What a scale ratio says
The notation 1:10 means one unit measured on the drawing represents ten of the same units on the real object. A 2000 mm object is 200 mm long on a correctly produced 1:10 drawing. The ratio has no preferred unit: 1 cm can represent 10 cm, and 1 inch can represent 10 inches, provided both sides use the same unit.
The first number belongs to the drawing; the second belongs to reality. At 1:50, divide real dimensions by 50 to obtain drawing dimensions. To recover a real dimension from the drawing, multiply by 50.
drawing dimension = real dimension × drawing factor / real factorat 1:n, drawing dimension = real dimension / nCommon reduction scales
| Scale | Meaning | 1000 mm in reality appears as | Typical use |
|---|---|---|---|
| 1:1 | Full size | 1000 mm | Templates and small details |
| 1:2 | Half size | 500 mm | Large components |
| 1:5 | One fifth | 200 mm | Fabrication details |
| 1:10 | One tenth | 100 mm | Assemblies and details |
| 1:20 | One twentieth | 50 mm | Rooms and structural details |
| 1:50 | One fiftieth | 20 mm | Building plans and elevations |
| 1:100 | One hundredth | 10 mm | General arrangements and site plans |
An enlargement reverses the relationship. At 2:1, two drawing units represent one real unit, so a real 25 mm component appears 50 mm on the drawing. Enlargements are useful for small details that would otherwise be hard to dimension.
Worked conversions
Reality to drawing: 4.8 m at 1:50
First use one unit throughout. Convert 4.8 m to 4800 mm, then divide by 50.
4800 mm / 50 = 96 mm on the drawingIf the drawing sheet is output at the intended size, the line should measure 96 mm.
Drawing to reality: 37 mm measured at 1:20
Multiply the drawing measurement by 20.
37 mm × 20 = 740 mm in realityDo not scale from a reproduction unless its output scale has been verified. A photocopy, screenshot or “fit to page” PDF may have changed the ratio.
Dimensions outrank ruler measurements
In technical drawing practice, the written dimension is the declared size. Measuring a line with a ruler is a secondary check and may be misleading if the sheet has been reduced, enlarged or distorted. This is why a drawing can communicate exact geometry even when a view is marked “not to scale”: the dimension text remains meaningful while the physical line length does not.
A reliable print usually includes a known scale bar or check dimension. Confirm the paper size, choose 100% or “actual size” rather than “fit,” print, and measure the reference. If the reference is wrong, every ruler-derived measurement is wrong by the same output factor.
Why a monitor is not automatically physical scale
Browsers lay out pages in CSS pixels, not verified millimetres on every device. Pixel density, operating-system scaling, browser zoom, responsive layout and the physical display all change the size of a line on screen. A 200-pixel line on two monitors can have different physical lengths.
Draw to Scale uses proportional geometry: if one side is twice another, the view shows that relationship. It also uses dimension labels to state calculated values. It does not claim that a line on an arbitrary display measures at a certified 1:10 or 1:50 physical scale.
Scale factor and area or volume
Lengths change directly with the scale factor, but area changes with its square and volume with its cube. A model at 1:10 has lengths one tenth of full size, face areas one hundredth, and volume one thousandth. This is a common source of estimating mistakes.
length factor = k · area factor = k² · volume factor = k³If a rectangular drawing is doubled in both directions, its area becomes four times as large—not twice. If a 3D model doubles in length, width and height, its volume becomes eight times as large.
Scale bars, check dimensions and tolerances
A graphic scale bar changes size with the sheet and can reveal that a print or image was resized. A written check dimension serves a similar purpose: compare its physical plotted length with the value expected at the stated scale. If a 1000 mm check dimension on a 1:20 drawing does not measure 50 mm, do not scale other distances from that output.
Drawing scale is also separate from dimensional tolerance. A line may plot neatly at 1:5 while the permitted fabrication variation is stated elsewhere. The scale controls presentation; dimensions, notes, specifications and standards control the required size and acceptance criteria.
Common scale mistakes
- Reversing 1:50 and multiplying when you should divide.
- Mixing metres and millimetres inside the ratio.
- Applying the linear factor directly to area or volume.
- Measuring a PDF or screenshot without confirming output size.
- Assuming a drawing marked 1:50 stayed at 1:50 after copying or page fitting.
- Scaling a written dimension. Unless clearly overridden, use the stated number rather than a ruler measurement.
How this informs Draw to Scale
Russell’s drafting perspective shapes the site’s central idea: a calculation becomes easier to interpret when dimensions are shown in their geometric relationship. The calculators redraw proportions from the inputs and place values beside the relevant edges, radii or angles. That makes the view useful for understanding and checking without pretending the screen is a calibrated sheet.
For the distinction between proportional display, numerical accuracy and project-specific verification, see Methodology & Accuracy.