What it does
Stable isotopes are reported as δ values in per mil (‰): how far a sample’s heavy-to-light isotope ratio sits above or below an agreed standard.
δ = (R sample ÷ R standard − 1) × 1000
A seawater-like sample is near 0 ‰ for δ¹⁸O. Rain in cold places is strongly negative, and marine limestone is around +30 ‰ on the same scale. This tool does the everyday sums around δ in five boxes.
- δ and ratio: turn a δ into an absolute ratio and heavy-isotope share, or a ratio into δ, for common standards: VSMOW (water), VPDB (carbonate), AIR (nitrogen), VCDT (sulfur), NIST SRM 951 (boron) and SMOC (chlorine).
- Change the reference scale: exact conversion between δ¹⁸O on VPDB and VSMOW, or between any two standards when you know one on the other’s scale.
- Fractionation: from two phases’ δ values, the fractionation factor α, ε, 1000 ln α and the simple difference Δ.
- Triple oxygen: Δ′¹⁷O from δ¹⁷O and δ¹⁸O with your choice of reference slope λ.
- Mixing: the δ of a mixture of two sources that carry different amounts of the element, and the fraction needed for a target δ, with the mixing curve.
How to use it
- Pick the isotope and standard, then type either δ or the sample ratio; the other fills in. Choose “Other” and type the standard’s ratio for anything not listed.
- For a scale change, pick the direction and enter δ on the old scale. For “Any”, also give the old standard’s δ on the new scale.
- For fractionation, use the same isotope and scale for both phases.
- For mixing, give each source’s δ and how concentrated the element is in it, then the fraction of source A.
Worked examples
All numbers here are made up for illustration.
- δ¹⁸O = −8.50 ‰ vs VSMOW is a ¹⁸O/¹⁶O ratio of 0.0019881558, so about 0.198 % of the oxygen (counting only ¹⁶O and ¹⁸O) is ¹⁸O.
- A calcite with δ¹⁸O = −5.20 ‰ vs VPDB is +25.56 ‰ vs VSMOW. Just adding 30.92 would give 25.72, off by 0.16 ‰.
- Calcite at +25.0 ‰ and water at −5.0 ‰: α = 1.030151, ε = +30.15 ‰ and 1000 ln α = +29.71 ‰.
- δ¹⁷O = 5.30 ‰ and δ¹⁸O = 10.10 ‰ with λ = 0.528 give Δ′¹⁷O = −20 per meg.
- Mixing 60 % of source A (−28 ‰, concentration 1) with 40 % of source B (−12 ‰, concentration 3) gives −17.33 ‰. Only a third of the element comes from A. Reaching −18 ‰ needs 64.3 % of A.
Good to know
- Labs report δ against reference materials measured alongside samples, so you rarely need absolute ratios. When you do, check which standard ratio your field uses; for example δ¹³C work sometimes uses an older VPDB ratio.
- ε and Δ are close only when δ values are small. For large differences use α or 1000 ln α, which are what temperature equations use.
- The mixing box uses the standard δ mass balance. It is accurate to a few hundredths of a per mil for ordinary δ values.
FAQ
Why can’t I just add 30.92 to go from VPDB to VSMOW? δ values multiply, not add: (1 + δ₁)(1 + δ₂). Adding is close only for values near zero.
What is a per meg? One thousandth of a per mil. Triple oxygen differences are tiny, so they are often quoted in per meg.
Where the numbers come from
- Delta notation, scale changes, fractionation factors and Δ′17O: standard stable isotope geochemistry, written from the definitions (IUPAC recommendations on delta notation).
- Reference ratios of VSMOW, VPDB, AIR, VCDT, NIST SRM 951 and SMOC, and VPDB = +30.92 ‰ on the VSMOW scale: commonly adopted reference constants, shown on the page with a note that labs differ slightly. Checked 2026-11-08.
- Worked examples written by fibub with made-up numbers.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.