Quick & Accurate Volume Tool

Tank Volume Calculator: Your Free Online Tool

This free online calculator provides a quick and reliable way to determine the volume of your storage tank. Our scientific calculator supports ten distinct container shapes, including standard rectangular and cylindrical designs, as well as more specialized capsule, elliptical, and conical bottom tanks. You can even compute the volume of a frustum. Simply input your tank's dimensions, and this free calculator will instantly compute the total capacity. By optionally providing the current fill height, the tool will also calculate the volume of liquid present.

Curious about the mathematics behind it? Continue reading to discover all the essential formulas for capsule tanks, elliptical tanks, cone bottom tanks (often called conical tanks), and many other shapes.

How to Operate This Free Tank Volume Calculator

This free online calculator is a straightforward tool designed to find both the total tank volume and the filled volume. You can select from the following ten tank configurations:

• Vertical cylinder
• Horizontal cylinder
• Rectangular prism (box)
• Vertical capsule
• Horizontal capsule
• Vertical oval (elliptical)
• Horizontal oval (elliptical)
• Cone bottom
• Cone top
• Frustum (truncated cone, funnel-shaped)

Using the calculator is simple. Here is a basic step-by-step guide:

1. First, select your tank's shape. For example, to calculate the volume of a vertical cylindrical tank, choose that option from the list. A schematic diagram will appear for confirmation.
2. Next, enter the required tank dimensions. For a vertical cylinder, this would be the height and diameter. For instance, use a height of 32 inches and a diameter of 24 inches. You can also input the fill height, say 28 inches.
3. The calculator will then display the results. The total tank volume might be 62.7 US gallons, with a filled volume of 54.8 US gallons. You can easily change the measurement units by clicking on them.

Calculating Cylindrical Tank Volume

To determine the total volume of a cylindrical tank, you only need the cylinder's diameter (or radius) and its height (or length if positioned horizontally).

For a vertical cylinder tank, the total volume is calculated using the standard formula: the base area multiplied by the height. The base is a circle, so its area is π × radius². Thus, the formula is:

V_total = π × r² × h = π × (d/2)² × h

Where 'r' is the base radius and 'h' is the cylinder height.

To find the filled volume for a vertical cylinder, simply use the fill height (f) instead of the total height:

V_filled = π × r² × f

For a horizontal cylindrical tank, the total volume is similarly the area of the circular end multiplied by the cylinder's length (l):

V_total = π × r² × l = π × (d/2)² × l

Calculating the partially filled volume of a horizontal cylinder is more complex. It involves finding the area of the circular segment covered by the liquid. The formula requires determining the central angle (θ) based on the fill height. The final formula for the filled volume (V_fhc) is:

V_fhc = 0.5 × r² × (θ - sin(θ)) × l

Where θ = 2 × arccos((r - f) / r). If the cylinder is more than half full, it's often easier to subtract the volume of the empty portion from the total volume.

Rectangular Tank Volume Calculation

A rectangular tank, properly called a rectangular prism or cuboid, has a simple volume formula. Multiply all three internal dimensions together:

V_total = height × width × length

To find the volume of liquid inside, replace the total height with the fill height (f):

V_filled = f × width × length

For this calculation, the tank's orientation (horizontal or vertical) does not matter, as long as the fill height is measured along the correct axis.

Capsule Tank Volume Formulas

A capsule tank is defined as a cylinder with two hemispherical ends. The total volume is the sum of the spherical and cylindrical volumes.

The formula differs based on orientation and fill level. For a horizontal capsule, the filled volume calculation combines the formula for a partially filled horizontal cylinder with that of a spherical cap. For a vertical capsule, the calculation depends on how high the liquid reaches relative to the hemispheres and the cylinder, requiring different formulas for different fill height ranges.

Elliptical (Oval) Tank Volume

An elliptical tank in our tool is a cylinder with elliptical ends. The total volume formula is:

V_total = π × width × length × (height / 4)

Calculating the partially filled volume for an elliptical tank, whether horizontal or vertical, is more complex. It involves using the formula for the area of an ellipse segment and multiplying by the tank's length.

Frustum (Truncated Cone) Tank Volume

The volume of a frustum-shaped tank is calculated with a specific formula:

V_total = (1/3) × π × h_cone × [ (d_top/2)² + (d_top/2)×(d_bot/2) + (d_bot/2)² ]

Where d_top is the upper diameter, d_bot is the lower diameter, and h_cone is the height of the conical section.

To find the volume for a given fill height in a frustum, you must first calculate the top radius of the filled portion using geometric similarity, then apply a modified version of the frustum volume formula.

Cone Bottom and Cone Top Tanks

The total volume of a cone bottom tank is the sum of the volume of the frustum (conical bottom) and the volume of the cylindrical section above it.

To find the filled volume, add together the filled volumes of the frustum and cylinder sections based on the liquid level. The calculation for a cone top tank is analogous, but the filling order is reversed: the cylinder fills first, then the frustum.

Frequently Asked Questions