How do I calculate rectangular prism volume with different units?

First convert all three dimensions to the same unit (for example, all to centimeters), then multiply: V = l × w × h. Our calculator lets you choose a unit for each side and automatically converts them before computing the volume.

What is the difference between volume and surface area of a rectangular prism?

Volume measures how much space is inside the prism and is given in cubic units (like cm³). Surface area measures the total area of all six faces and is given in square units (like cm²). For a rectangular prism, V = l × w × h, while surface area S = 2(lw + lh + wh).

Can I use this formula for cubes?

Yes. A cube is a special case of a rectangular prism where all edges are equal: l = w = h. The volume formula becomes V = a³, where a is the edge length of the cube.

How do I find one side length if I know the volume?

Rearrange the formula V = l × w × h. For example, if you know V, w, and h, then l = V ÷ (w × h). Our calculator supports this: leave one side blank, enter the other two and the volume, and it will solve for the missing dimension.

Rectangular Prism Volume Calculator (Cuboid)

Q: What is the formula for the volume of a rectangular prism?

The volume V of a rectangular prism (cuboid) is V = l × w × h, where l is length, w is width, and h is height. All three dimensions must be in the same units. The result is in cubic units, such as cm³ or m³.

Rectangular prism volume formula

A rectangular prism (also called a cuboid) is a 3D solid with 6 rectangular faces and right angles at every corner. Its three edge lengths are usually called length (ℓ), width (w), and height (h).

Volume of a rectangular prism

\( V = \ell \times w \times h \)

where:

\( \ell \) = length
\( w \) = width
\( h \) = height

All three dimensions must be in the same unit. The volume is then in cubic units (cm³, m³, in³, ft³, etc.).

Surface area and space diagonal

Our calculator also gives you the total surface area and the space diagonal of the prism:

Surface area

\( S = 2(\ell w + \ell h + w h) \)

Space diagonal

\( d = \sqrt{\ell^2 + w^2 + h^2} \)

How to calculate the volume of a rectangular prism (step by step)

Example 1 – Basic volume

Find the volume of a rectangular prism with:

length ℓ = 5 cm
width w = 3 cm
height h = 2 cm

Step 1. Write the formula:

\( V = \ell \times w \times h \)

Step 2. Substitute the values:

\( V = 5 \,\text{cm} \times 3 \,\text{cm} \times 2 \,\text{cm} \)

Step 3. Multiply:

\( V = 30 \,\text{cm}^3 \)

Example 2 – Mixed units

Suppose a box has length 20 cm, width 0.5 m, and height 10 cm. To use the formula, convert everything to the same unit.

0.5 m = 50 cm

Now compute:

\( V = 20 \,\text{cm} \times 50 \,\text{cm} \times 10 \,\text{cm} = 10{,}000 \,\text{cm}^3 \)

To convert to liters, recall that \( 1 \,\text{L} = 1000 \,\text{cm}^3 \):

\( V = 10{,}000 \,\text{cm}^3 = 10 \,\text{L} \).

Example 3 – Solving for a missing side

A storage box has volume 60 cm³, width 3 cm, and height 2 cm. What is the length?

Step 1. Start from \( V = \ell w h \) and solve for ℓ:

\( \ell = \dfrac{V}{w h} \)

Step 2. Substitute the values:

\( \ell = \dfrac{60}{3 \times 2} = \dfrac{60}{6} = 10 \,\text{cm} \)

Common mistakes to avoid

Mixing units (e.g., using cm and m together without converting).
Forgetting cubic units – volume is always in units like cm³, m³, in³, ft³.
Confusing surface area with volume – surface area uses square units (cm², m²), not cubic.
Using only two dimensions – you must multiply all three: length, width, and height.

Rectangular prism vs. cube

A cube is a special case of a rectangular prism where all three sides are equal: \( \ell = w = h = a \). The volume formula becomes:

\( V = a^3 \)

You can still use this calculator for cubes: just enter the same value for length, width, and height.

FAQ

What is the formula for the volume of a rectangular prism?

The formula is \( V = \ell \times w \times h \), where ℓ is length, w is width, and h is height. Make sure all three are in the same unit.

Can I calculate volume if one side is missing?

Yes. If you know the volume and the other two sides, rearrange the formula:

\( \ell = \dfrac{V}{w h} \)
\( w = \dfrac{V}{\ell h} \)
\( h = \dfrac{V}{\ell w} \)

In this calculator, leave the unknown side blank, enter the other two sides and the volume, and it will solve it for you.

How do I use this calculator for real-world problems?

Typical uses include:

Finding how much water a fish tank or pool can hold.
Estimating storage capacity of boxes or containers.
Solving geometry homework and exam questions.