Rectangular Prism Volume Calculator

Enter length, width and height to get the volume and surface area of a rectangular box, drawn to scale. Click any dimension on the drawing to change it.

Dimensions

Rectangular Prism
Blueprint · Isometric Click an amber dimension to edit it · isometric, not to printed scale

Result

Volume of a rectangular prism

A rectangular prism (cuboid) multiplies length by width by height. Its surface area is the sum of three pairs of matching rectangular faces, and the space diagonal is the straight-line distance between opposite corners.

Editing on the drawing

Each of the three dimensions is editable on the figure — click a value, type a new one and press Enter to redraw to scale.

How to find the volume of a rectangular prism

A rectangular prism — also called a box or cuboid — is the everyday solid behind rooms, tanks, cartons and footings. Three measurements describe it: length, width and height. Once you have those, the volume and surface area follow directly.

The formulas

Volume is the three dimensions multiplied together. Surface area adds up three pairs of matching rectangles.

V = l · w · h
A = 2(lw + wh + hl)

Worked example

Take a box 84 long, 50 wide and 58 high.

Step 1 — volume

Multiply the three dimensions.

V = 84 × 50 × 58 = 243,600
Step 2 — surface area

Three pairs of rectangles.

A = 2(84·50 + 50·58 + 58·84) = 2(4,200 + 2,900 + 4,872) = 23,944
Step 3 — space diagonal

Longest straight line that fits inside.

d = √(84² + 50² + 58²) = √12,920 ≈ 113.67

What else the calculator returns

You also get the base area (l·w) and the space diagonal, the longest object that will fit corner to corner inside the box. Units and decimals are adjustable, and the figure redraws to the proportions you enter.

Where it comes up

Box volumes are used for room and tank capacities, shipping cartons, concrete footings and excavation. Because the order of multiplication doesn't matter, you can label the sides however suits the job — only the drawing cares which is which.

Frequently asked questions

How do you calculate the volume of a box?

Multiply length by width by height: V = l · w · h. The order doesn't matter, so a 2×3×4 box and a 4×2×3 box hold the same 24 cubic units.

Does it matter which side is length, width or height?

No. The volume is the product of all three, so any ordering gives the same answer. The labels only affect how the box is drawn.

How do I find one dimension from the volume?

Divide the volume by the product of the other two dimensions. For example, height = V / (l · w).

What is the space diagonal of a box?

It is the straight-line distance between opposite corners, √(l² + w² + h²) — the longest rigid object that will fit inside.

How is surface area different from volume?

Surface area is the total area of the outside skin, measured in square units, while volume is the space enclosed, measured in cubic units.