Convert a drawing to real size

How do I read an architectural scale?

The scale says how many inches on the drawing stand for one foot of the real thing. At ¼ inch = 1 foot, every ¼ inch on the plan is a foot, so a wall that measures 3 inches on paper is 3 × 4 = 12 feet long.

What ratio is ¼ inch to a foot?

1:48 — a foot is 12 inches, and 12 ÷ ¼ = 48, so the real thing is 48 times larger. ⅛ inch = 1 foot is 1:96, ½ inch = 1 foot is 1:24 and 1 inch = 1 foot is 1:12.

How do I draw something to scale?

Divide the real length by the scale ratio. A 30 ft wall at ¼ inch = 1 foot: 30 ft is 360 inches, and 360 ÷ 48 = 7½ inches on paper.

What is an engineering scale?

Engineering scales read 1 inch = 10, 20, 30, 40, 50 or 60 feet and are used for site plans and surveys. 1 inch = 20 feet is 1:240: 2 inches on the plan is 40 feet on the ground.

How do metric scales work?

A metric scale is a plain ratio. At 1:50, 1 centimeter on the drawing is 50 centimeters in reality; at 1:100, 1 centimeter is 1 meter. Check that a printed plan says "not to scale" or has a scale bar before measuring from it — printers and PDFs often resize.

How does scale affect area?

Area scales with the square of the ratio. At ¼ inch = 1 foot (1:48), one square inch on the drawing stands for 2,304 square inches, or 16 square feet, in reality. A drawing that is half the size in each direction shows a quarter of the area.

Working with the ratio

Every scale is a ratio of real size to drawing size. An architectural scale of x inches to the foot means that 12 ÷ x real inches are shown by 1 drawing inch, so ¼ inch = 1 foot is 1:48. An engineering scale of 1 inch = n feet is 1:240 when n is 20. To go from the drawing to the real size, multiply by the ratio; to go the other way, divide. Both lengths must use the same unit before the ratio is applied.

Worked examples

A 30 ft wall at ¼ inch = 1 foot is 360 inches, which is 7.5 inches on paper. A room that measures 5½ inches on the same plan is 264 inches, or 22 feet, in real life. On a metric drawing at 1:50, a line 7.3 cm long represents 365 cm, or 3.65 m. On an engineering plan at 1 inch = 20 feet (1:240), a distance of 3¼ inches is 65 feet on the ground.

Common mistakes

Measuring a drawing that has been enlarged or reduced when printed gives the wrong answer, since the printed scale is then no longer true; check against a scale bar or a known dimension, and don't trust a stated scale on a copy. Mixing the architectural way of writing a scale (inches per foot) with the ratio way (1:48) is another source of errors. The third is applying the length ratio to an area or a volume, which scale with its square and cube. Also, dimensions written on the drawing take precedence over lengths you measure with a ruler.

Sources: the definition of drawing scale as a ratio of drawing length to real length, as in standard architectural and engineering graphics texts; conversions (12 inches to the foot, 2.54 cm to the inch) from NIST SP 811. Related: ratio calculator, proportion calculator, feet and inches calculator and paper size calculator.