Carbon-14 Dating Calculator
Estimate the age of an organic sample from its remaining carbon-14, or find how much C-14 is left after a given time. Carbon-14 decays with a half-life of 5,730 years, so the ratio of current to original activity reveals the sample's age — the method behind radiocarbon dating.
Formula
age = (t_half * ln(N0/N)) / ln(2), or N/N0 = (1/2)^(age/t_half)
- Carbon-14 decays radioactively with a half-life (t_half) of 5,730 years.
- Age from the remaining fraction: age = t_half × ln(N0/N) ÷ ln(2), where N/N0 is the current activity ratio.
- Remaining activity after a time: N/N0 = (1/2)^(age / t_half).
- An activity ratio of 0.5 means one half-life (≈ 5,730 years) has passed.
- Radiocarbon dating is reliable up to roughly 50,000 years, after which too little C-14 remains.
- Real lab dates apply calibration curves; this is a simplified estimate.
Activity ratio of 0.5
Inputs
- Activity ratio (current / original): 0.5
- Age (years) - for activity mode: 5730
With N/N0 = 0.5, age = 5,730 × ln(1/0.5) ÷ ln(2) = 5,730 × ln(2) ÷ ln(2) = 5,730 years — exactly one half-life.
Frequently asked questions
How does carbon-14 dating work?
Living things take in carbon-14 until they die; afterwards the C-14 decays at a known rate. Measuring how much remains relative to the original level reveals how long ago the organism died.
What is the half-life of carbon-14?
About 5,730 years. After one half-life, half the original C-14 remains; after two, a quarter, and so on.
What is the activity ratio?
It's the current C-14 activity divided by the original (N/N0). A ratio of 0.25, for example, indicates two half-lives, or roughly 11,460 years.
How far back can it date?
Practically up to about 50,000 years. Beyond that, the remaining carbon-14 is too small to measure reliably, and other methods are used.