How to Figure Volume of a Rectangle: Formula & Examples
To figure the volume of a rectangle, multiply its length × width × height — the three dimensions of a rectangular prism (a box shape with six rectangular faces). The result is always expressed in cubic units, such as cubic inches (in³) or cubic centimeters (cm³). For example, a box measuring 5 cm long, 3 cm wide, and 2 cm tall has a volume of 5 × 3 × 2 = 30 cm³. If you can measure the three sides, you can find the volume. This guide walks through the formula, a worked example, and the mistakes that trip people up.
Volume Formula Explained
Strictly speaking, a rectangle is a flat, two-dimensional shape — it has length and width, but no height. So when someone asks how to figure volume of a rectangle, what they usually mean is the volume of a rectangular prism: the 3D solid you get when a rectangle is extended into space, like a brick, a shoebox, or a fish tank.
Volume measures how much three-dimensional space an object occupies, and it is always reported in cubic units because you are multiplying three lengths together. The formula is:
V = l × w × h
Where:
- V = volume
- l = length (the longest side of the base)
- w = width (the shorter side of the base)
- h = height (how tall the solid stands)
This is the same reasoning behind any prism: find the area of the base (length × width) and multiply by the height. Math is Fun presents it exactly this way — base area times height. Because multiplication is commutative, the order in which you multiply the three dimensions does not change the answer: l × w × h gives the same result as w × h × l.
One vocabulary note: when all six faces are squares and all edges are equal, the shape is a cube, and the formula simplifies to V = s³. A cube is just a special rectangular prism.
Step-by-Step Calculation
Finding volume comes down to three measurements and one multiplication. Khan Academy emphasizes labeling each dimension before you calculate, which prevents mix-ups later.
- Measure the length. Pick the longest edge of the base and measure it with a ruler, tape measure, or calipers.
- Measure the width. Measure the shorter edge of the base, perpendicular to the length.
- Measure the height. Measure straight up from the base to the top face.
- Convert all three to the same unit. If the length is in inches, the width and height must be in inches too.
- Multiply the three numbers. V = l × w × h.
- Attach cubic units. If you measured in centimeters, the answer is in cm³.
The unit you measure in determines the unit of your answer — you do not convert at the end, you cube whatever unit you started with. Inches become in³, feet become ft³, meters become m³. This is why step 4 matters so much: multiplying a length in inches by a width in centimeters produces a meaningless number.
In homework problems, the three dimensions are usually supplied in the prompt, so you can skip straight to multiplying. In real life, you measure. Either way, the multiplication step is identical.
A Worked Example
A jewelry box is 8 cm long, 5 cm wide, and 4 cm tall.
V = 8 × 5 × 4 = 160 cm³
The base area is 8 × 5 = 40 cm², and multiplying by the height of 4 cm gives 160 cm³. Notice how the units work out: cm × cm × cm = cm³.
Common Mistakes to Avoid
Confusing area with volume. Area is two-dimensional (l × w) and uses square units like cm². Volume is three-dimensional (l × w × h) and uses cubic units like cm³. If your answer is in square units, you forgot to multiply by height.
Mixing units. Multiplying 10 inches by 2 feet by 3 feet does not give a valid volume. Convert everything to one unit first — 2 feet is 24 inches, so the calculation becomes 10 × 24 × 36.
Mixing up length, width, and height. Since multiplication is commutative, swapping length and width changes nothing. But using a diagonal measurement, or measuring the height at an angle instead of straight up, produces a wrong answer. Measure perpendicular edges only.
Forgetting to cube the unit. Writing “cm” instead of “cm³” is a common slip. Volume is always in cubic units.
Assuming every 3D shape uses this formula. A cylinder uses πr²h, a sphere uses (4/3)πr³, and a pyramid uses (1/3) × base area × height. The l × w × h formula applies only to rectangular prisms and cubes.
Rounding too early. If you convert units mid-problem, keep the full precision until the final step, then round once.
Key Takeaways
- Volume of a rectangular prism = length × width × height (V = l × w × h).
- A rectangle itself is flat; its 3D counterpart is a rectangular prism, which is what actually has volume.
- Always measure in the same unit, and report the answer in cubic units (cm³, in³, m³, ft³).
- A cube is a special case where V = s³.
- Area (square units) and volume (cubic units) are different measurements — do not confuse them.
- For non-rectangular shapes like cylinders or spheres, a different formula is required.
