Scale Calculator (drawing & map scale to real size and back)

Understanding the scale calculator — concept and principle

This calculator converts between a length on a drawing or map and the real length, using a scale such as 1 : 100 or 1 : 50,000. It works in both directions and in metric and imperial units. Use it for architectural plans, maps, model making, floor plans and technical drawings.

Every length on a 1:100 drawing is multiplied by 100, so 4.5 cm becomes 4.5 m.

How it is calculated

For a scale a : b (a on the drawing, b in reality):

Scale factor k = b ÷ a.
Real length = drawing length × k.
Drawing length = real length ÷ k.

Lengths are converted through metres using exact factors: 1 in = 0.0254 m, 1 ft = 0.3048 m, 1 yd = 0.9144 m, 1 mi = 1,609.344 m. For an enlargement such as 10 : 1, enter 10 on the drawing side and 1 on the real side.

The principle

A scale is a ratio of lengths in the same unit. "1 : 100" means 1 cm on the drawing stands for 100 cm in reality, 1 inch for 100 inches, and so on. Because it is a pure ratio, you can measure in any unit as long as you convert the result. Every length on a scaled drawing is multiplied by the same factor, so shapes and angles stay the same. Areas, however, scale with k² and volumes with k³: a room drawn at 1 : 100 has a real floor area 10,000 times the area on paper.

Worked example

Default inputs: real size from a drawing length, scale 1 : 100, length 4.5 cm, result in metres.

Scale factor k = 100 ÷ 1 = 100.
Real length = 4.5 cm × 100 = 450 cm.
Convert: 450 cm = 4.5 m.
So 1 cm on the drawing represents 1 m in reality.

Each point is the calculator re-run with only “Scale — drawing side (the 1 in 1:100)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Scale — drawing side (the 1 in 1:100)	Result
0.25	18 m
0.5	9 m
0.75	6 m
1	4.5 m
1.25	3.6 m
1.5	3 m
2	2.25 m

How to read the result

The result is the real-world length in the unit you chose. The line "1 cm on the drawing represents" gives a handy rule of thumb for reading the rest of the drawing. If the answer seems too big or small by a factor of 10 or 100, check that the drawing length and result units are what you intended.

Common mistakes

Swapping the two sides of the scale.
Mixing units, such as measuring in millimetres but reading the result as centimetres.
Scaling areas with k instead of k².
Measuring a printed or on-screen drawing that was resized, so the stated scale no longer holds.

Keep in mind: Drawings may be printed at a different size from the original. Check a dimensioned length or the scale bar before relying on measurements, and use the written dimensions for construction.

Frequently asked questions

What does 1 : 50,000 mean on a map?

1 cm on the map is 50,000 cm, or 500 m, on the ground.

How do I find the scale from a known length?

Divide the real length by the drawing length in the same unit; the result is the scale factor.

How does scale affect area?

Area scales with the square of the factor; at 1 : 100, 1 cm² on paper is 1 m² in reality.

Sources: U.S. Geological Survey, "Map Scales", Fact Sheet FS-015-02 · NIST Special Publication 811 (2008), Appendix B

Checked 9 Nov 2026. U.S. Geological Survey, “Map Scales” fact sheet FS-015-02 (scale as a representative fraction: one unit on the map equals that many of the same units on the ground; 1:24,000 = 2,000 ft per inch); exact length factors from NIST Special Publication 811 (2008), Appendix B.

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