Radiocarbon Dating Calculator
Estimate the elapsed time since an organic sample stopped exchanging carbon with its environment using exponential carbon-14 decay.
Sample inputs
Estimated age
Carbon-14 decay over time
Decay checkpoints
| Checkpoint | Elapsed time | Carbon-14 remaining |
|---|
How to use this radiocarbon dating calculator
What this calculator does. It estimates the time elapsed since an organic sample stopped exchanging carbon with the biosphere. It applies the exponential radioactive-decay law to the measured percentage of carbon-14 remaining and a chosen half-life. The result is a mathematical conventional radiocarbon age, not a fully calibrated calendar date, a laboratory uncertainty analysis, or proof that a sample is uncontaminated.
When to use it. Use the calculator to check a classroom decay problem, estimate the approximate age implied by a laboratory-reported fraction modern, compare how quickly carbon-14 falls across successive half-lives, or test the sensitivity of an age estimate to the half-life convention. NIST explains why carbon-14 works as an age clock in its overview of dating organic remains with radioactive decay.
How to calculate. The calculator opens with a complete demonstration: 92% carbon-14 remaining and a 5,730-year half-life. Its result and a validated example workbook are ready immediately.
- Replace Percentage of carbon-14 left with the measured percentage for the sample.
- Keep Carbon-14 half-life at 5,730 years for the modern physical value, or enter another positive value only when reproducing a stated convention.
- Read Time elapsed, the rounded age line, Decay constant, and Half-lives elapsed. The chart and table update from the same model.
- Select Download Excel to export the current typed inputs, outputs, formula notes, and decay checkpoints. Reset clears the demonstration data and disables export until both required fields are valid again.
Input guide. Percentage of carbon-14 left is required, accepts a decimal number in percent, and must be greater than 0 and at most 100. For example, enter 92 for 92%. Lower percentages produce older ages; 100% produces an age of zero. Do not enter 0.92 when you mean 92%, and do not use a negative value. Carbon-14 half-life is also required, is measured in years, and must be a positive finite number. A realistic value is 5730. Increasing it scales every elapsed time upward in direct proportion. Do not confuse the half-life with the sample age.
Output guide. Time elapsed is the model age in years. The Conventional rounded age reports the value rounded to the nearest ten years with a ±5-year rounding interval; it is not a laboratory confidence interval. Decay constant is ln(2) divided by the selected half-life, in inverse years. Half-lives elapsed is the dimensionless number of half-life periods represented by the measured fraction. The summary pills repeat the current percentage, half-life, and elapsed half-lives. The Decay checkpoints table lists half-life count, elapsed time, and ideal remaining percentage. The chart shows that same percentage against elapsed years and marks the current sample.
Worked example. With 92% remaining and a 5,730-year half-life, the fraction remaining is 0.92. The age is – 5730 × ln(0.92) ÷ ln(2), which is about 689.4 years. The display rounds this to 689 years, while the conventional line reports 690 ± 5 years BP. The decay constant is about 0.00012097 yr⁻¹ and the elapsed interval is about 0.1203 half-lives. These values match the first-open controls, chart marker, table logic, and workbook.
Model, assumptions, and interpretation
The ideal decay model is N = N₀e – λt, where N/N₀ is the fraction of carbon-14 remaining, λ is the decay constant, and t is elapsed time. Solving for time gives t = – ln(N/N₀)/λ. The selected half-life T1/2 sets λ through λ = ln(2)/T1/2. The Nobel Prize history of carbon-14 dating describes the development of the method, while the U.S. Environmental Protection Agency summarizes beta decay and radioactive atoms.
Real radiocarbon analysis is more involved. Atmospheric carbon-14 has varied through time, samples can be contaminated, marine and freshwater reservoir effects can shift apparent ages, and laboratory measurements have uncertainty. Specialists therefore calibrate conventional radiocarbon ages against datasets and tools such as the Oxford Radiocarbon Accelerator Unit's OxCal resources. Treat this calculator as an educational and preliminary consistency tool rather than a substitute for laboratory calibration.