Renard series

The Renard series is a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. The preferred values are rounded forms of a geometric sequence and can be extended above or below this interval by multiplication or division by powers of ten.

The system is named after the French army engineer Colonel Charles Renard, who developed a system of preferred values during the late nineteenth century. It was later adopted for international standardization and became the basis of ISO Recommendation R3, first published in the 1950s and subsequently superseded by ISO 3.

The factor between consecutive Renard numbers is constant: it is the fifth, 10th, 20th, or 40th root of 10 for the R5, R10, R20, and R40 series, respectively. Since their exact theoretical values are all irrational, they are rounded when used in practice.

The resulting spacing allows a range of sizes to be covered while limiting the number of values that must be standardized, manufactured, or stocked. Renard values have been used for engineering dimensions and ratings, including electrical-component ratings such as fuse currents and capacitor voltages.

Comparison of preferred numbers of the 1–2–5, Renard and f-stop series on a logarithmic scale divided into 40 equal intervals (blue)

Base R5 series

The most basic R5 series consists of five rounded values, which approximate successive powers of the fifth root of 10:

R5: 1.00 1.60 2.50 4.00 6.30

The R5 series may be extended through powers of ten. For example, its values can be expressed as 16, 25, 40, 63, 100, 160, and 250 millimetres when selecting a limited range of nominal product lengths.

Likewise, values such as 100, 160, 250, 400, and 630 volts are examples of preferred voltage ratings derived from the series.

R10, R20, R40, and R80 series

If a finer resolution is needed, intermediate values can be added to form the R10, R20, R40, and R80 series. The R10 series adds five values to R5, while the R20, R40, and R80 series provide successively finer gradations.

In some applications, the values are rounded to fewer decimal places because they are easier to specify, manufacture, or use with integer quantities. ISO 497 provides guidance on selecting such more-rounded preferred-number series. In the table below, rounded values that differ from their less rounded counterparts are shown in bold.

Because Renard values repeat after each tenfold change in scale, they can be used conveniently with SI-based dimensions and other decimal quantities.

Each of the Renard sequences can be reduced to a subset by taking every nth value in a series, which is designated by adding the number n after a slash. For example, "R10″/3 (1…1000)" designates a series consisting of every third value in the R″10 series from 1 to 1000, that is, 1, 2, 4, 8, 15, 30, 60, 120, 250, 500, 1000.

Applications

Renard series are used when designers must balance a wide range of possible values against the cost and complexity of maintaining many different sizes. ISO 17 recommends choosing the series with the widest spacing that still satisfies the technical requirement.

The series have also influenced standard preferred-frequency systems used in acoustics. ISO 266 specifies preferred frequencies for acoustical measurement.

See also

Preceded by
ISO 2		 Lists of ISOs
ISO 3		 Succeeded by
ISO 4
Preceded by
ISO 16		 Lists of ISOs
ISO 17		 Succeeded by
ISO 18

References

  1. 1 2 3 4 5 6 7 8 9 ISO 3:1973 – Preferred numbers – Series of preferred numbers. International Organization for Standardization. April 1973. Retrieved 2026-09-03.
  2. ↑ Hazeltine, Louis Alan (January 1927). "Preferred Numbers". Proceedings of the Institute of Radio Engineers. 14 (4). Institute of Radio Engineers: 785–787. doi:10.1109/JRPROC.1926.221089. ISSN 0731-5996.
  3. ↑ Kienzle, Otto Helmut (1950). Normungszahlen [Preferred numbers] (in German). Springer-Verlag.
  4. ↑ Paulin, Eugen (2007-09-01). Logarithmen, Normzahlen, Dezibel, Neper, Phon – natürlich verwandt! [Logarithms, preferred numbers, decibel, neper, phon – naturally related!] (PDF) (in German). Retrieved 2026-09-03.
  5. 1 2 3 4 ISO 17:1973 – Guide to the use of preferred numbers and of series of preferred numbers. International Organization for Standardization. April 1973. Retrieved 2026-09-03.
  6. ↑ De Simone, Daniel V. (July 1971). U.S. Metric Study Interim Report – Engineering Standards (PDF). National Bureau of Standards. Retrieved 2026-09-03.
  7. 1 2 Van Dyck, Arthur F. (February 1936). "Preferred Numbers". Proceedings of the Institute of Radio Engineers. 24 (2). Institute of Radio Engineers: 159–179. doi:10.1109/JRPROC.1936.228053. ISSN 0731-5996. S2CID 140107818.
  8. 1 2 Hirshfeld, Clarence Floyd; Berry, C. H. (1922-12-04). "Size Standardization by Preferred Numbers". Mechanical Engineering. 44 (12). American Society of Mechanical Engineers: 791–.
  9. 1 2 3 4 "Preferred numbers". Sizes, Inc. 2014-06-10 [2000]. Archived from the original on 2017-11-01. Retrieved 2026-09-03.
  10. ↑ ISO 497:1973 – Guide to the choice of series of preferred numbers and of series containing more rounded values of preferred numbers. International Organization for Standardization. May 1973. Retrieved 2026-09-03.
  11. ↑ Van Dyck, Arthur F. (March 1951). "Preferred Numbers". Proceedings of the IRE. 39 (2). Institute of Radio Engineers: 115. doi:10.1109/JRPROC.1951.230759. ISSN 0096-8390.
  12. ↑ Tuffentsammer, Karl; Schumacher, P. (1953). "Normzahlen – die einstellige Logarithmentafel des Ingenieurs" [Preferred numbers – the engineer's single-digit logarithm table]. Werkstattechnik und Maschinenbau (in German). 43 (4): 156.
  13. ↑ Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers]. VDI-Zeitschrift (in German). 98: 267–274.
  14. ↑ "ISO 266:1997 – Acoustics — Preferred frequencies". International Organization for Standardization. April 1997. Retrieved 2026-09-03.

Further reading