delta notation for water isotopes  -  conversion to ppm

δ¹⁸O
The  ¹⁸O concentration of  VSMOW is 2005.2 ppm which is defined as δ¹⁸O = 0.0 ‰ on the VSMOW scale.

Conversion from δ¹⁸O to ppm ¹⁸O is linear:
   conc ¹⁸O [ppm] = (1000 + δ¹⁸O ) x 2.0052

 δ¹⁸O = 0 ‰ (VSMOW)  is equivalent to an ¹⁸O concentration of 2005.2 ppm
 δ¹⁸O = -55.5  ‰ (SLAP) is equivalent to an ¹⁸O concentration of 1893.91 ppm
Our lab water has  δ¹⁸O =  -7.75 ‰ ( equivalent to an ¹⁸O concentration of 1990 ppm)
  δ¹⁸O = -1000 ‰ is equivalent to an ¹⁸O concentration of 0 ppm thus ¹⁸O-free water.

Picarro claims their L2130-i CRDS machines have standard deviations of 0.03 ‰ for δ¹⁸O.
this is equivalent to a standard deviation of 0.06 ppm at a concentrations around 1900 to 2000 ppm !!

Simple conversion of  ¹⁸O concentration to  δ notation on the VSMOW scale

     δ¹⁸O [‰] = conc ¹⁸O  /  2.0052   - 1000           (conc ¹⁸O in ppm)

δ D =  δ ²H

The deuterium (D, ²H) concentration of  VSMOW is 155.76 ppm which is defined as  δ ²H = 0.0 ‰ on the VSMOW scale

The conversion from  δ ²H to  ²H concentration in ppm is linear:

  conc ²H [ppm] = (1000 +  δ ²H) x 0.15576

δ ²H = 0 ‰ (VSMOW)  is equivalent to a ²H concentration of 155.76 ppm
δ ²H = -427.5 ‰ (SLAP) is equivalent to a ²H concentration of 89.173 ppm
Our lab water has   δ ²H =  -52.3 ‰ ( equivalent to a ²H concentration of 147.6 ppm)
δ ²H = -1000 ‰ is equivalent to a ²H concentration of 0 ppm thus deuterium-free water.

Picarro claims their L2130-i CRDS machines have standard deviations of 0.3‰ for  δ ²H.
this is equivalent to a standard deviation of 0.047 ppm at concentrations around 90 to 160 ppm !!

Simple conversion from  ²H concentration in ppm to δ ²H in ‰ on the VSMOW scale
     δ ²H [‰] = ppm D / 0.15576 - 1000

100% heavy water (D₂O) is equivalent to a ²H concentration of 1000000 ppm.

This corresponds to   δ ²H [‰] =1000000 / 0.15576 - 1000 = + 6419135  ‰ !! (almost 6.5 Mio ‰)

Since the conversions are linear, you can calculate linear mixtures of two solutions in either concentrations or in δ notation.

e.g.  a 1+1 mix of SLAP (δ ²H = -427.5 ‰)   and  VSMOW (δ ²H = 0 ‰) :
δ ²H = (1x(-427.5)+1x0) / (1+1) = -213.75 ‰ or (1x89.173 ppm + 1x 155.76 ppm) / (1+1) = 122.4665 ppm
δ ²H = 122.4665 / 0.15576 - 1000 = 786.25 - 1000  = - 213.75 ‰
1 part heavy water (  δ²H = 6419135 ‰ ) + 99 parts pure water ( δ²H = -52.3 ‰ - this counts for our lab water)
= (1x6419135+99x(-52.3)) / (1+99) = + 64139.573 ‰
so a 1% D₂O solution has a  δ ²H = + 64140 ‰ or 10146 ppm ²H

If you dilute more to get a 0.01% D₂O solution  (1 part heavy water + 9999 parts pure water)
= (1x6419135 + 9999x(-52.3)) / (1+9999) = + 589.619 ‰
so a 0.01% D₂O solution has a  δ ²H = + 589.62 ‰ or 247.59 ppm ²H

If you have enough house standards to choose from, you can mix your own VSMOW and SLAP

All δ values on this page are related to the VSMOW scale

original time stamp 06.April 2016,  edit 7, 15 Feb 2018, 06 Sep 18, 29Jan19, 22.Jul20, 05.Dec24