MATH · FREE
Carbon-14 Half-Life Calculator
Carbon-14 is the clock behind radiocarbon dating. Enter how much carbon-14 is left in a sample and get its age, or enter an age and get the amount remaining.
The half-life
The half-life of carbon-14 is 5,730 years (NOAA, NIST; NNDC lists 5700 ± 30 years). Half is left after 5,730 years and a quarter after 11,460 years.
Math only. Real radiocarbon dates from a laboratory are calibrated, so treat this as the simple decay arithmetic behind them.
AMOUNT REMAINING
Amount left
Percent left
Half-lives elapsed
| Half-lives | Time | Amount left | Percent left |
|---|
Math only. Real radiocarbon dates from a laboratory are calibrated, so treat this as the simple decay arithmetic behind them.
How carbon dating works
A living organism keeps exchanging carbon with its surroundings, so its carbon-14 level matches the environment. When it dies, the exchange stops and the carbon-14 already in it decays by half every 5,730 years. Measure how much is left, compare it to the level in a living reference, and the decay formula gives the time since death.
Worked example: a sample with 70% left
- Measured fraction of the living level: 70%, so N ÷ N0 = 0.70.
- Number of half-lives: log2(1 ÷ 0.70) ≈ 0.5146.
- Age: 0.5146 × 5,730 years ≈ 2,949 years.
The default setting of the calculator above gives that answer in "Time to reach an amount" mode. A second sample with 12% left is 5,730 × log2(1 ÷ 0.12) ≈ 17,500 years old.
Amount left after a given age
For the other direction, 10,000 years gives 100 × (1/2)10000 ÷ 5730 ≈ 29.8% left. At 50,000 years only about 0.24% remains, which is near the practical limit of the method.
Sources
- NOAA Global Monitoring Laboratory, Education: Stable Isotopes (accessed October 2026). States that 14C has a half-life of 5,730 years and that detection becomes very difficult after about 10 half-lives (57,300 years).
- NIST, How Do You Know the Age of Fossils and Other Old Things? (accessed October 2026). Describes carbon-14 as decaying over a period of 5,730 years.
- NNDC (Brookhaven National Laboratory), NuDat 3, C-14 decay data (accessed October 2026). Lists 5700 ± 30 y (Ajzenberg-Selove, Nuclear Physics A523, 1991).
- USGS, Volcano Watch: charcoal and young volcanic terrains (accessed October 2026). Uses a rounded half-life of 5,700 years.
Frequently asked questions
What is the half-life of carbon-14?
NOAA's Global Monitoring Laboratory and NIST give 5,730 years. The USGS rounds it to 5,700 years and the NNDC lists 5700 ± 30 years. This page uses 5,730 years, the value most often used for radiocarbon.
How does carbon dating work?
Living plants and animals take in carbon-14 while they are alive, so their carbon-14 level stays close to that of the air. After death no new carbon-14 comes in and what is there decays with a 5,730 year half-life. Comparing the amount left with the amount in a living reference gives the time since death: age = 5,730 × log2(reference ÷ measured).
How do I find the age if 70% of the carbon-14 is left?
Age = 5,730 × log2(1 ÷ 0.70) = 5,730 × 0.5146 ≈ 2,949 years. The calculator above is already set up for this: starting amount 100, target 70% left, half-life 5,730 years.
What is the limit of carbon dating?
After 10 half-lives, which is 57,300 years, less than 0.1% of the carbon-14 is left, and NOAA notes it becomes very difficult to detect. That is why carbon-14 suits samples from tens of thousands of years, not millions.
Is carbon dating exact?
No. Samples carry measurement uncertainty, the half-life itself has an uncertainty (±30 years in the NNDC listing) and laboratories calibrate raw results. The formula here is the idealized core of the method.
Math only. Real radiocarbon dates from a laboratory are calibrated, so treat this as the simple decay arithmetic behind them.
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