Scale Calculator: Drawing and Real Size

What is a scale?

A scale is the ratio of a length on the drawing to the same length in reality. At 1:50, one unit on the drawing is 50 units in reality: a wall drawn 1 cm long is 50 cm, or half a metre.

Real size from a drawing size

Multiply the drawing size by the scale factor: real size = drawing size × n. A room edge that measures 84 mm on a 1:50 plan is 84 × 50 = 4200 mm, or 4.2 m.

Drawing size from a real size

Divide instead: drawing size = real size / n. A facade 12.5 m long is drawn 12 500 / 100 = 125 mm at 1:100.

Two handy equivalents: at 1:100, 1 cm is 1 metre, and at 1:50, 2 cm is 1 metre.

Finding the scale

Bring the drawing size and the real size to the same unit and divide. With 25 mm on the drawing and 5 m in reality, 5000 / 25 = 200, so the scale is 1:200. To check the scale of a printout, measure an edge that carries a written dimension and compare.

Area and volume scale

Area has two dimensions, so it changes with the square of the scale. A plot that measures 12 cm² on a 1:500 site plan is 12 × 500² = 3 000 000 cm², or 300 m². Volume changes with the cube: 8 cm³ in a 1:50 model is 1 m³ in reality.

Changing scale

When the same object is redrawn at another scale, sizes change by the old factor divided by the new one. Taking a 1:50 drawing to 1:100 means a 50 percent reduction, and the reverse a 200 percent enlargement.

Limits

The calculator only does the scale arithmetic. A size scaled off a drawing with a ruler never replaces a written dimension.