Volume Rectangular Prism Calculator

This calculator works out the volume of a rectangular prism (also called a cuboid or a box) from its length, width, and height. You enter the three dimensions in any order, and it returns the volume in cubic units, along with the surface area. The formula is simply Volume = Length × Width × Height.

Formula

The volume of a rectangular prism is the product of its three dimensions:

V = l × w × h

• V – volume, in cubic units (e.g., m³, cm³, ft³)
• l – length, in linear units (m, cm, ft)
• w – width, in linear units
• h – height, in linear units

The surface area is the sum of the areas of all six faces:

A = 2(lw + lh + wh)

Both formulas assume the prism has straight, perpendicular edges and flat rectangular faces.

Worked Example

Using the default values from the calculator above: length = 5 m, width = 3 m, height = 2 m.

1. Multiply length by width: 5 × 3 = 15 m² (this is the base area).
2. Multiply the base area by height: 15 × 2 = 30 m³.
3. For surface area: 2 × (5×3 + 5×2 + 3×2) = 2 × (15 + 10 + 6) = 2 × 31 = 62 m².

The calculator shows volume = 30.00 m³ and surface area = 62.00 m², matching the steps above.

When to Use This Calculator

You need this calculation whenever you are filling, packing, or covering a box-shaped space. Common situations include:

• Finding how much soil, sand, or concrete is needed for a rectangular planter, raised bed, or slab.
• Working out the capacity of a fish tank or storage container (then converting cubic meters to liters: 1 m³ = 1000 L).
• Estimating the volume of a moving box or shipping crate to choose the right size.
• Calculating the amount of water in a rectangular pool or aquarium (1 m³ = 1000 liters).
• Determining the volume of a room for air conditioning or heating estimates.

In all these cases, the prism must be a true rectangular box – all angles 90°, opposite faces parallel. If the shape is tapered or irregular, this formula will not be accurate.

How to Read the Result

The volume is always in cubic units. If you enter dimensions in meters, the volume is in cubic meters (m³). If you enter centimeters, you get cubic centimeters (cm³). A common real-world conversion: 1 liter = 1,000 cm³ = 0.001 m³. So if your fish tank is 60 cm × 30 cm × 40 cm, the volume is 72,000 cm³, which is 72 liters.

The surface area is in square units (m², cm², ft²). It is useful for estimating paint, fabric, or sheet material needed to cover the outside of the box.

Common Mistakes and Tips

• Mixing units: All three dimensions must be in the same unit. If you mix meters and centimeters, the result is meaningless. Convert first.
• Forgetting the cubic unit: Volume is not just a number – it is always cubic units. Write m³, cm³, or ft³.
• Using the wrong formula: A rectangular prism is not a cylinder or a pyramid. Do not use πr²h or (1/3)bh unless the shape is actually different.
• Rounding too early: If you round intermediate steps, the final answer can be off. Keep full precision until the end.

Limits of the Formula

The formula V = lwh is exact only for a perfect rectangular prism. Real objects rarely have perfectly flat faces or right angles. For a slightly irregular box, the error is usually small, but for a shape that is significantly tapered (like a flower pot or a pyramid), this formula will overestimate the volume. For such shapes, use the appropriate formula for a frustum or pyramid.

Also, the calculator assumes the interior volume equals the exterior dimensions product. If the walls are thick (e.g., a concrete tank), the interior volume is smaller. Subtract the wall thickness from each dimension before calculating.

Frequently Asked Questions

How do I find the volume of a rectangular prism if I only know the surface area?

You cannot – there are infinitely many prisms with the same surface area but different volumes. You need at least two dimensions, or one dimension and the surface area, to solve for the third and then compute volume.

What is the difference between a rectangular prism and a cube?

A cube is a special case where all three dimensions are equal. The volume formula is the same: V = l × w × h, and if l = w = h = a, then V = a³.

How do I convert cubic meters to liters?

Multiply by 1000. 1 m³ = 1000 liters. So a prism with volume 0.5 m³ holds 500 liters.

Can I use this calculator for a box with different units on each side?

No. All three dimensions must be in the same unit. If you have one side in feet and another in inches, convert first (1 ft = 12 in).

Does the order of length, width, and height matter?

No. Multiplication is commutative, so the volume is the same regardless of which side you call length, width, or height. The surface area formula also does not depend on the order.

How do I find the height if I know the volume and the base area?

Rearrange the formula: h = V / (l × w). For example, if the volume is 60 m³ and the base is 5 m × 3 m, then h = 60 / 15 = 4 m.

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in l | Length | m | 5 | 0
in w | Width | m | 3 | 0
in h | Height | m | 2 | 0
out volume | Volume | m³ | l * w * h | 2
out area | Surface area | m² | 2 * (l * w + l * h + w * h) | 2