Carbon Dating Calculator
Radiocarbon age from the remaining C-14 fraction
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Carbon Dating Calculator turns the numbers behind radiocarbon age from the remaining C-14 fraction into a result, step by step. Type C-14 Remaining (% of living level) and C-14 Half-life (years) into Carbon Dating; each keystroke re-runs the math. Every Carbon Dating answer can be reproduced by hand. Use Carbon Dating for a reliable number, fast. You can disconnect once Carbon Dating has loaded; the arithmetic runs locally. Looking for carbon dating calculator radiocarbon age c14 half life archaeology or free online carbon dating calculator? Carbon Dating covers both. Keep Carbon Dating bookmarked for next time. No sign-up or email — Carbon Dating answers as you type.
From remaining C-14 to an age
Age = half-life × log₂(100 ÷ percent remaining). At the defaults — 25% remaining, 5,730-year half-life — the log term is 2, so the age is 11,460 years.
The formula is the decay curve read backwards. C-14 leaves the atmosphere at a known ratio while a plant or animal is alive; once it dies, the fraction falls by half every 5,730 years, and the surviving fraction is what the laboratory measures.
Why the answer is logarithmic
Halving is multiplicative, not linear. After one half-life 50% remains, after two 25%, after three 12.5% — so equal drops in the measured fraction correspond to very unequal spans of time. The base-2 logarithm converts that back into years.
Practically, it means resolution is best on young samples. Going from 50% to 25% remaining adds 5,730 years; going from 3% to 1.5% adds the same 5,730 years but the measurement uncertainty on that small a fraction is far larger.
Worked example: 25% remaining
Fraction remaining = 0.25.
100 ÷ 25 = 4.
log₂(4) = 2 half-lives.
Age = 5,730 × 2 = 11,460 years.
At 50% remaining the same formula gives one half-life, 5,730 years. At 12.5% it gives three, 17,190 years. The arithmetic is exact; the uncertainty comes from the measurement and from the assumptions below.
What the real lab result carries
- A stated error bar. A published date is written as, for example, 11,460 ± 60 years. Quoting the central value alone overstates the precision.
- Calibration. Raw radiocarbon years are not calendar years; the atmospheric C-14 ratio has varied, so laboratories convert through a calibration curve before quoting a calendar date.
- Contamination. A small amount of modern carbon makes an old sample look younger, which is why sample preparation matters more than the arithmetic.
- The 50,000-year wall. Beyond roughly that age too little C-14 remains to measure, and the dating method changes (potassium-argon, uranium-series).
Common misreadings
- Reading a fraction as a percentage. 0.25 and 25 are different inputs and give answers centuries apart.
- Assuming a constant half-life is the only assumption. The 5,730-year figure is convention, not a universal constant you must keep — other isotopes use their own.
- Treating the output as a calendar year. It is an age in radiocarbon years before present, not a date you can put in a history book.
Frequently Asked Questions
Why does 25% remaining mean 11,460 years?
Because 25% is two halvings (100 → 50 → 25), and each halving is one 5,730-year half-life. log₂(100 ÷ 25) = 2, and 2 × 5,730 = 11,460.
How old can carbon dating measure?
Roughly 50,000 years. At that point only about 0.2% of the original C-14 remains, which is near the limit of what a laboratory can separate from background contamination.
Is the result a calendar date?
No — it is an age in radiocarbon years. Atmospheric C-14 has varied over time, so laboratories apply a calibration curve to convert it into a calendar date with its own error range.
What if the sample is 50% remaining?
The age is exactly one half-life: 5,730 years. Every halving of the remaining fraction adds another 5,730 years, which is why the relationship is logarithmic rather than linear.
Why do published dates have a ± figure?
Because counting decays is a statistical measurement. A date of 11,460 ± 60 means the measurement’s uncertainty covers roughly that range, and the true age is quoted as a probability distribution, not a single year.
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