How Carbon-14 Half-Lives Reveal Fossil Age

Radioactive decay leaves a measurable clock

Carbon-14 is an unstable isotope. While an organism is alive, carbon exchange helps maintain a relationship between carbon-14 and stable carbon in its tissues. After death, that exchange stops and the carbon-14 already present decays at a predictable average rate.

A half-life is the time required for half of the radioactive parent isotope to remain. For carbon-14, the commonly used half-life is about 5,730 years. The remaining fraction follows exponential decay:

$$\frac{N}{N_0}=\left(\frac{1}{2}\right)^{t/T}.$$

Here, $N_0$ is the estimated starting amount, $N$ is the measured amount, $T$ is the half-life, and $t$ is elapsed time.

Count halvings when the fraction is a power of one-half

If the remaining fraction is exactly $1/2$, $1/4$, $1/8$, or another power of one-half, the exponent gives the number of half-lives directly. Multiplying that count by the isotope's half-life gives the elapsed time.

For an arbitrary fraction, solve the exponential relation with logarithms:

$$t=T\frac{\ln(N_0/N)}{\ln 2}.$$

For example, if a hypothetical organic sample retained 30% of its estimated initial carbon-14, the model would give approximately $5{,}730\times\ln(1/0.30)/\ln 2$, or about 9,950 years before calibration and uncertainty adjustments.

Match the isotope to the material and time range

Carbon-14 dating applies to carbon-bearing material that was once living, such as wood, plant fibers, or bone collagen. It is not the standard clock for the age of very old rocks; isotopes with much longer half-lives are used for those timescales.

As carbon-14 becomes scarce after many half-lives, measurement becomes less precise and contamination becomes more influential. Introductory calculations usually assume an ideal closed sample and a known starting ratio. Real dates also depend on sample preparation, calibration data, measurement uncertainty, and whether later carbon entered the specimen.