What this calculator does
Radiocarbon dating estimates how long ago an organism died by measuring how much carbon-14 remains in its remains, compared with the level found in a living organism today. Carbon-14 is created in the upper atmosphere and taken up by living things at a roughly constant ratio; once an organism dies, it stops exchanging carbon with the environment, and its carbon-14 decays away at a fixed, known rate.
The decay is a straightforward first-order process, the same mathematics used for any radioactive half-life calculation, just rearranged to solve for elapsed time rather than remaining amount. The standard Libby half-life of 5,730 years is used by default, though the field also uses a slightly different conventional value in some contexts, which is why the half-life is left as an adjustable input rather than fixed in the formula.
The formula
Divide 100 by the percentage of carbon-14 remaining, take the base-2 logarithm of that ratio, and multiply by the half-life. This is the standard half-life equation solved for elapsed time instead of remaining amount.
| Term | Meaning |
|---|---|
| t½ (half-life) | The time for half of the carbon-14 in a sample to decay; conventionally 5,730 years. |
| Percent modern | The measured carbon-14 activity in the sample, expressed as a percentage of the level found in a living reference standard. |
| Half-lives elapsed | The estimated age divided by the half-life, showing how many decay half-lives have passed. |
The inputs explained
| Field | What to enter |
|---|---|
| Carbon-14 remaining (percent of modern) (%) | The measured carbon-14 remaining in the sample, as a percentage of the modern (pre-death) reference level. |
| Half-life used (years) | The half-life value to use; 5,730 years (the Cambridge value) is the modern convention, though some older published dates use the Libby value of 5,568 years. |
When to use it
Estimating the age of an archaeological sample
Wood, charcoal, bone collagen and other organic remains from an archaeological site are dated by comparing their measured carbon-14 activity against the modern reference standard.
Sanity-checking a published radiocarbon date
Reworking a reported percentage-modern-carbon figure through the decay equation independently checks the age calculation behind a cited radiocarbon date.
Understanding the practical dating limit
Because so little carbon-14 remains after many half-lives, radiocarbon dating becomes unreliable for samples older than roughly 50,000 years; this calculator flags results at 0% remaining rather than reporting a spurious infinite age.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How estimated age changes with carbon-14 remaining
A range of measured carbon-14 levels, converted to an estimated age.
| Carbon-14 remaining | Estimated age | Half-lives elapsed |
|---|---|---|
| 90% | 871 years | 0.15 |
| 75% | 2,378 years | 0.42 |
| 50% | 5,730 years | 1.00 |
| 25% | 11,460 years | 2.00 |
| 10% | 19,035 years | 3.32 |
| 1% | 38,069 years | 6.64 |
Questions
Why is 5,730 years used as the default half-life?
This is the Cambridge half-life for carbon-14, the currently accepted physical value and the one used for calculating conventional radiocarbon ages today. Some historical literature used the earlier Libby value of 5,568 years, which is why the half-life is adjustable here rather than fixed.
Does this calculator give a calendar (calibrated) date?
No. This gives the conventional radiocarbon age based on a constant atmospheric carbon-14 level, which real dating labs then calibrate against tree-ring and other records to correct for historical fluctuations in atmospheric carbon-14. This calculator performs only the raw decay-equation step, not that calibration.
Why does the calculator refuse a result at 0% remaining?
Mathematically, 0% remaining implies an infinite age, which is not meaningful; in practice, radiocarbon dating loses reliability once around 8 to 10 half-lives have passed, since so little carbon-14 is left that measurement uncertainty overwhelms the result.
What assumptions does this calculation rely on?
It assumes the sample has been a closed system since death (no carbon exchange with the environment afterwards) and that the atmospheric carbon-14 level was the same as today's reference standard when the organism was alive, an assumption real calibration curves are built to correct for.
For the general radioactive decay relationship this calculator is built on, see the radioactive decay and half-life calculator. For a related activity-based decay figure, see the radioactive activity calculator.