Isotopic Ratio Calculator

Isotope system

Pick a common pair or choose custom.

Custom label

Used in the result summary and exports.

Measurement unit

Any consistent unit works for ratios.

Heavy isotope amount

Must be positive.

Light isotope amount

Must be positive.

Standard ratio (R_std)

If you select “typical standard”, the ratio auto-fills for convenience. Always confirm your lab convention.

Uncertainty (heavy), σH (optional)

Used for σ(R) and σ(δ) if both given.

Uncertainty (light), σL (optional)

Same unit as the isotope amounts.

Note (optional)

Included in CSV/PDF.

Optional: fractionation vs reference sample

Reference heavy amount

Reference light amount

If provided, the calculator reports α = R_sample/R_ref and ε = (α−1)×1000 (per mil).

Example data table

System	Heavy amount	Light amount	R = heavy/light	R_std used	δ (‰)
Carbon (13C/12C)	152,340	13,560,000	0.0112345133	0.0112372000	-0.2391

Example values are for demonstration only. Use your instrument outputs and the standard ratio specified by your lab method.

Formula used

Isotopic ratio: R = N_heavy / N_light
Atom percent (heavy): Atom% = 100 × N_heavy / (N_heavy + N_light)
Delta notation: δ = (R_sample/R_std − 1) × 1000 ‰
Optional fractionation: α = R_sample/R_ref, and ε = (α − 1) × 1000 ‰

Uncertainty propagation (optional): σ(R) = R × √[(σH/H)² + (σL/L)²], and σ(δ) = (1000/R_std) × σ(R).

How to use this calculator

Select an isotope system (or choose custom and enter a label).
Enter heavy and light isotope amounts using consistent units.
Provide R_std manually, or select the typical standard option.
(Optional) Add uncertainties to estimate σ(R) and σ(δ).
(Optional) Add reference sample amounts to compute α and ε.
Click Calculate. Use CSV/PDF buttons in the results panel.

Why isotopic ratios matter

Isotopic ratios separate sources and processes when concentrations overlap. In stable‑isotope work, tiny shifts carry meaning: 1 per mil equals a 0.1% change relative to a standard. Many projects report delta values from about −50 to +50 per mil. Radiogenic systems commonly report absolute R with uncertainty, not delta. This calculator turns raw measurements into comparable numbers.

From counts to ratio R

The fundamental quantity is R = Nheavy/Nlight. Any consistent unit works, including counts, moles, or concentrations, because the ratio is dimensionless. Example: 13C = 152,340 and 12C = 13,560,000 gives R = 0.0112363. Atom percent heavy is also reported: 100×Nheavy/(Nheavy+Nlight). The chart compares Rsample with Rstd and summarizes delta and epsilon.

Delta notation and standards

Delta expresses deviation from a reference: delta = (Rsample/Rstd − 1) × 1000. Typical reference ratios include VPDB for 13C/12C (Rstd ≈ 0.0112372) and VSMOW for 18O/16O (Rstd ≈ 0.0020052) or D/H (Rstd ≈ 0.00015576). For 15N/14N, AIR uses Rstd around 0.0036765; for 34S/32S, VCDT is near 0.0441626. Always use your method’s standard to keep datasets comparable.

Uncertainty and quality control

If sigmaH and sigmaL are provided, uncertainty propagates as sigma(R) = R√[(sigmaH/H)² + (sigmaL/L)²], then sigma(delta) = (1000/Rstd)×sigma(R). For instance, if sigmaH/H = 0.10% and sigmaL/L = 0.05%, sigmaR/R ≈ 0.112%. Replicate precision often falls near 0.05–0.2 per mil for many IRMS runs.

Fractionation, alpha, and epsilon

With a reference sample, alpha = Rsample/Rref and epsilon = (alpha − 1) × 1000. Positive epsilon indicates heavy‑isotope enrichment relative to the reference. For small effects, epsilon is close to delta(sample) − delta(reference), but alpha remains the rigorous multiplicative expression for modeling and mixing calculations. Use alpha in fractionation equations; use epsilon for concise per mil reporting.

Reporting, comparability, and exports

Report the isotope system, Rstd value, standard name, and any uncertainty assumptions. Keep amounts with delta to diagnose drift, background, and detector nonlinearity. CSV export supports LIMS ingestion, while the PDF suits lab notebooks and audits. Store exports with sample ID, instrument, and calibration batch for reproducibility. The optional note and timestamp improve traceability across runs and review later.

FAQs

What should I enter as the heavy and light amounts?

Enter your measured signal for each isotope, such as ion counts or moles. The units can be anything, but both inputs must share the same unit for the ratio to be correct.

How do I choose the standard ratio (Rstd)?

Use the standard required by your method or lab protocol. You can type an official value or select the typical preset as a starting point, then verify it against your calibration documentation.

What does a negative delta value mean?

A negative δ means the sample ratio is lower than the standard ratio, indicating depletion of the heavy isotope relative to that standard. The magnitude in per mil shows how far the sample deviates.

Do I need uncertainties to use the calculator?

No. Uncertainties are optional and only affect the reported σ(R) and σ(δ). If you are comparing small δ differences, adding realistic uncertainties or replicate statistics improves interpretation.

When should I use the reference sample fields?

Use them when you want fractionation between a sample and a specific reference material. The calculator then reports α and ε, which are useful for process studies and direct sample‑to‑sample comparisons.

Why can the graph look flat for delta or epsilon?

R values are often around 10⁻4 to 10⁻2, while δ and ε are in per mil. Different scales can compress bars visually; use the hover tooltips to read exact values.