Radiocarbon Dating Calculator
Estimate a sample’s age from its measured and initial carbon-14 activity using the standard radioactive decay equation.
Carbon-14 age calculation
Compare current carbon-14 activity with the initial activity to estimate elapsed time.
About radiocarbon dating
Radiocarbon dating estimates the age of once-living material by measuring carbon-14, a radioactive isotope formed continuously in the upper atmosphere. Plants take in atmospheric carbon during photosynthesis, and animals acquire it through food. While an organism is alive, exchange with the environment keeps its carbon-14 proportion broadly related to the atmosphere. After death that exchange stops, and the carbon-14 already present begins to decline through radioactive decay while stable carbon remains.
The calculator compares a sample’s measured carbon-14 amount or activity with an estimate of its initial value. Those values may be percentages, disintegrations per minute, or another consistent measure because only their ratio enters the equation. The age equals half-life divided by the natural logarithm of two, multiplied by the natural logarithm of initial activity divided by measured activity. With 25 units measured from an initial 100, one quarter remains. That represents two half-lives, or 11,460 years when the half-life is 5,730 years.
A half-life of 5,730 years is the modern conventional value for carbon-14. Some historical reports use the Libby half-life of approximately 5,568 years and then apply a correction. The field is editable so a calculation can match the convention used by a particular source, but values should not be mixed without documenting the choice. The reported unit is a label; changing it does not convert the entered half-life, so the label should describe the half-life’s time scale.
Actual radiocarbon laboratories do more than substitute numbers into an equation. They clean samples to remove contamination, measure isotope ratios with calibrated instruments, correct for isotopic fractionation, and compare conventional radiocarbon ages with calibration curves. Atmospheric carbon-14 has varied over time, so a radiocarbon age is not automatically identical to a calendar age. Calibration datasets based on tree rings and other archives convert measurements into probability ranges on a calendar scale.
Contamination can strongly bias old samples because only a small carbon-14 fraction remains. Modern carbon introduced during handling makes a specimen appear younger, while ancient carbon from some environments can make it appear older. Marine reservoir effects, groundwater chemistry, reused wood, and uncertain archaeological context also affect interpretation. Beyond roughly 50,000 years, residual activity may be too small for reliable routine dating.
Use this result as an educational exponential-decay estimate or to check a reported activity ratio. It is not a substitute for laboratory pretreatment, uncertainty analysis, calibration, or archaeological interpretation. For research decisions, retain the measured error, laboratory background, reference standard, half-life convention, and calibration method alongside the calculated age. Transparent assumptions are essential because a precise arithmetic result can still be historically inaccurate when the sample history or initial carbon assumption is wrong.
Radiocarbon dating examples
These ratios illustrate how lower remaining activity corresponds to greater age.
| Carbon-14 values | Estimated age | Example |
|---|---|---|
| Measured 25, initial 100, half-life 5,730 years | 11,460 years | An ancient wooden tool with one quarter of the initial activity. |
| Measured 12, initial 100, half-life 5,730 years | About 17,527 years | A fossilized plant with relatively little carbon-14 remaining. |
| Measured 40, initial 100, half-life 5,730 years | About 7,575 years | An animal bone retaining forty percent of initial activity. |
| Measured 15 dpm, initial 60 dpm, half-life 5,730 years | 11,460 years | Absolute activities produce the same age when their ratio is one quarter. |
How to estimate a radiocarbon age
- Enter the measured carbon-14 amount or activity from the sample.
- Enter the corresponding initial amount or reference activity in the same units.
- Confirm the carbon-14 half-life and enter the time-unit label used by that value.
- Select Calculate Age and review the estimated age and decay constant.
- Apply laboratory uncertainty and a suitable calibration curve before interpreting calendar age.
Radiocarbon dating FAQ
Why must measured and initial activity use the same unit?
The equation depends on their ratio, so the units must cancel. Mixing percentages, mass, or activity scales would create an invalid ratio and therefore an invalid age.
Why are radiocarbon ages calibrated?
Atmospheric carbon-14 concentration has changed over time, so the simple decay age differs from calendar age. Calibration curves use independently dated records to account for those variations.
What is the useful age range of carbon-14 dating?
It is most useful for once-living material up to roughly 50,000 years old. At greater ages, so little carbon-14 remains that contamination and instrument background can dominate.
Can radiocarbon dating determine the age of a rock?
Not usually, because carbon-14 dates organic carbon rather than the mineral’s formation. It may date associated charcoal, shell, or other carbon-bearing material if the context is understood.
What happens if measured activity exceeds initial activity?
The basic model would produce a negative age, which is not meaningful for dating. Recheck units, reference activity, contamination, and whether the assumptions apply to the sample.