Radiocarbon Dating (Carbon-14) Equation
Calculates the radiocarbon age of organic archaeological and fossil specimens up to ~50,000 years old based on remaining ¹⁴C activity relative to pre-industrial modern carbon.
\[ t = -\frac{T_{1/2}}{\ln(2)} \cdot \ln\left( \frac{A}{A_0} \right) = -8267 \cdot \ln\left( \frac{A}{A_0} \right) \]
Plain Text Formula:
t = -(5730 / ln(2)) * ln(A / A0) = -8267 * ln(A / A0)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ t \] | Radiocarbon Age | years Before Present (BP) | Time elapsed since specimen ceased carbon assimilation |
| \[ A / A_0 \] | Activity Fraction | percent or ratio | Current ¹⁴C specific activity divided by modern standard (13.56 dpm/g C) |
| \[ T_{1/2} \] | C-14 Half-Life | 5,730 years | Cambridge standard physical half-life of Carbon-14 |
💡 Worked Engineering Example
Problem Statement:
A fossil bone displays 25% of modern ¹⁴C activity (A/A0 = 0.25). Calculate its age.
Step-by-Step Solution:
- ln(0.25) = -1.38629
- t = -8,267 * (-1.38629) = 11,460 years BP
- Alternatively: 2 half-lives elapsed = 2 * 5,730 = 11,460 years
🎯 Result: The specimen dates to 11,460 years BP (Younger Dryas / end of the Pleistocene epoch).