Carbon Isotope Calculator

Carbon isotope reporting commonly uses delta notation (per mil, ‰) relative to a standard:

• δ¹³C (‰) = ((R_sample / R_standard) − 1) × 1000
• R_sample = R_standard × (δ¹³C/1000 + 1)
• α = R1 / R2 and ε (‰) = (α − 1) × 1000
• Two‑source mixing: f_A = (δ_mix − δ_B) / (δ_A − δ_B)

Notes: Uncertainty is estimated using standard first‑order propagation, assuming independent inputs.

1. Select a calculation mode that matches your goal.
2. Enter your values using consistent units (ratios or per mil, ‰).
3. If needed, choose a standard preset or switch to a custom standard.
4. Click Submit to display results above the form.
5. Use Download CSV or Download PDF to export outputs.

Practical tip: Keep 3–4 decimals for δ values, and 6–8 for ratios.

Delta notation outputs and units

Delta values are expressed in per mil (‰) and compare a sample ratio to a reference ratio. The calculator reports δ¹³C, the fractionation factor α, and enrichment ε, so you can move between reporting styles without manual rework. A δ shift of 1.0‰ equals a 0.1% change relative to the standard ratio, which helps interpret small variations in carbon pools across processes. Natural materials often span roughly −35‰ to +5‰, depending on source pathways.

Standard handling for consistent comparisons

Most laboratories reference VPDB for carbon work, but inter-lab workflows sometimes require a fixed house ratio. The standard selector supports a default preset or a custom R_standard value, keeping calculations traceable when methods change. For routine checks, a reference run near δ ≈ 0.0‰ indicates alignment with the chosen standard, while repeated offsets suggest calibration or drift issues. Document the chosen ratio in reports to keep datasets comparable over years.

Precision, uncertainty, and rounding control

Analytical reporting typically keeps 3–4 decimals for δ values and more for ratios. The output decimals option lets you match internal QA templates and reduce transcription risk. Optional uncertainty fields estimate σ for δ, α, or ε using first-order propagation, assuming inputs are independent. When σ(R) is small, the propagated σ(δ) remains stable, supporting repeatable comparisons across batches and instruments. If left blank, uncertainty is not computed for that field.

Two-source mixing for quick screening

The mixing mode solves fractions for two endmembers using δ values, producing f_A and f_B plus percentage contributions. This is useful for rapid screening of binary mixtures, such as organic versus carbonate carbon, before running more complex models. Clamping can keep results within 0–1 when δ_mix falls outside endmembers due to non-binary inputs or measurement noise.

Export-ready outputs for documentation

CSV export supports downstream spreadsheets, LIMS uploads, and batch notes, while PDF export creates a compact report with both the calculation summary and the example table. Timestamps are included to aid audits and reproducibility. By keeping metrics and units in a single output table, teams can reduce copy errors, standardize reporting language, and share results across projects with consistent formatting.

What does δ13C represent in this calculator?

It expresses the per mil difference between a sample 13C/12C ratio and the selected standard ratio, allowing small isotopic shifts to be compared consistently across runs.

Which mode should I use for typical lab reporting?

Use “δ13C from ratio” when you have measured ratios, and “Ratio from δ13C” when you need a ratio for modeling or instrument checks based on reported delta values.

How do I use a custom standard ratio?

Select Standard = Custom ratio, then enter R_standard as a positive 13C/12C value. The calculator applies it to delta and ratio conversions and keeps outputs consistent with your lab reference.

Why can the mixing fractions be clamped?

Real samples may not be purely binary, or δ_mix can be noisy. Clamping forces fA and fB to remain between 0 and 1 so percentages do not display as negative or above 100%.

How are uncertainty values handled?

When you provide σ for a ratio or delta input, the calculator estimates output uncertainty using first‑order propagation with independent inputs. If a field is blank, that uncertainty term is skipped.

Do exports store my data on the server?

No. CSV and PDF files are generated in your browser from the displayed tables. Submissions are calculated on the page request only, and nothing is saved automatically by the tool.