Radiocarbon Dating Calculator
Free Radiocarbon dating Calculator for nuclear chemistry. Enter variables to compute results with formulas and detailed steps.
Formula
t = -ln(A/A0) / lambda | lambda = ln(2) / 5730
The age t is calculated by comparing the sample activity (A) to the modern standard activity (A0). Lambda is the decay constant for C-14, derived from its half-life of 5,730 years. BP dates are measured from 1950 CE.
Worked Examples
Example 1: Ancient Wood Sample
Problem: A piece of charcoal from an archaeological site has a C-14 activity of 6.78 dpm/g. Modern activity is 13.56 dpm/g. What is the age?
Solution: t = -ln(6.78/13.56) / (ln(2)/5730)\nt = -ln(0.5) / 0.000121\nt = 0.6931 / 0.000121\nt = 5,730 years BP (exactly 1 half-life)
Result: 5,730 years BP (approximately 3780 BCE)
Example 2: Percent Remaining Method
Problem: A bone fragment has 25% of its original C-14 remaining. How old is it?
Solution: t = -ln(0.25) / (ln(2)/5730)\nt = -(-1.3863) / 0.000121\nt = 1.3863 / 0.000121\nt = 11,460 years (exactly 2 half-lives)
Result: 11,460 years BP (approximately 9510 BCE)
Frequently Asked Questions
What is radiocarbon dating?
Radiocarbon dating is a method used to determine the age of organic materials by measuring the amount of Carbon-14 remaining in a sample. Living organisms continuously exchange carbon with the atmosphere, maintaining a constant ratio of C-14 to C-12. Once an organism dies, it stops absorbing C-14, and the existing C-14 begins to decay with a half-life of 5,730 years. By comparing the remaining C-14 activity to the modern standard, scientists can calculate how long ago the organism died.
What does BP mean in radiocarbon dating?
BP stands for Before Present, where Present is defined as the year 1950 CE by international convention. This reference point was chosen because atmospheric nuclear weapons testing after 1950 significantly altered the global C-14 levels, making post-1950 measurements unreliable as a baseline. So an age of 3,000 years BP means approximately 1050 BCE. Calibrated dates account for variations in atmospheric C-14 over time and are denoted as cal BP.
What is the effective range of radiocarbon dating?
Radiocarbon dating is effective for samples up to about 50,000 to 60,000 years old, which corresponds to roughly 8 to 10 half-lives of Carbon-14. Beyond this range, the remaining C-14 is so minute that it becomes indistinguishable from background radiation and contamination. For very old samples, other radiometric methods like potassium-argon dating or uranium-lead dating are used instead. Modern accelerator mass spectrometry (AMS) has pushed the practical limit closer to 60,000 years.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Can I use Radiocarbon Dating Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Is Radiocarbon Dating Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.