A scale drawing is a drawing of a real object in which every length is multiplied by the same number, so it has the same shape but a different size. Its scale, such as 1 cm = 2 m, links a length on the drawing to the actual length. Maps, floor plans and blueprints are scale drawings.
Each drawing length is multiplied by 2 to get meters. Find the actual lengths first, then the area: 12 × 8 = 96 m².
Formal definition and notation
A scale drawing is a figure whose lengths are all proportional to the corresponding lengths of the actual object, with equal corresponding angles. The scale states the ratio drawing length : actual length, with units (1 in : 10 ft) or without (1 : 50, meaning the same unit on both sides). If lengths are multiplied by a scale factork, areas are multiplied by k2.
Symbol
Read it as
Meaning
1 cm : 2 m
one centimeter represents two meters
a scale with units
1 : 200
one to two hundred
a scale without units: 1 unit on the drawing is 200 of the same unit in real life
Key facts
Every length in the drawing uses the same scale, so angles and shape stay the same: the drawing and the object are similar figures.
A scale like 1 cm = 5 m is a rate: 5 m of real length per 1 cm of drawing.
A scale without units, such as 1 : 50, uses the same unit on both sides: 3 cm on the plan is 150 cm in real life.
Areas do not use the scale once: if 1 cm stands for 2 m, then 1 cm² stands for 2 × 2 = 4 m².
A scale drawing can be larger than the object, as in a diagram of an insect (say 5 cm : 1 cm).
Using a scale
Using a scale
drawing lengthactual length = scale drawing partscale actual part
drawing to actual
multiply the drawing length by the actual part of the scale (for 1 cm : 2 m, times 2)
actual to drawing
divide the actual length by it
Set up a proportion with the scale on one side and keep drawing lengths in the same position on both sides.
Try it: drawing to actual
Interactive
With a scale of 1 cm = 3 m, each row pairs a drawing length with its actual length. The ratio stays the same in every row, which is what makes the drawing to scale.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Scale Drawing examples, step by step
Example 1: Reading a map
Warm-up
On a map, 1 inch represents 25 miles. Two towns are 3.5 inches apart on the map. How far apart are they?
Each inch stands for 25 miles.
3.5 × 25 = 87.5.
Answer: The towns are 87.5 miles apart.
Example 2: From actual to drawing
Core
An architect uses a scale of 1 cm = 4 m. A wall is 18 m long. How long is it on the drawing?
Proportion: 1 cm4 m = d cm18 m.
Cross multiply: 4d = 18.
d = 4.5.
Answer: The wall is 4.5 cm long on the drawing.
Example 3: Area from a scale drawing
Test-style
A floor plan shows a rectangular room 6 cm by 4 cm at a scale of 1 cm = 2 m. What is the actual area of the room?
Actual length: 6 × 2 = 12 m. Actual width: 4 × 2 = 8 m.
Actual area: 12 × 8 = 96 m².
Shortcut check: drawing area 24 cm² times 22 = 4 gives 96. Multiplying 24 by 2 would give the wrong answer 48.
The scale names two lengths, often with different units (1 cm = 2 m). The scale factor is the single number that multiplies lengths with the same units: 1 cm = 2 m is a scale factor of 200 from drawing to room.
Every scale drawing is similar to the real object. Similar figures is the general geometry idea; a scale drawing is a practical use of it with a stated scale.
A dilation is a transformation on the coordinate plane that resizes a figure from a center point. A scale drawing is a picture of a real object; the resizing idea is the same.
Quick check: 3 questions
Question 1 of 3
A map scale is 1 cm = 15 km. Two cities are 6 cm apart on the map. What is the real distance?
Show answer and explanation
Answer: C.6 × 15 = 90 km. 21 adds, 2.5 divides 15 by 6, and 0.4 divides 6 by 15.
Question 2 of 3
A model car is built at a scale of 1 : 24. The model is 18 cm long. How long is the real car?
Show answer and explanation
Answer: A.18 × 24 = 432 cm (4.32 m). 42 adds, 0.75 divides, and 432 m uses the wrong unit: a scale without units keeps the same unit.
Question 3 of 3
A garden is drawn as a 3 in by 5 in rectangle at a scale of 1 in = 4 ft. What is the actual area of the garden?
Show answer and explanation
Answer: C. Actual sides: 12 ft and 20 ft, so the area is 12 × 20 = 240 ft². 15 is the drawing area, 60 multiplies it by 4 once, and 120 multiplies it by 8.
Scale Drawing: frequently asked questions
What is the scale of a scale drawing?
The scale is the ratio that tells how a length on the drawing compares with the real length, such as 1 in = 10 ft or 1 : 100. Multiply a drawing length by the real part of the scale to get the actual length, and divide an actual length by it to get the drawing length.
How do you find the area from a scale drawing?
Convert the lengths first, then find the area. A 4 cm by 3 cm rectangle at 1 cm = 5 m becomes 20 m by 15 m, so its area is 300 m². Multiplying the drawing area, 12 cm², by 5 would give 60, which is wrong; area changes by the square of the scale, here 52 = 25.
Can a scale drawing be bigger than the real object?
Yes. A scale drawing of something tiny, such as a computer chip or an ant, is often an enlargement. A scale of 10 : 1 means 10 cm on the drawing stands for 1 cm in real life. Every length is still multiplied by the same number, so the shape stays the same.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.G.A.1
Cite this entry
Effortless Math Team. “Scale Drawing.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/scale-drawing/
Flashcard
TermScale Drawing1 cm = 2 m
DefinitionA drawing where every length is scaled by the same ratio. At 1 cm = 2 m, a 6 cm line is 12 m; areas scale by 22 = 4.
LengthLength 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 3Corresponding AnglesCorresponding angles are two angles in the same relative position at each place where a transversal crosses two lines, such as the top-left corner at both crossings. When the two lines are parallel, corresponding angles are equal. A transversal across two lines makes four pairs of corresponding angles.Geometry · Grade 8, GeometryRatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8SideA 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 2Scale FactorA scale factor is the number used to multiply side lengths when making a similar figure larger or smaller. A scale factor of 2 doubles every length, and a scale factor of 12 makes lengths half as large. Find it by dividing a new length by the matching original length. Areas change by the square of the scale factor.Ratios and Proportions · Grade 7, Grade 8, Algebra 1Similar FiguresSimilar figures have the same shape but not necessarily the same size. Corresponding angles match, and corresponding side lengths are proportional: each side of one figure is the same multiple, the scale factor, of the matching side of the other. A scale drawing is similar to the real object.Geometry · Grade 7, Grade 8, Algebra 1ProportionA proportion is an equation that says two ratios are equal, such as 12 = 36. It is read 1 is to 2 as 3 is to 6. In a true proportion the cross products are equal, which lets you find a missing value. Proportions are often used to solve scale, percent, and rate problems.Ratios and Proportions · Grade 6, Grade 7, Grade 8InchAn 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 4MileA mile (mi) is a US customary unit of length for long distances, equal to 5,280 feet or 1,760 yards. One mile is about 1.61 kilometers, so it is longer than a kilometer. Road distances and speed limits in the United States use miles and miles per hour.Measurement · Grade 4, Grade 5, Grade 6SquareA 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 3MeterA 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 5CentimeterA 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 5NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2DilationA dilation is a transformation that enlarges or shrinks a figure by a scale factor k from a fixed center point. Each point moves along the ray from the center to k times its distance. With center at the origin, (x, y) → (kx, ky). The image keeps its shape, so it is similar, not congruent.Geometry · Grade 8, GeometryTransformationA transformation moves or changes a figure on the coordinate plane. The four common transformations are translations (slides), reflections (flips), rotations (turns) and dilations (resizing). The original figure is the preimage and the result is the image, labeled with primes such as A′. Only a dilation changes the size.Geometry · Grade 7, Grade 8, Algebra 1Coordinate PlaneThe coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin, (0, 0). Every point is located by an ordered pair, x first then y, such as (3, −2). The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.Geometry · Grade 5, Grade 6, Grade 7Unit RateA unit rate is a rate that compares a quantity to one unit of another quantity, such as 50 miles per hour or 4 dollars per notebook. To find it, divide the first quantity by the second: 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour. The word per means for each one.Ratios and Proportions · Grade 6, Grade 7, Grade 8AreaArea 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 5PerimeterPerimeter 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 5Cross MultiplicationCross multiplication is a shortcut for solving a proportion: if ab = cd, then ad = bc. Multiply each numerator by the denominator on the other side and set the two products equal. To solve x6 = 1015, write 15x = 60, so x = 4. It works only when one fraction equals one fraction.Ratios and Proportions · Grade 7, Grade 8, Algebra 1Unit ConversionUnit conversion is rewriting a measurement in a different unit without changing the amount, such as writing 3 feet as 36 inches. You multiply by a conversion factor, a fraction equal to 1 such as 12 in1 ft. Converting to a smaller unit gives a larger number; converting to a larger unit gives a smaller number.Measurement · Grade 4, Grade 5, Grade 6