Calculator inputs
Choose an input method, then enter the measured values. The form uses a three-column layout on large screens, two on smaller screens, and one on mobile.
Example data table
| Case | Remaining Fraction | pMC | Approximate Age (years) | Interpretation |
|---|---|---|---|---|
| Fresh organic reference | 1.0000 | 100.00 | 0 | Modern reference level |
| Half remaining | 0.5000 | 50.00 | 5,730 | One half-life elapsed |
| Quarter remaining | 0.2500 | 25.00 | 11,460 | Two half-lives elapsed |
| Low measurable residue | 0.0625 | 6.25 | 22,920 | Four half-lives elapsed |
Formula used
N = N₀e-λt
λ = ln(2) / T1/2
t = -T1/2 × ln(N / N₀) / ln(2)
t = -T1/2 × ln(A / A₀) / ln(2)
Fraction remaining = pMC / 100
This calculator treats Carbon-14 decay as exponential. Once the remaining fraction, percent modern carbon, or activity ratio is known, the sample age follows directly from the half-life equation. The calendar estimate then subtracts the age from the reference year.
How to use this calculator
- Select the input mode that matches your available data.
- Enter the Carbon-14 half-life, or keep the default value.
- Provide the reference year for the calendar estimate.
- Enter the measured fraction, pMC, activity values, or known age.
- Add an optional relative uncertainty percentage if available.
- Press the calculate button to show the result above the form.
- Review the metrics, table, and decay graph.
- Use the CSV or PDF buttons to export the result summary.
FAQs
1) What does Carbon-14 dating measure?
It measures how much Carbon-14 remains in formerly living material. By comparing the remaining amount with the original amount, the sample age can be estimated from radioactive decay.
2) Why does the calculator use a half-life?
The half-life defines how quickly Carbon-14 decays. It is the time required for half of the original Carbon-14 atoms to disappear through radioactive decay.
3) Can I use activity instead of fraction remaining?
Yes. Activity is proportional to the number of radioactive atoms present. When measured and initial activity share the same unit, their ratio works like the remaining fraction.
4) What is percent modern carbon?
Percent modern carbon expresses the sample’s Carbon-14 level relative to a modern reference. A value of 100 pMC means modern-level Carbon-14, while lower values indicate older material.
5) Why might a result become negative?
Negative ages happen when the entered fraction exceeds one hundred percent of the reference level. That can occur with contamination, recent carbon exchange, or bomb-carbon effects.
6) Is the calendar year exact?
No. It is a direct arithmetic estimate from the chosen reference year and the calculated age. Real laboratory interpretation often needs calibration curves and context.
7) How reliable are very old Carbon-14 ages?
Reliability decreases for very old samples because little Carbon-14 remains. Measurement noise, contamination, and background effects become more important as the fraction approaches zero.
8) Why add uncertainty to the input?
Uncertainty shows how sensitive the age estimate is to measurement precision. Even small relative errors can create noticeable age ranges, especially for older samples.