The half-life of carbon-14 is 5,730 years. Every 5,730 years, half of the atoms that are left decay, so after 2 half-lives (11,460 y) a quarter is left, and after 10 (57,300 y) about 0.10%.
Written as a rate, the decay constant is λ = ln 2 ÷ T½ = 3.833 × 10⁻¹² per second, and the average atom survives for the mean life τ = 8,267 years. One gram of the pure isotope contains 4.30 × 10²² atoms and has an activity of 165 GBq.
Carbon-14 decay table
Each row is a number of half-lives, the time that takes for C-14, and what is left. The fraction is 2 raised to minus the number of half-lives, for any sample size.
| Half-lives | Time | Fraction left | Odds an atom survives |
|---|---|---|---|
| 1 | 5,730 y | 50% | 1 in 2 |
| 2 | 11,460 y | 25% | 1 in 4 |
| 3 | 17,190 y | 13% | 1 in 8 |
| 4 | 22,920 y | 6.3% | 1 in 16 |
| 5 | 28,650 y | 3.1% | 1 in 32 |
| 6 | 34,380 y | 1.6% | 1 in 64 |
| 8 | 45,840 y | 0.39% | 1 in 256 |
| 10 | 57,300 y | 0.10% | 1 in 1,024 |
N = N₀ × 2^(−t ÷ 5,730 years). With only 400 atoms in the simulation the count scatters about the curve, because each atom decays at a random time.
How long until C-14 drops to a given level
Running the law backwards gives the time for the sample to fall to a chosen fraction, t = −T½ log₂(fraction). This is also how a measured fraction becomes an age.
| Fraction left | Time needed | Half-lives |
|---|---|---|
| 90% | 871 y | 0.152 half-lives |
| 50% | 5,730 y | 1.00 half-lives |
| 25% | 11,460 y | 2.00 half-lives |
| 10% | 19,035 y | 3.32 half-lives |
| 1.0% | 38,069 y | 6.64 half-lives |
| 0.10% | 57,104 y | 9.97 half-lives |
About carbon-14
Carbon-14 is made high in the atmosphere when cosmic rays knock neutrons loose and those neutrons hit nitrogen-14. The new carbon-14 is oxidised to carbon dioxide and taken in by plants, and by everything that eats them, so a living thing holds about 1 carbon-14 atom for every trillion ordinary carbon atoms. When it dies the intake stops and the decay clock starts.
That is why the half-life of 5,730 years matters so much. Roughly ten half-lives is the practical limit: by about 50,000 years under 0.3% is left, too little to measure against background. Dates are also corrected against tree rings, because the amount of carbon-14 in the air has not been constant.
A worked example
A wooden beam has 30% of the carbon-14 of living wood. How old is it?
t = −5,730 × log₂(0.30) = 5,730 × 1.74 = 9,953 y.
Compare with other isotopes
The half-lives in the simulation span twenty orders of magnitude, from microseconds to billions of years. Each has its own page.
| Isotope | Half-life | Activity per gram |
|---|---|---|
| Carbon-14 | 5,730 years | 165 GBq |
| Uranium-238 | 4.47 billion years | 12.4 kBq |
| Iodine-131 | 8.02 days | 4.6 PBq |
| Polonium-214 | 164 microseconds | 11.9 YBq |
| Technetium-99m | 6.0 hours | 195 PBq |
This page is one case from the full guide, Half-life and radioactive decay simulator, which covers every case, the assumptions behind the model and what it leaves out.
Other cases
- Uranium-238 half-life 4.47 billion years
- Iodine-131 half-life 8.02 days
- Polonium-214 half-life 164 microseconds
- Technetium-99m half-life 6.0 hours
Frequently asked questions
What is the half-life of carbon-14?
5,730 years. After that time half of any sample has decayed, and half remains.
How much C-14 is left after 3 half-lives?
One eighth, 13%, after 17,190 y.
Does the half-life depend on how much there is?
No. Each atom has the same chance of decaying in any moment, so the time for half of a sample to decay is the same for a gram or a ton. Heat, pressure and chemistry do not change it for ordinary decay.
When is C-14 gone?
It never reaches exactly zero, but after 10 half-lives (57,300 y) only 0.10% remains, which is the usual rule of thumb for “gone”.
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