Rectangular Prism: Definition, Volume & Surface Area

Definitionnoun phrase

What is a rectangular prism in math?

A rectangular prism is a solid shape with six rectangular faces, where opposite faces match and every corner is a right angle. A shoebox and a brick are rectangular prisms. It has 12 edges and 8 vertices, and its volume is length times width times height: V = lwh.

In Spanish: prisma rectangular
Also called: cuboid, rectangular solid, right rectangular prism, box
Grade level: K-5

Grade 5Grade 6Grade 7GeometryCCSS 5.MD.C.5.bCCSS 6.G.A.2GEDSATACTASVABTABEHiSET

Rectangular Prism in a picture

Multiply the three edges that meet at a corner: 6 × 3 × 4 = 72 unit cubes fill this box.

Formal definition and notation

A (right) rectangular prism is a polyhedron bounded by three pairs of congruent, parallel rectangular faces that meet at right angles. With edge lengths l, w and h, its volume is V = lwh cubic units and its surface area is S = 2lw + 2lh + 2wh square units.

Symbol	Read it as	Meaning
l, w, h	length, width, height	the three edge lengths that meet at one corner
B	capital B	the area of the base, B = lw, so V = Bh
cm³	cubic centimeters	a unit of volume

Key facts

A rectangular prism has 6 faces, 12 edges and 8 vertices, and opposite faces are identical rectangles.
Volume: V = lwh, or base area times height, V = Bh. The answer is in cubic units.
Surface area: S = 2lw + 2lh + 2wh, the area of three pairs of matching faces. The answer is in square units.
A cube is a rectangular prism whose length, width and height are all equal.
You may call any face the base; the volume comes out the same.

Rectangular prism formulas

V = l × w × h

V: volume: how many unit cubes fill the prism (cubic units)
l, w, h: length, width and height, in the same unit
S = 2lw + 2lh + 2wh: surface area: the total area of the six faces (square units)

Volume fills the inside; surface area covers the outside. A 5 by 4 by 3 box has V = 60 cubic units but S = 94 square units.

Rectangular Prism examples, step by step

Example 1: Volume of a box

Warm-up

A box is 5 cm long, 4 cm wide and 3 cm tall. What is its volume?

Use V = l × w × h.
V = 5 × 4 × 3 = 60.

Answer: The volume is 60 cubic centimeters.

Example 2: Surface area of the same box

Core

How much paper covers the outside of that 5 cm by 4 cm by 3 cm box, with no overlap?

Top and bottom: 2 × (5 × 4) = 40.
Front and back: 2 × (5 × 3) = 30.
Two ends: 2 × (4 × 3) = 24.
Add: 40 + 30 + 24 = 94.

Answer: The surface area is 94 square centimeters.

Example 3: Fill a fish tank

Test-style

A fish tank is 50 cm long, 30 cm wide and 40 cm tall. One liter is 1,000 cubic centimeters. How many liters does the full tank hold?

Volume: 50 × 30 × 40 = 60,000 cubic centimeters.
Convert: 60,000 ÷ 1,000 = 60.

Answer: The tank holds 60 liters.

Common mistakes

✗ MistakeVolume of a 5 by 4 by 3 box: 5 + 4 + 3 = 12.

✓ InsteadMultiply: 5 × 4 × 3 = 60 cubic units.

Volume counts the unit cubes inside: 5 by 4 cubes on the bottom layer, stacked 3 layers high.

✗ MistakeWriting the volume as 60 square centimeters.

✓ InsteadVolume is in cubic units: 60 cubic centimeters.

Multiplying three lengths gives cubes (cm × cm × cm). Square units are for area.

✗ MistakeA box 2 m long, 50 cm wide and 30 cm tall: 2 × 50 × 30 = 3,000.

✓ InsteadConvert first: 2 m = 200 cm, so 200 × 50 × 30 = 300,000 cubic centimeters.

All three edges must be in the same unit before you multiply.

Not to be confused with

Rectangular Prismvs.Rectangle

A rectangle is flat (2-D) with area lw. A rectangular prism is a solid (3-D) whose six faces are rectangles, with volume lwh.

Rectangular Prismvs.Pyramid

A pyramid with the same base and height holds one third as much: a 6 by 6 base and height 10 give a prism of 360 but a pyramid of 120.

Quick check: 3 questions

Question 1 of 3

What is the volume of a rectangular prism that is 8 in long, 2 in wide and 5 in tall?

Show answer and explanation

Answer: B. 8 × 2 × 5 = 80. Choice A adds the edges, C is the surface area, and D multiplies only two of the edges.

Question 2 of 3

How many faces does a rectangular prism have?

Show answer and explanation

Answer: D. It has 6 faces: top, bottom, front, back, left and right. It has 8 vertices and 12 edges, which are choices B and C.

Question 3 of 3

A cube has edges of 3 cm. What is its volume?

Show answer and explanation

Answer: A. A cube is a rectangular prism with l = w = h = 3: 3 × 3 × 3 = 27. Choice B is one face, C is the surface area, D is 4 × 3.

Rectangular Prism: frequently asked questions

Is a cube a rectangular prism?

Yes. A cube is a rectangular prism whose length, width and height are all equal, so all six faces are squares. Every formula for a rectangular prism works for a cube: with edge 4, the volume is 4 times 4 times 4, or 64 cubic units, and the surface area is 6 times 16, or 96 square units.

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

Volume measures the space inside, in cubic units: how much the box holds. Surface area measures the outside covering, in square units: how much wrapping paper you need. A 5 by 4 by 3 box has a volume of 60 cubic units and a surface area of 94 square units.

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

Not for volume or surface area. Multiplication can be done in any order, so 5 × 4 × 3 and 3 × 5 × 4 both give 60. Labels matter only when a problem tells you which edge is the height, for example to find how deep the water is in a tank.

Practice and tools

Volume CalculatorCheck the volume of a box Surface Area CalculatorCheck the area of all six faces

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 5.MD.C.5.b, CCSS 6.G.A.2

Cite this entry

Effortless Math Team. “Rectangular Prism.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/rectangular-prism/

Flashcard

TermRectangular PrismV = lwh

DefinitionA box-shaped solid with 6 rectangular faces, 12 edges and 8 vertices. A 6 by 3 by 4 box has volume 72 cubic units.

Study the full deck

Browse all terms in the Math Dictionary · More geometry terms · Random term

CongruentCongruent means exactly the same size and shape. Two segments are congruent when they have the same length, two angles when they have the same measure, and two figures when one can be turned, flipped or slid onto the other. The symbol is ≅: AB ≅ CD reads “segment AB is congruent to segment CD.”Geometry · Grade 8, GeometryRight AngleA right angle is an angle that measures exactly 90 degrees, a quarter of a full turn. It looks like the corner of a square or a sheet of paper, and it is marked with a small square at the vertex. Two lines that meet at a right angle are perpendicular.Geometry · Grade 2, Grade 3, Grade 4LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3VolumeVolume measures the amount of space inside a three-dimensional figure, in cubic units such as cubic centimeters or cubic feet. You can find it by counting the unit cubes that fill the solid. For a rectangular prism, V = l × w × h; for any prism, it equals the area of the base multiplied by the height.Geometry · Grade 5, Grade 6, Grade 7Surface AreaSurface area is the total area of all outside faces of a three-dimensional figure, measured in square units. To find it, unfold the solid into a flat net, find the area of each face and add them. A box with length l, width w and height h has surface area 2lw + 2lh + 2wh.Geometry · Grade 6, Grade 7, Grade 8SquareA square is a quadrilateral with four equal sides and four right angles. It is a special rectangle and a special rhombus at the same time. For a square with side s, the perimeter is 4s, the area is s², and each diagonal is s√2.Geometry · Kindergarten, Grade 2, Grade 3HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6CentimeterA centimeter is a metric unit of length equal to one hundredth of a meter, about the width of a fingernail. Its symbol is cm. There are 100 centimeters in 1 meter and 10 millimeters in 1 centimeter, and 1 inch equals 2.54 centimeters.Measurement · Grade 3, Grade 4, Grade 5PyramidA pyramid is a solid figure with one polygon as its base and triangular faces that rise from the base edges and meet at a single top point, the apex. A pyramid is named by its base, such as a square pyramid. Its volume is one third of the base area times the height: V = 13Bh.Geometry · Grade 6, Grade 7, Grade 8MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4AreaArea is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.Geometry · Grade 3, Grade 4, Grade 5WidthWidth is the distance across a shape or object from side to side. In a rectangle, width is one of the two side measurements used with length, usually the shorter one, and multiplying length by width gives the area of a rectangle. Width is measured in length units such as inches, feet, centimeters or meters.Measurement · Grade 3, Grade 4, Grade 5SphereA sphere is a perfectly round solid shape, like a ball, in which every point on the surface is the same distance from the center. That distance is the radius. A sphere has no faces, edges or vertices. Its volume is V = 43π r³ and its surface area is 4π r².Geometry · Kindergarten, Grade 8, Geometry

Rectangular Prism

What is a rectangular prism in math?

Rectangular Prism in a picture

Formal definition and notation

Key facts

Rectangular prism formulas

Rectangular Prism examples, step by step

Example 1: Volume of a box

Example 2: Surface area of the same box

Example 3: Fill a fish tank

Common mistakes

Not to be confused with

Quick check: 3 questions

Rectangular Prism: frequently asked questions

Is a cube a rectangular prism?

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

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

Related terms

Practice and tools

Sources

Flashcard

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