Delta values are how we report the relative amounts of the different isotopes of a single element. For example δ13C (said delta-thirteen-see) provides a measure of the relative amounts of carbon-13 and carbon-12 in a material.

The “delta notation” or delta value used in stable isotope geochemistry is often confusing, especially to people outside of the science trying to understand our work. It’s confusing because these delta values are reported in “permil” (‰) which is often interpreted as a concentration like percent (%). But the permil in the delta notation is not a concentration at all, which becomes a little more clear when we realize that delta values can be negative, but concentrations cannot. (You can’t buy lemonade that -15% lemon juice!)

What the delta notation really is, is a ratio of ratios. It’s a measurement of difference. And the ‘permil’ part is just a matter of convenience. No doubt this still does not help clarify what delta values are.

But what’s done is that a natural material is assigned a delta value of zero. For carbon, this natural substance was a fossil relative of the modern squid. For oxygen and hydrogen, we use ocean water. For nitrogen, we use air. Each of these natural substances has a ratio of heavy isotope to light isotope. We don’t know exactly what that is, but we just call the substance’s delta value zero. Materials of assigned values are called standard reference materials, standards, references – all sorts of things – but are used by everyone so that we can make comparisons among each other’s labs.

When we measure something of unknown delta value, we compare it to this natural standard material. If our unknown has relatively more of the heavier isotope than the reference, then the delta value is more positive. If the unknown sample has relatively less of the heavier isotope, then its delta value is more negative. The delta value is the comparison of two ratios (one of the standard and one of the unknown), and therefore has no units.

However, this number tends to be very, very small. Like 0.0012 small. Because it’s a pain to have to say “point zero-zero-one-two”, isotope chemists simply multiply the number by 1000 to get something more pronounceable: 1.2 (one point two). And that’s where the permil comes from. It’s a reminder that we multiplied by 1000. It’s not a concentration at all.