Width in Math: Definition, Formulas & Examples

Definitionnoun

What is width in math?

Width 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.

In Spanish: ancho
Also called: side-to-side distance, breadth, w (in formulas)
Grade level: K-5

Grade 3Grade 4Grade 5Grade 6CCSS 4.MD.A.3GED

Width in a picture

In a flat rectangle, the width is the side-to-side measure next to the length. In a box, it is the front-to-back measure. Width is always a distance, in plain length units.

Formal definition and notation

For a rectangle, the width w is the length of a side adjacent to the side chosen as the length l, so the rectangle has area A = lw and perimeter P = 2l + 2w. For a rectangular prism, width is the edge running front to back, with V = lwh. More generally, the width of an object in a given direction is its extent across that direction.

Symbol	Read it as	Meaning
w or W	w	the width in a formula
A = lw	A equals l times w	area of a rectangle
P = 2l + 2w	P equals 2 l plus 2 w	perimeter of a rectangle
V = lwh	V equals l times w times h	volume of a rectangular prism

Key facts

Width is a distance, so it should use length units such as inches, feet, centimeters, or meters.
In a rectangle, width is usually the shorter side and length the longer, but either name works if you use it consistently.
Multiplying length by width gives the area of a rectangle: a 7 by 3 rectangle has area 21 square units.
A rectangle has two widths and two lengths, which is why the perimeter is 2l + 2w.
For a box, the three measurements are length, width and height, and volume is their product.

Finding the width of a rectangle

w = Al or w = P − 2l2

A: the area, in square units
P: the perimeter, in length units
l: the length of the rectangle

Both formulas come from undoing A = lw and P = 2l + 2w. The answer is a distance, so it gets plain length units (feet, not square feet).

Try it: change the width

Interactive

Drag the corner, or use the arrow keys, to change the length and the width. Try to build a rectangle with area 24 square units and width 3: what must the length be?

This interactive needs JavaScript. The worked examples below show the same ideas step by step.

Width examples, step by step

Example 1: Width from area

Warm-up

A rectangular patio has an area of 54 square feet and a length of 9 feet. What is its width?

Use A = lw: 54 = 9w.
Divide both sides by 9: w = 54 ÷ 9 = 6.
Units: square feet divided by feet gives feet.

Answer: The width is 6 feet.

Example 2: Width from perimeter

Core

A rectangle has a perimeter of 46 centimeters and a length of 15 centimeters. Find its width.

Use P = 2l + 2w: 46 = 2(15) + 2w.
Simplify: 46 = 30 + 2w, so 2w = 16.
Divide by 2: w = 8.
Check: 2(15) + 2(8) = 30 + 16 = 46.

Answer: The width is 8 centimeters.

Example 3: Length given in terms of width

Test-style

A rectangular garden is 3 times as long as it is wide. Its perimeter is 64 meters. What is the width of the garden?

Let the width be w. Then the length is 3w.
Perimeter: 2(3w) + 2w = 64.
Combine: 8w = 64, so w = 8.
The length is 3 × 8 = 24. Check: 2(24) + 2(8) = 64.

Answer: The width is 8 meters (and the length is 24 meters).

Common mistakes

✗ MistakeThe width of the patio is 6 square feet.

✓ InsteadThe width is 6 feet.

Width is a distance, so it should use length units such as inches, feet, centimeters, or meters. Square units are for area.

✗ MistakeArea 40, length 10, so width = 40 − 10 = 30.

✓ InsteadWidth = 40 ÷ 10 = 4, because 10 × 4 = 40.

Area is length times width, so you undo it with division, not subtraction.

✗ MistakePerimeter 26, length 8, so width = 26 − 8 = 18.

✓ Instead26 = 2(8) + 2w, so 2w = 10 and w = 5.

The perimeter goes around all four sides: two lengths and two widths.

Not to be confused with

Widthvs.Length

Length and width are the two side measures of a rectangle. By habit, length is the longer one: a 7 by 3 rectangle has length 7 and width 3.

Widthvs.Perimeter

Width is one side. Perimeter is the distance all the way around: for length 7 and width 3, the perimeter is 20.

Widthvs.Height

Height measures up and down. In a box, the width goes front to back while the height goes from the bottom to the top.

Quick check: 3 questions

Question 1 of 3

A rectangle has an area of 60 square inches and a length of 12 inches. What is its width?

Show answer and explanation

Answer: B. 60 ÷ 12 = 5, and a width is a distance, so 5 inches. Choice A has the wrong units, C subtracts, and D multiplies.

Question 2 of 3

Which unit makes sense for the width of a door?

Show answer and explanation

Answer: C. Width is a distance, so it uses a length unit such as inches. Square feet measure area, cubic feet measure volume, and pounds measure weight.

Question 3 of 3

A rectangle has a perimeter of 30 meters and a width of 6 meters. What is its length?

Show answer and explanation

Answer: A. 30 = 2l + 2(6), so 2l = 18 and l = 9. Choice B subtracts only one width, C divides 30 by 6, and D forgets to divide by 2.

Width: frequently asked questions

Is the width always shorter than the length?

Usually, but it is a habit, not a rule. Most textbooks call the longer side of a rectangle the length and the shorter side the width. Some problems name them the other way, and for a square they are equal. The formulas A = lw and P = 2l + 2w give the same answer either way.

What is the difference between width and height?

Width measures side to side (or front to back for a box), and height measures up and down. For a picture on a wall, the width is how far it stretches across and the height is how tall it is. Screens and frames are often described as width by height, such as 16 by 9.

How do you find the width of a rectangle?

If you know the area and the length, divide: w = A ÷ l. If you know the perimeter and the length, subtract two lengths and halve: w = (P − 2l) ÷ 2. For area 54 and length 9, the width is 6. Always label the answer with length units.

Practice and tools

Area and Perimeter CalculatorArea and perimeter from length and width Unit ConverterChange a width from inches to feet or meters Volume CalculatorVolume of a box from length, width and height

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.MD.A.3

Cite this entry

Effortless Math Team. “Width.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/width/

Flashcard

TermWidthw in A = lw

DefinitionThe side-to-side distance of a shape. A rectangle with area 40 and length 10 has width 40 ÷ 10 = 4.

Study the full deck

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

AreaArea 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 5LengthLength 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 3SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2PerimeterPerimeter is the total distance around a two-dimensional shape. To find it, add the lengths of all the sides. A rectangle with sides 5 and 3 has perimeter 5 + 3 + 5 + 3 = 16. Perimeter is a length, so it uses length units such as inches or meters, never square units.Geometry · Grade 3, Grade 4, Grade 5Rectangular PrismA 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.Geometry · Grade 5, Grade 6, Grade 7VolumeVolume 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 7InchAn inch is a US customary unit of length equal to one twelfth of a foot, about the width of an adult thumb. Its abbreviation is in. Rulers split each inch into halves, quarters, eighths and sixteenths. One inch is exactly 2.54 centimeters, and 12 inches make 1 foot.Measurement · Grade 2, Grade 3, Grade 4CentimeterA 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 5MeterA meter (m) is a metric unit of length equal to 100 centimeters. It is the base unit of length in the metric system, a little over three feet (about 3.28 feet). A doorway is about 2 meters tall, and 1,000 meters make a kilometer. To change meters to centimeters, multiply by 100.Measurement · Grade 3, Grade 4, Grade 5SquareA 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 6SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6DivisionDivision is the operation of splitting a number into equal groups. In 12 ÷ 3 = 4, the dividend 12 is shared into 3 equal groups (the divisor), and each group gets 4 (the quotient). Division undoes multiplication, because 3 × 4 = 12. If the groups do not come out even, the amount left over is the remainder.Operations · Grade 3, Grade 4, Grade 5Surface 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 8FormulaA formula is a rule written with symbols that shows how quantities are related. It is an equation with two or more variables, such as A = lw for the area of a rectangle. Formulas help solve problems the same way each time: substitute the values you know, then compute the one you need.Problem Solving · Grade 5, Grade 6, Grade 7

Width

What is width in math?

Width in a picture

Formal definition and notation

Key facts

Finding the width of a rectangle

Try it: change the width

Width examples, step by step

Example 1: Width from area

Example 2: Width from perimeter

Example 3: Length given in terms of width

Common mistakes

Not to be confused with

Quick check: 3 questions

Width: frequently asked questions

Is the width always shorter than the length?

What is the difference between width and height?

How do you find the width of a rectangle?

Related terms

Practice and tools

Sources

Flashcard

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