Calculating the Volume of a Tank: Rectangular vs Round
By The Calcumatix Team Reviewed by Calcumatix Editorial Review 4 min read
Quick Answer
Rectangular tank volume = length × width × height. Vertical cylindrical tank volume = π × r² × height. Horizontal (side-lying) cylindrical tank volume at partial fill uses a circular-segment formula: V = L × [r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)]. Use the Tank Volume Calculator for rectangular and vertical cylindrical tanks. Use the Horizontal Tank Volume Calculator for any side-lying tank with partial fill.
The formula for tank volume depends entirely on the shape of the tank. A rectangular tank, a vertical cylindrical tank, and a horizontal (side-lying) cylindrical tank each use a different formula, and treating one as another gives a wrong result. This guide covers all three shapes, explains which calculator to use for each, and shows unit conversions from cubic feet to gallons and litres.
Rectangular vs Round vs Horizontal: Which Formula Do You Need?
The three most common tank shapes in construction, agriculture, and industry require three separate formulas. The key distinction is not just the shape of the cross-section but also the orientation: a vertical cylinder is simpler than a horizontal one because the fill level rises uniformly with volume. A horizontal cylinder does not fill uniformly because the width of the liquid surface changes as the level rises.
| Tank Shape | Orientation | Formula Type | Best Calculator |
|---|---|---|---|
| Rectangular (box) | Any | Length × Width × Height | Tank Volume Calculator |
| Cylindrical, vertical (upright) | Tank stands on end | π × r² × height | Tank Volume Calculator |
| Cylindrical, horizontal (side-lying) | Tank lies on its side | Circular-segment formula | Horizontal Tank Volume Calculator |
Use this guide to understand which formula applies. Use the tank volume calculator for rectangular and vertical cylindrical tanks. If your tank is a horizontal cylinder lying on its side, go directly to the horizontal tank volume calculator instead, because the circular-segment formula that tool uses is not the same as a standard cylinder formula.
How Do You Calculate the Volume of a Rectangular Tank?
A rectangular tank (also called a box tank) has a rectangular cross-section on all sides. Its volume is simply the product of the three internal dimensions.
Rectangular tank volume formula: V = L × W × H
Variables:
- L: internal length (ft)
- W: internal width (ft)
- H: internal height or fill depth (ft)
- V: volume in cubic feet
Rectangular Tank Worked Example
Inputs: Internal dimensions: 8 ft long × 4 ft wide × 3 ft tall. Currently filled to 2.5 ft depth.
Step 1: Substitute into the formula V = 8 × 4 × 2.5
Step 2: Calculate V = 80 cubic feet
Step 3: Convert to gallons 80 cu ft × 7.48052 gal/cu ft = 598.4 US gallons (rounded to one decimal place)
Result: The tank holds 598.4 gallons at a 2.5-foot fill depth. Its full capacity at 3 ft is 8 × 4 × 3 = 96 cu ft = 718.1 gallons.
How Do You Calculate the Volume of a Vertical Cylindrical Tank?
A vertical cylindrical tank stands upright with the circular cross-section as its base. The formula multiplies the circular base area by the height (or fill depth).
Vertical cylindrical tank volume formula: V = π × r² × h
Variables:
- r: internal radius (ft), equal to diameter ÷ 2
- h: fill height (ft), measured from the tank bottom to the liquid surface
- π: approximately 3.14159
Vertical Cylindrical Tank Worked Example
Inputs: Tank diameter = 6 ft (radius = 3 ft), fill depth = 4 ft.
Step 1: Substitute V = π × 3² × 4
Step 2: Calculate r² 3² = 9
Step 3: Multiply V = 3.14159 × 9 × 4 = 113.1 cubic feet (rounded to one decimal place)
Step 4: Convert to gallons 113.1 × 7.48052 = 846.0 US gallons (rounded to one decimal place)
Result: The tank holds 846.0 gallons at a 4-foot fill depth.
Why a Horizontal Cylindrical Tank Needs a Different Calculator
A horizontal cylindrical tank lies on its side. As liquid is added, the width of the liquid surface changes because the cross-section is circular rather than rectangular. This means volume does not increase at a constant rate per inch of fill depth: the tank fills faster per inch in the middle (where the cylinder is widest) and slower near the top and bottom. The formula uses a circular-segment calculation, not the simple π × r² × h formula.
If you use the vertical cylinder formula for a horizontal tank at partial fill, you will overstate or understate the actual volume by a significant margin. Use the horizontal tank volume calculator for any cylinder lying on its side. Enter the tank diameter, tank length, and fill depth measured straight up from the bottom of the tank, and the calculator applies the circular-segment formula automatically.
How Do You Convert Tank Volume to Gallons or Litres?
Once the volume in cubic feet is known, convert using standard factors:
| From | To US Gallons | To Litres |
|---|---|---|
| Cubic feet (cu ft) | × 7.48052 | × 28.3168 |
| Cubic inches (cu in) | ÷ 231 | × 0.016387 |
| Cubic metres (m³) | × 264.172 | × 1,000 |
For metric dimensions (length in metres), the volume in cubic metres converts directly to litres by multiplying by 1,000. For imperial dimensions (length in feet), multiplying cubic feet by 7.48052 gives US gallons. To get imperial (UK) gallons, divide cubic feet by 0.1605.
Sources
- CalculatorSoup: Tank Volume Calculator, geometric volume formulas and unit conversions for rectangular and cylindrical tanks.
- USDA NRCS: Tank Volume Calculation Reference, rectangular and cylindrical tank capacity tables.
See all volume tools in the construction calculators hub.
Frequently asked questions
Do I Use the Internal or External Tank Dimensions?
Always use internal dimensions. The internal dimensions reflect the actual space available for liquid. External dimensions include the tank wall thickness, which ranges from a few millimetres for plastic tanks to several centimetres for insulated steel tanks. Using external dimensions overstates the capacity.
What Is the Difference Between the Tank Volume Calculator and the Horizontal Tank Volume Calculator?
The Tank Volume Calculator handles rectangular tanks and vertical cylindrical tanks using simple formulas. The Horizontal Tank Volume Calculator handles cylindrical tanks lying on their sides at any fill depth using the circular-segment formula. They handle different geometries. A vertical cylinder fully filled can be calculated with π × r² × h, but a horizontal cylinder at partial fill cannot.
How Do I Calculate Tank Volume in Litres from Metric Measurements?
Measure all dimensions in metres. Apply the appropriate formula (L × W × H for rectangular, π × r² × h for cylindrical). The result in cubic metres multiplied by 1,000 gives litres. For a 2 m × 1.5 m × 1 m rectangular tank: 2 × 1.5 × 1 = 3 m³ = 3,000 litres.
What Is the Full Capacity of a Cylindrical Tank?
Full capacity equals the formula evaluated at fill height = tank height (vertical cylinder) or fill depth = tank diameter (horizontal cylinder). For a vertical cylinder: V_full = π × r² × total height. For a horizontal cylinder: V_full = π × r² × length. This equals the circular cross-section area (π × r²) multiplied by the tank length in both cases.