Volume of an L-Shaped Prism: Formula & Calculator

This calculator works out the volume of an L-shaped prism in cubic units. You enter the three outer dimensions (height, width, and depth) and the two inner cutout dimensions, and it returns the volume of the solid. The result is given in the same cubic unit you used for the inputs (e.g., cubic inches, cubic feet, cubic centimeters, cubic meters).

Formula

The volume of any prism is the area of its cross-section multiplied by its length (or depth). For an L-shaped prism, the cross-section is an L-shape, so the formula is:

Volume = (H × W − (H − T) × (W − T)) × D

Where:

• H = outer height of the L-shape (same unit as W and T)
• W = outer width of the L-shape
• T = thickness of the two legs (assumed equal)
• D = depth or length of the prism (the distance the L-shape is extruded)

The expression (H × W) is the area of the full rectangle that encloses the L-shape. The expression (H − T) × (W − T) is the area of the missing corner rectangle. Subtracting gives the area of the L-shape itself. Multiplying by D gives the volume.

Worked Example

Using the default values from the calculator:

• Outer height H = 10 in
• Outer width W = 8 in
• Thickness T = 2 in
• Depth D = 6 in

Step 1: Area of the enclosing rectangle = 10 × 8 = 80 in².

Step 2: Area of the missing corner = (10 − 2) × (8 − 2) = 8 × 6 = 48 in².

Step 3: Area of the L-shape = 80 − 48 = 32 in².

Step 4: Volume = 32 × 6 = 192 in³.

The calculator returns 192.00 in³, matching this result.

When to Use This Calculator

Use this tool whenever you need the volume of a solid that has an L-shaped cross-section and a constant depth. Common real-world situations include:

• Estimating concrete needed for an L-shaped footing or retaining wall corner.
• Calculating the volume of an L-shaped aquarium or water tank.
• Finding the amount of soil or gravel to fill an L-shaped planter box.
• Determining the volume of an L-shaped metal bracket or plastic component for shipping or material cost estimates.

If your L-shape has legs of different thicknesses, you cannot use this simple formula directly. In that case, split the shape into two rectangles (one vertical leg and one horizontal leg) and add their volumes.

How to Read the Result

The result is in cubic units. If you entered inches, the volume is cubic inches (in³). If you entered feet, it is cubic feet (ft³). For metric, centimeters give cm³ and meters give m³.

To convert to other volume units:

• 1 cubic foot = 1,728 cubic inches
• 1 cubic yard = 27 cubic feet
• 1 cubic meter = 1,000,000 cubic centimeters
• 1 liter = 1,000 cubic centimeters
• 1 US gallon ≈ 231 cubic inches

For example, 192 in³ is about 0.83 US gallons (192 ÷ 231).

Common Mistakes and How to Avoid Them

• Mixing units: All dimensions must be in the same unit. If you measure height in feet and width in inches, convert one first. Otherwise, the volume will be off by a factor of 12 or 144.
• Using the inner cutout dimensions directly: The formula subtracts the missing corner, but you must use the outer dimensions and the thickness. Do not enter the inner dimensions as if they were the outer ones.
• Forgetting the depth: The volume of a prism requires the depth. If you only have the area of the L-shape, you must multiply by the depth to get volume.
• Rounding too early: Keep full precision during intermediate steps, then round the final answer. Rounding the area before multiplying by depth can change the result noticeably.

Limitations of the Formula

This formula assumes the L-shape has two legs of equal thickness (T). If the vertical leg is thicker than the horizontal leg, the shape is not a simple L with equal legs, and the formula above does not apply. Also, the formula assumes the prism is straight (not tapered) and that the cross-section is constant along the depth. For a tapered L-shaped column or a shape with rounded corners, this calculation will not be accurate.

For an L-shape with unequal leg thicknesses, break the cross-section into two rectangles: one rectangle for the vertical leg (width = T1, height = H) and one for the horizontal leg (width = W − T1, height = T2, where T2 is the thickness of the horizontal leg). Then volume = (H × T1 + (W − T1) × T2) × D. This is just the sum of two rectangular prisms.

Frequently Asked Questions

How do I find the volume of an L-shaped prism without a calculator?

Split the L-shape into two rectangles. For example, if the L has a vertical leg of height H and thickness T, and a horizontal leg of width W and thickness T, the area is H×T + (W−T)×T. Then multiply by the depth. This is equivalent to the calculator’s formula.

What if my L-shape has different leg thicknesses?

Use the two-rectangle method described above. Let T1 be the thickness of the vertical leg and T2 the thickness of the horizontal leg. The area is H×T1 + (W−T1)×T2. Then multiply by depth. Do not use the equal-thickness formula.

Can I use this for an L-shaped swimming pool?

Yes, if the pool has a constant depth and vertical walls. If the pool slopes, you need to calculate the volume in sections or use an average depth, which is less accurate.

How do I convert cubic inches to gallons?

Divide the volume in cubic inches by 231. For example, 192 in³ ÷ 231 ≈ 0.83 US gallons. For imperial gallons, divide by 277.42.

What is the difference between volume and surface area?

Volume measures the space inside the solid, in cubic units. Surface area measures the total area of all faces, in square units. This calculator gives volume only. For surface area, you would need to add the areas of all six faces (or more, depending on the shape).

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in h | Outer height | in | 10 | 0
in w | Outer width | in | 8 | 0
in d | Depth (length) | in | 6 | 0
in t | Thickness of both legs | in | 2 | 0
out vol | Volume | in³ | (h*w - (h-t)*(w-t)) * d | 2