BIZOMAT MAKEOS · Mathematics
Preferred Number (Renard) Series
Which preferred numbers fall between these limits in the chosen Renard series?
Theoretical values of the Renard preferred number series R5, R10, R20, R40 and R80 (the n-th roots of ten) lying between two limits, with the step ratio and the values rounded to three significant figures, for choosing standard sizes, capacities and speeds.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Series | choice | Renard series: n values per factor of ten. |
| Lowest value | Smallest size of interest. | |
| Highest value | Largest size of interest. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Series
- What it is
- Which Renard series to list. The number after R is how many values the series has in each factor of ten, so higher numbers give finer steps.
- Units and format
- Choose one of 5 options from the list: R5 (ratio 1.58); R10 (ratio 1.26); R20 (ratio 1.12); R40 (ratio 1.06); R80 (ratio 1.03).
- Example
- The form opens with “R10 (ratio 1.26)” selected as a worked example. Choose the option that matches your case.
- Get it right
- The theoretical values are listed with three-figure roundings; national standards may round some values differently, so check the standard you work to.
What this means: Lowest value
- What it is
- The smallest size, capacity or speed of interest. The list starts at the first preferred number at or above it.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same unit for both limits; the series itself has no unit.
What this means: Highest value
- What it is
- The largest size, capacity or speed of interest. The list ends at the last preferred number at or below it.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must exceed the lowest value; a range giving more than 200 values is refused.
Method and formulas
- Theoretical values are 10^(i ÷ n) times a power of ten, for the series Rn.
- The step ratio between neighbours is 10^(1/n).
- Standard (ISO 3) rounded values differ slightly from simple rounding at a few steps; use the standard list for final designations.
- Example: R10 between 1 and 10 gives 11 values.
Limitations
- At most 200 values are listed.
- Rounded values shown are to three significant figures, not the standard’s rounded designations.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a rational range of sizes or ratings for a product family
- Pick standard capacities, speeds or pressures
- Check that a size range steps evenly
Who it is for
- Product engineers
- Design engineers
- Standards engineers
What you get
- Values in the range
- Step ratio
- Count of values
Interpreting the result
- Coarser series (R5) keep a product range small; finer series (R40) fit closer to demand.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 672. Topic reference; no source tables or recommended settings are reproduced.
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