The Radiocarbon Dating Calculator is a scientific tool that estimates the age of organic materials by analyzing the remaining Carbon‑14 (¹⁴C) isotope in a sample. Carbon‑14 dating, also called radiocarbon dating, is widely used in archaeology, geology, paleontology, and environmental science to determine how long ago a living organism died.
This calculator allows researchers, students, and enthusiasts to quickly estimate sample age without manually solving radioactive decay equations.
Carbon‑14 dating is a method of determining the age of once-living matter based on the natural decay of ¹⁴C, a radioactive isotope of carbon. All living organisms maintain a constant level of ¹⁴C while alive. After death, ¹⁴C decays at a predictable rate, allowing scientists to estimate the time elapsed since death.
The half-life of Carbon‑14 is 5,730 years, making it effective for dating organic materials up to approximately 50,000 years old.
The calculator uses the standard radioactive decay formula:
t = (ln(N₀ / N) / λ)
Where:
t = age of the sample
N₀ = original ¹⁴C activity (or fraction modern carbon)
N = measured ¹⁴C activity in the sample
λ = decay constant of ¹⁴C
The decay constant λ is calculated from the half-life (T₁/₂):
λ = ln(2) / T₁/₂
T₁/₂ (Carbon-14) = 5730 years
Highlighted Formula for User Experience:
t = (ln(N₀ / N) × 5730) / ln(2)
This frame ensures users can clearly see the main calculation formula at a glance.Suppose a sample has 70% of its original ¹⁴C remaining.
Step 1: Identify variables
N/N₀ = 0.70
Step 2: Apply the formula
t = (ln(1 / 0.70) × 5730) / ln(2)
Step 3: Calculate logarithms
ln(1 / 0.70) = ln(1.42857) ≈ 0.3567
t = (0.3567 × 5730) / 0.693 ≈ 2947 years
Result: The sample is approximately 2,950 years old.