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Isotope Delta To Ratio Standard Term Tool

Delta notation delta=1000*(Rsample/Rstandard-1), with an explicit positive standard ratio.

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Description

Return sampleRatio equal to standardRatio times (1+deltaPerMil/1000).

An isotope ratio depends on which isotope is in the numerator and denominator. Delta notation compares a ratio with a reference on a per-mil scale, while mixing and decay models require explicit amount and system assumptions.

Return sampleRatio equal to standardRatio times (1+deltaPerMil/1000).

When to use this tool

Use Isotope Delta To Ratio Standard Term when you need a stated isotope-reference, mixing, or one-step decay calculation.

How to use the tool and how it works

  1. Enter deltaPerMil, standardRatio. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read sampleRatio. Use the output convention below.

Require deltaPerMil at least -1000 and positive standardRatio. Return sampleRatio equal to standardRatio times (1+deltaPerMil/1000).1

A per-mil delta value inverts to reference ratio times (1+delta/1000), with the same isotope-ratio orientation.2

Input fieldMeaning and unitsAccepted input
deltaPerMilDelta Per Mil Unit: ‰.Required. Finite number; minimum -1000.
standardRatioStandard RatioRequired. Finite number; strictly above 0.
Output fieldInterpretationReturned shape
sampleRatioSample RatioRequired. Finite number.
json
{
  "input": {
    "deltaPerMil": 10,
    "standardRatio": 0.01
  },
  "output": {
    "sampleRatio": 0.0101
  }
}

Limitations and assumptions

  • Delta is per mil, not percent, and both ratios use the same numerator/denominator isotope convention. The tool does not select a standard or apply instrument and fractionation corrections.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use the appropriate reference materials and full isotope model for interpretation. Preserve ratio orientation, reference scale, denominator-isotope weighting, uncertainty, and any open-system or fractionation effects.

References

  1. Calculation and input contract: geochemistry/isotope-delta-to-ratio-standard-term — tool.io

  2. Fundamentals of Isotope Geochemistry: delta notation — USGS, Kendall and Caldwell

Similar or alternative tools

  • Isotope Standard Delta Residual

    Compute delta as 1000 times (sample ratio divided by standard ratio minus one), then return reported minus derived delta as the residual.

  • Isotope Ratio Mixing Weight

    Scale both amounts by their maximum, form normalized weights, and interpolate the two ratios stably; return mixedRatio and firstWeight.

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