Surface and Microanalysis Science Division (Chemical Science and Technology Laboratory)
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Web-based Tool for Converting Carbon Dioxide Isotope Measurements into Standardized delta–13–C and delta–18–O Values


Background Information...

This program calculates delta-13-C and delta-18-O values (versus VPDB) from measurement data and other information supplied by the user. Required measurement data are the delta-45 and delta-46 measurements of samples and reference materials against a single 'working machine gas' in dual inlet mode. Data from one reference material allows single-point realization of the VPDB scale; data from two reference materials allows two-point realization and normalization of the sample values.

The data reduction program utilized to convert delta-45 and delta-46 measurements into delta-13-C and delta-18-O values uses an iterative algorithm [similar to ref. 1] that calculates the results exactly. Users may wish to validate the algorithm integrated into their laboratory instrumentation, or specify the values of several variables usually fixed in reduction programs in order to see the effect upon the calculations. These variables are:

    1. the constant (a) describing the oxygen isotope relationship, where r17/S17 = [r18/S18]^a. For historical reasons and simplicity, the IAEA recommends [ref. 2] that a = 0.5 continue to be used, although they note that other values may be more accurate [refs. 1, 3-6].
    2. the absolute oxygen isotope ratios (S17 and S18) of a single reference material, which are used as the basis for calculating r17 values of all other materials through the oxygen isotope relationship (above). The IAEA recommends the S17 and S18 values for VPDB consistent with the S18 value of VSMOW, where 1.03092 * S18 (VPDB) = S18 (VSMOW) [ref. 2, 11]. However, other values of S17 and S18 have sometimes been used, such as those listed in the Table below:

a = 0.5
[ref. 7, 8]

a = 0.5
[ref. 2]

VSMOW, where
a = 0.516
[ref. 3]

VSMOW, where
a = 0.516
[ref. 3]

VSMOW, where
a = 0.528
[ref. 6]
VPDB based on carbon ratio measurements of NBS-19
0.0111802 [ref. 14]




0.0003799 [ref. 9]

0.0004023261 [ref. 1]

0.000386913 [ref. 12]
0.000386913 [ref. 12]
0.0020052 [ref. 10]
0.0020052 [ref. 10]
0.0020052 [ref. 10]
0.0020052 [ref. 10]


Craig [ref. 7]
IAEA [ref. 2]
Santrock [ref. 1]
Assonov [ref. 12]
Assonov [ref. 12]


Based on original work

Consistency and comparability with historical data

Based on direct measurements of absolute abundances

Minimized co-variance of delta-13-C and delta-18-O

Minimized co-variance of delta-13-C and delta-18-O in multi-instrument study. See Table 10-D [ref. 13]
Bases the absolute value of the carbon ratio in VPDB (S13) on measurements of NBS-19 and the defined relationship between these two standards. The effect on calculated delta values in natural abundance samples, however, is insignificant.

K = S17/(S18)^a

All S17 and S18 values have significant uncertainties which are not reported here. These values are not certified, nor are their precisions necessarily justified by their uncertainties. The precisions reported for S17 and S18 values in VPDB are "accepted" by the measurement community to provide consistency for data reduction algorithms and high precision in the intercomparability of data.

Given the relationships defined by values of S17, S18 and a, all other dependent values in the program are calculated accordingly.

The IAEA recommends that the VPDB scale be realized through the internationally available standard carbonate NBS 19, where delta–13–C = +1.95 ‰ and delta–18–O = -2.2 ‰ versus VPDB, exactly. Through intercomparisons and measurements relating NBS 19 CO2 with other CO2 Reference Materials (RMs), these RMs may be used as proxies for the realization of the VPDB scale. Please note that the value assignments of reference materials listed here are calculated using the IAEA recommendations (ref. 2).

Values of delta-18-O may be reported against VPDB, VPDB-CO2, and VSMOW. VPDB-CO2 is the standard carbon dioxide derived from the hypothetical VPDB material by digestion in 100% phosphoric acid at 25.0 degrees Celsius, where the fractionation factor is 1.01025. Conversion formulae are:

d-18-O (vs.VPDB-CO2) = [d-18-O (vs.VPDB) - 10.25] / 1.01025

d-18-O (vs.VSMOW) = [1.03092 * d-18-O (vs.VPDB)] + 30.92

Uncertainty in measurement, and in the resulting values, is not directly treated in this program. Propagated, combined uncertainty will be a function of the uncertainty in all variables. Uncertainty may be explored by manually changing the values of the variables to see the effect upon the resulting delta values.

Other data corrections, such as peak tail and cross contamination, are not treated in this program. It is assumed that input measurement data have already been corrected for these effects, especially when only one RM is used to realize the VPDB scale. For two-point realization, data normalization by interpolation will tend to compensate for effects that act similarly on sample and reference materials. However, two-point realization should not be used to normalize a sample value outside the range of the two reference materials.


  1. Santrock, J., Studley, S.A. and Hayes, J.M. (1985) Anal. Chem. 57, 1444-1448.
  2. Allison, C. E., Francey, R. J. and Meijer, H. A. J. (1995) in Reference and Intercomparison Materials for Stable Isotopes of Light Elements, IAEA-TECDOC-825, pp. 155-162.
  3. Matsuhisa, Y., Goldsmith, J.R. and Clayton, R.N. (1978) Geochim. Cosmochim. Acta 42, 173-182.
  4. Thiemens, M.H. (1992) ACS Symp. Ser. 502 (Isotope Effects in Gas-Phase Chemistry, ed. J.A. Kaye), pp. 138-154.
  5. Robert, F., Rejou-Michel, A. and Javoy, M. (1992) Earth Planet. Sci. Lett. 108, 1-9.
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  8. Nier, A.O. (1950) Phys. Rev. 77, 789-793.
  9. Li, W.J., Ni, B.L., Jin, D.Q. and Chang, T.L. (1988) Kexue Tongbao (Chinese Science Bulletin) 33, 1610-1613.
  10. Baertschi, P. (1976) Earth Planet. Sci. Lett. 31, 341-344.
  11. Werner, R.A. and Brand W.A. (2001) Rapid Commun. Mass Spectrom. 15, 501-519.
  12. Assonov, S.S. and Brenninkmeijer, C.A.M. (2003) Rapid Commun. Mass Spectrom. 17, 1017-1029.
  13. Verkouteren, R.M. and Klinedinst, D.B. (2003) NIST Special Publication 260-149
  14. Chang, T.L and Li, W.J. (1990) Chin. Sci. Bull. 35, 290.