Scale Conversion Calculator

This professional-grade scale conversion calculator helps architects, engineers, makers, and modelers translate between real-world dimensions and drawing/model sizes. Instantly convert lengths using any ratio (e.g., 1:50), derive a scale from two measurements, or compute the exact print percentage to move between two scales.

Data Source and Methodology

Primary sources:

  • ISO 5455:1979 — Technical drawings — Scales. International Organization for Standardization. View ISO reference.
  • NIST Special Publication 811 (2019 Edition) — Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology. nist.gov/pml/special-publication-811.

All calculations are strictly based on the formulas and unit relationships provided by these sources.

The Formula Explained

For a general ratio a:b (drawing : real), the scale factor k that converts a real length L_real to a drawing length L_draw is:
$$ k = \frac{a}{b} $$
$$ L_{\mathrm{draw}} = L_{\mathrm{real}} \cdot k = L_{\mathrm{real}} \cdot \frac{a}{b} $$
Conversely:
$$ L_{\mathrm{real}} = \frac{L_{\mathrm{draw}}}{k} = L_{\mathrm{draw}} \cdot \frac{b}{a} $$
To normalize any ratio a:b to 1:n:
$$ n = \frac{b}{a} \quad\Rightarrow\quad 1:n $$
Print percentage to convert from scale a₁:b₁ to a₂:b₂:
$$ \text{Print \%} = 100 \times \frac{a_2/b_2}{a_1/b_1} = 100 \times \frac{a_2 \cdot b_1}{b_2 \cdot a_1} $$
When deriving a scale from two measurements:
$$ k = \frac{L_{\mathrm{draw}}}{L_{\mathrm{real}}} \quad\Rightarrow\quad 1:\frac{1}{k} $$

Glossary of Variables

  • a (drawing ratio): Units on the drawing or model corresponding to b units in reality.
  • b (real ratio): Units in real life corresponding to a units on the drawing.
  • k (scale factor): The multiplicative factor to go from real to drawing, k = a/b.
  • L_real: Real-world length before scaling.
  • L_draw: Length on the drawing/model after scaling.
  • Print %: Percentage to set in the print dialog to move from one scale to another.

How It Works: A Step-by-Step Example

Scenario: Scale a 3.2 m hallway to a drawing at 1:50.

  1. Set the ratio: a = 1, b = 50, so k = a/b = 1/50 = 0.02.
  2. Apply the factor: L_draw = L_real × k = 3.2 × 0.02 = 0.064 m.
  3. Convert to millimeters for clarity: 0.064 m = 64 mm.

Result: On the drawing, the hallway measures 64 mm. If you need to print a 1:100 drawing as 1:50, print at 200% because 100 ÷ 50 × 100 = 200%.

Frequently Asked Questions (FAQ)

What’s the difference between scale factor and scale ratio?

The scale ratio is written as a:b (drawing:real). The scale factor k is a decimal equal to a/b that multiplies real lengths to obtain drawing lengths.

Can I convert between metric and imperial?

Yes. Enter the length in one system and choose a different output unit. The tool converts via exact SI relationships (1 in = 25.4 mm, 1 ft = 0.3048 m).

Do I need to enter a = 1?

No. While many drawing scales use a = 1, you can input any positive a:b. The tool will also normalize to 1:n for readability.

How precise are the results?

Results are computed using double-precision floating point and rounded for display. You can adjust units to get practical values (e.g., mm instead of m).

How do I derive the scale from two measurements?

Measure a known feature on the drawing (L_draw) and input the real length (L_real). The scale factor is L_draw/L_real, and the ratio is 1:(1/k).

What print percentage converts 1:200 to 1:250?

Print at 80%. Using the formula, Print % = 100 × (a₂·b₁)/(b₂·a₁). For common ratios with a₁ = a₂ = 1, it reduces to 100 × (b₁/b₂) = 100 × (200/250) = 80%.

Tool developed by Ugo Candido. Content verified by Scale Calculator editorial team.
Last reviewed for accuracy on: .