Carbon-14 Dating Calculator

Radiocarbon dating determines the age of organic material by measuring the remaining concentration of Carbon-14 (¹⁴C), a radioactive isotope that decays at a known rate after an organism dies.

The Radioactive Decay Formula:

N(t) = N₀ × e^(−λt)

Where:

• N(t) = Remaining ¹⁴C atoms at time t
• N₀ = Initial ¹⁴C atoms at time of death
• λ = Decay constant = ln(2) / t½ = 0.693 / 5,730 = 0.0001209 per year
• t½ = Half-life of ¹⁴C = 5,730 years

Solving for age t:

t = −ln(N/N₀) / λ = (t½ / ln2) × ln(N₀/N)

Activity Ratio: Modern samples have a known ¹⁴C/¹²C ratio of ~1.2 × 10⁻¹². Measured ratio of sample divided by modern standard gives N/N₀.

Worked Example:

• A wooden artifact has 65% of modern ¹⁴C activity remaining (N/N₀ = 0.65)
• t = (5,730 / 0.693) × ln(1 / 0.65)
• t = 8,267 × ln(1.538)
• t = 8,267 × 0.4308
• t ≈ 3,561 years old

Calibration: Raw radiocarbon ages are corrected using IntCal20 calibration curves (tree rings, coral cores) because atmospheric ¹⁴C has varied over time.

Dating Range: ¹⁴C dating is reliable up to ~50,000 years. Beyond that, remaining ¹⁴C is too small to measure accurately. For older materials, scientists use potassium-40 (half-life 1.25 billion years) or uranium-lead dating instead.