Direct answer

What are the main rectangular prism formulas?

The main rectangular prism formulas are volume $V = l w h$ , surface area $S A = 2 (l w + l h + w h)$ , and base area $B = l w$ . Use length, width, and height in the same unit before multiplying or adding face areas.

Short answer

Rectangular Prism formulas at a glance

Volume: $V = l w h$ Surface area: $S A = 2 (l w + l h + w h)$ Base area: $B = l w$

Definition

What is a rectangular prism?

A rectangular prism is a 3D solid with six rectangular faces.

Diagram

Rectangular Prism diagram

Rectangular prism variables: length l, width w, and height h.

Quick formula table

Rectangular Prism Formulas quick table

Formula	Equation	Variables
Volume	$V = l w h$	l = length, w = width, h = height
Surface area	$S A = 2 (l w + l h + w h)$	Sum of all six rectangular faces
Base area	$B = l w$	Area of the rectangular base

Formula explanation

How to use these formulas

Volume is base area times height. Surface area adds the areas of the three unique face pairs and doubles the sum.

Calculator

Rectangular Prism Calculator

Enter measurements to get the result, unit, formula, and calculation steps.

Examples

Step-by-step examples

Find volume

Given l = 8 cm, w = 4 cm, h = 3 cm.
Use $V = l w h$ .
$V = 8 \times 4 \times 3 = 96 c m^{3}$ .

Find surface area

Given l = 8, w = 4, h = 3.
Use $S A = 2 (l w + l h + w h)$ .
$S A = 2 (32 + 24 + 12) = 136 c m^{2}$ .

Find base area

Given l = 8 cm and w = 4 cm.
Use $B = l w$ .
$B = 8 \times 4 = 32 c m^{2}$ .

Find height from volume

Given V = 120 cm³, l = 10 cm, w = 4 cm.
Use $h = V / l w$ .
$h = 120/40 = 3 c m$ .

Real-world box problem

A box is 5 in by 4 in by 9 in.
Use $S A = 2 (l w + l h + w h)$ .
$S A = 2 (20 + 45 + 36) = 202 i n^{2}$ .

Reverse calculations

Solve backwards from known values

Task	Formula	When to use it
Find height from volume	$h = V / l w$	Use when volume, length, and width are known.
Find width from volume	$w = V / l h$	Use when volume, length, and height are known.
Find length from volume	$l = V / w h$	Use when volume, width, and height are known.

Common mistakes

Using only one face area for surface area.
Writing volume in square units.
Mixing different units before multiplying dimensions.

Practice

Practice problems with answers

1. Find volume when l = 6, w = 5, h = 4.

$V = 120 c u bi c u ni t s$ .

2. Find surface area when l = 6, w = 5, h = 4.

$S A = 2 (30 + 24 + 20) = 148 s q u a r e u ni t s$ .

3. Find height when V = 180 cm³, l = 9 cm, w = 5 cm.

$h = 180/45 = 4 c m$ .

4. Find base area when l = 12 in and w = 7 in.

$B = 84 i n^{2}$ .

5. A box is 10 ft by 3 ft by 2 ft. Find volume.

$V = 60 f t^{3}$ .

Related formulas

FAQ

Rectangular Prism Formulas FAQ

What is the rectangular prism volume formula?

The formula is $V = l w h$ .

What is the surface area formula?

The formula is $S A = 2 (l w + l h + w h)$ .

Is a cube a rectangular prism?

Yes. A cube is a rectangular prism with length, width, and height all equal.