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.

That correction is not a rounding detail. Atmospheric ¹⁴C swung by several percent over the Holocene, so a raw age can sit a few centuries away from the calendar date, and in some stretches of the curve a single measurement maps onto two or three separate date ranges at once. Archaeologists never publish the number this calculator gives you. They run it through OxCal or CALIB and quote a calibrated range with a confidence interval, written as cal BP rather than BP.

Two half-lives, and the one you will see in journals

Willard Libby’s original 1949 figure was 5,568 years. It was measured more accurately in 1962 as 5,730 ± 40, but by then thousands of dates had been published on the old number, so the field kept 5,568 as the conventional half-life and folded the difference into calibration instead. This calculator uses the true 5,730-year value, which is the right choice for understanding the physics. If you are comparing against a published laboratory date, expect a discrepancy of about 3 percent from that convention alone, before calibration touches it.

Contamination moves the answer more than the maths does. A sample picking up 1% modern carbon caps its apparent age near 37,000 years no matter how old it really is, and old carbonate leaching in from groundwater pushes the age the other way. Sample preparation is most of the real work in this field.

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.