Scale and ratios
On a drawing at 1 : 50 everything is 50 times smaller than in reality. Calculate both ways — and use the same thinking for prices and recipes.
The explanation is shown. Quick: scale and measurement — units are cm and m. Advanced: all units, volume, rule of three and proportional division, and the answer at the typical scales.
Your numbers
Common scales
More options: units
Answer
In reality
4m
How to work it out
- 18 cm · 50 = 400 cm
- 2400 cm = 4 m
The formula
1 : n
1 cm on the drawing is n cm in reality. 1 : 50 means everything is drawn 50 times smaller.
reality = drawing · n · drawing = reality / n
Remember to work in the same unit before you multiply or divide.
area: · n²
If you measure an AREA on the drawing, multiply by n · n — so at 1 : 50 by 2,500, not by 50.
volume: · n³
A VOLUME (a model) is multiplied by n · n · n — so at 1 : 50 by 125,000.
a → b ⇒ c → b/a · c
Rule of three: first find what 1 gives, then multiply up.
In depth: more numbers and “what if”
8 cm on the drawing at the typical scales
| Scale | In reality |
|---|---|
| 1 : 10 | 0.8 m |
| 1 : 20 | 1.6 m |
| 1 : 50 | 4 m |
| 1 : 100 | 8 m |
| 1 : 200 | 16 m |
| 1 : 500 | 40 m |
More: Equations and functions
- EquationsSolve equations and inequalities step by step — and isolate a quantity in a formula.
- Formula with three quantitiesThe formula triangle: find the third quantity in A = B · C — e.g. U = R · I.
- FunctionsQuadratic function, inverse proportionality and power function — with a graph.
- Linear functiony = ax + b as a graph and table — the line through two points or the line of best fit.
- Two equations with two unknownsSolve a system of equations step by step and see the intersection on the graph.
- Growth and decayPercentage growth, the growth rate from two measurements, and doubling time.