Radiocarbon Age Calculation for Cellulosic Textiles

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 5 inputs are read from the form on every keystroke: Measured Activity, Measurement Uncertainty, Delta-13C, Half-Life Used and Reservoir Correction.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Conventional Radiocarbon Age together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Counting Uncertainty, Mean Life, Activity Fraction, Fractionation Correction and Uncalibrated Year — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Conventional Radiocarbon Age shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Measurement and Constants & Corrections. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Conventional Radiocarbon Age in the dark results panel — that is the headline figure, expressed in years BP.
4. Check the supporting rows underneath (Counting Uncertainty, Mean Life, Activity Fraction, Fractionation Correction and Uncalibrated Year) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Conventional Radiocarbon Age before a trial is booked, so machine time and material in Conservation, Forensics & Legal Textiles are committed against a calculated figure rather than an estimate.
• Costing and quotation — Conventional Radiocarbon Age is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Measured Activity) shows how much of the gap in Conventional Radiocarbon Age each variable explains.
• Teaching and study — the accepted ranges bracket normal Conservation, Forensics & Legal Textiles practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The uncalibrated year shown here is **not a date** and must never be reported as one. Atmospheric carbon-14 has varied substantially over time, so a conventional age has to be converted through a calibration curve such as IntCal, which frequently maps a single radiocarbon age onto several disjoint calendar ranges — and the resulting probability distribution is rarely symmetric about the value shown. The uncertainty here is counting statistics only and excludes laboratory and calibration uncertainty, which usually dominate. Contamination is the practical hazard with textiles: conservation treatments, consolidants, adhesives, later repairs and even handling introduce modern carbon, and pretreatment chemistry is what determines whether a result means anything. Dating significant objects is specialist laboratory work.
• Every input is bounded to the range normal practice occupies (Measured Activity 0.1 to 200 pMC, Measurement Uncertainty 0.01 to 10 pMC and Delta-13C -35 to -5 ‰, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask