Radiocarbon Dating Calculator

What is Radiocarbon Dating?

Radiocarbon dating (also known as carbon dating or carbon-14 dating) is a scientific method used to determine the age of organic materials. Developed by Nobel laureate Willard F. Libby in the 1940s, this technique measures the amount of radioactive carbon-14 remaining in a sample to calculate how long it has been since the organism died.

All living organisms absorb carbon-14 from the atmosphere throughout their lifetime. When they die, they stop absorbing new carbon-14, and the existing C-14 begins to decay at a known rate. By measuring the remaining percentage of carbon-14 and comparing it to the original amount, we can calculate the time elapsed since death using the exponential decay formula.

How Does Carbon Dating Work?

Carbon-14 has a half-life of approximately 5,730 years. This means that after 5,730 years, half of the original carbon-14 atoms in a sample will have decayed into nitrogen-14. The decay follows an exponential pattern described by the equation:

$$N = N_0 e^{-\lambda t}$$

where $N$ is the remaining amount of carbon-14, $N_0$ is the original amount, $\lambda$ is the decay constant, and $t$ is the time elapsed. The decay constant is calculated as $\lambda = \ln(2) / t_{1/2}$ where $t_{1/2}$ is the half-life of 5,730 years.

By rearranging the formula, we can solve for the age of the sample: $t = \frac{\ln(N_0/N)}{\lambda}$. The calculator performs these calculations instantly when you enter the percentage of remaining carbon-14.

Applications of Radiocarbon Dating

Carbon dating has been used in numerous groundbreaking archaeological discoveries, including dating the Shroud of Turin, uncovering modern art forgeries, determining the age of ancient Egyptian mummies, and verifying historical chronologies. It is most effective for samples up to 50,000-60,000 years old, beyond which the remaining carbon-14 levels become too small to measure accurately.

Understanding exponential decay is key to carbon dating — explore our Exponential Growth Calculator for related calculations and the Average Atomic Mass Calculator for atomic mass computations.