How to Use Radiocarbon Dating Calculator
The Radiocarbon Dating Calculator converts a measured ¹⁴C activity ratio into an estimated age in years. Choose the input type that matches your data and enter the value.
- Select input type – Choose Remaining ¹⁴C (%) if you know the percentage of original ¹⁴C still present. Choose Ratio N/N₀ if you have the fractional activity (0 to 1). Choose Decayed ¹⁴C (%) if you know how much has decayed.
- Enter the value – For percentage modes, enter a number between 0 and 100. For ratio mode, enter a value between 0 and 1.
- Review the result – The Radiocarbon Dating Calculator shows the formula, substitution steps, number of half-lives elapsed, and the estimated age in years.
Formula & Theory - Radiocarbon Dating Calculator
The Radiocarbon Dating Calculator uses this core formula or rule: the radioactive decay age equation derived from the exponential decay law:
t = −T₁/₂ × ln(N/N₀) / ln(2)| Symbol | Meaning | Value |
|---|---|---|
| t | Age of the sample | years |
| T₁/₂ | Half-life of ¹⁴C | 5730 years |
| N | Current ¹⁴C activity in the sample | — |
| N₀ | Original ¹⁴C activity (at time of death) | — |
Carbon-14 is produced in the upper atmosphere by neutron bombardment of nitrogen-14. Living organisms continually exchange carbon with the environment, maintaining a roughly constant ¹⁴C/¹²C ratio. After death, no new ¹⁴C is incorporated and the existing ¹⁴C decays at a constant rate with a half-life of 5730 years.
Assumptions and Limits
- The initial ¹⁴C/¹²C ratio is assumed to have been constant over time. In reality this varies, requiring calibration with dendrochronology records (IntCal curves).
- Reliable age range: roughly 300 – 50,000 years before present. Younger samples may be affected by atmospheric nuclear testing; older samples have too little ¹⁴C.
- This Radiocarbon Dating Calculator gives a theoretical age estimate. Real-world dates require laboratory AMS or liquid scintillation counting, calibration, and uncertainty analysis.
Use Cases for Radiocarbon Dating Calculator
The Radiocarbon Dating Calculator is useful in science education and preliminary research. Common uses include:
- Archaeology – Estimating the age of organic artefacts such as wood, charcoal, or textile fragments.
- Geology and palaeontology – Dating organic material in sediment cores or fossil assemblages.
- Chemistry and physics education – Illustrating radioactive decay and half-life calculations.
- Environmental science – Estimating ages of peat, soil organic matter, or lake sediment layers.
The Radiocarbon Dating Calculator provides a transparent, step-by-step derivation that is ideal for learning how the half-life formula translates a measured ¹⁴C ratio into a calendar age.