This radiocarbon dating calculator converts a sample’s remaining carbon-14 (as a percent of the modern living level) into its age, using the decay law with the 5,730-year half-life: age = −8,267 × ln(N/N₀).

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A Clock That Starts at Death

Living things exchange carbon with the atmosphere, so their tissues hold the air’s ratio of radioactive ¹⁴C to stable ¹²C. Death stops the exchange, and from that moment the ¹⁴C simply decays — half of it every 5,730 years — while the ¹²C stays. Measuring the surviving fraction therefore measures time since death, with the decay law N/N₀ = (½)^(t/5730), equivalently t = −8,267 × ln(N/N₀), where 8,267 years is the mean lifetime (half-life ÷ ln 2). The anchors are worth memorizing: 50% remaining is exactly one half-life (5,730 years BP), 25% is two (11,460 BP), and the defaults’ 78% remaining gives ≈ 2,054 years BP — roughly 104 BCE, a wooden artifact from the late Roman Republic.

Willard Libby, who built the method in the 1940s and took a Nobel for it, used a conventional half-life of 5,568 years — and, in one of science’s great acts of coordination, laboratories STILL report raw ages on Libby’s number so that decades of dates stay comparable, applying the truer 5,730 inside calibration. This calculator uses 5,730 directly, so its raw output can differ from an uncalibrated lab figure by ~3% before calibration moves things further. The method dates anything that was once alive and stopped exchanging carbon: wood, bone, cloth, seeds, charcoal — but not stone, metal or pottery directly (those are dated by their organic company), and nothing older than roughly 50,000–60,000 years, where surviving ¹⁴C is a whisper under modern contamination’s shout.

Worked Examples (Verified)

  • Defaults: 78% remaining → −8,267 × ln(0.78) = ≈ 2,054 years BP (≈ 104 BCE).
  • One half-life: 50% → 5,730 BP exactly.
  • Two half-lives: 25% → 11,460 BP (late Ice Age hunter territory).
  • Recent sample: 95% → ≈ 424 BP (≈ 1526 CE).
  • Near the limit: 1% → ≈ 38,070 BP — measurable, but calibration and contamination own the error bars.

Radiocarbon Discipline

  • BP means “before 1950,” not before today — a 2,054 BP sample is from ≈104 BCE, not 29 BCE.
  • Raw BP ages are not calendar ages until calibrated against IntCal curves; offsets of centuries are normal and era-dependent.
  • Reservoir effects: ocean and lake organisms drink old carbon and date centuries too old straight out of the water — marine samples need reservoir corrections.
  • Contamination is asymmetric doom: 1% modern carbon in a truly 40,000-year sample makes it read ~37,000; ancient samples are cleaned ferociously for a reason.
  • The method needs the organism to have equilibrated with the atmosphere while alive — which is why it dates death, and why a living snail eating limestone can look centuries dead (the hard-water effect).

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Frequently Asked Questions

How does radiocarbon dating work?

While an organism lives, it exchanges carbon with the atmosphere and holds the atmosphere’s ¹⁴C/¹²C ratio. When it dies, exchange stops and the radioactive ¹⁴C decays with a 5,730-year half-life while ¹²C stays constant. Measuring the surviving fraction N/N₀ and applying age = −8,267 × ln(N/N₀) gives the time since death. This calculator runs that formula for any measured percentage — 78% remaining, for instance, dates to about 2,054 years BP.

What does BP mean in radiocarbon dating?

“Before Present,” where Present is fixed at 1950 CE — chosen because it’s just before nuclear testing doubled atmospheric ¹⁴C and muddied the baseline. So 2,000 BP is 50 BCE, not 26 CE. The convention lets dates from any laboratory and any decade be compared without drifting as the calendar advances. When this calculator shows a calendar estimate, it computes 1950 − BP; treat it as approximate until calibration has had its say.

How old can radiocarbon dating measure?

Reliably to about 50,000 years, heroically to ~60,000. Each half-life halves the signal: at 50,000 years (≈8.7 half-lives) only ~0.24% of the original ¹⁴C remains, and modern contamination at the 0.1–1% level — a fingerprint’s worth of today’s carbon — swamps the true signal and makes old samples read too young. Beyond that range, geology hands over to potassium-argon, uranium-series and luminescence clocks, which is why dinosaur bones (66+ million years) contain no measurable ¹⁴C at all.

Why do radiocarbon dates need calibration?

Because the starting ratio wasn’t constant: the atmosphere’s ¹⁴C level has drifted with solar activity, geomagnetic field strength, ocean circulation, industrial fossil carbon (which dilutes it) and nuclear tests (which spiked it). A raw BP age assumes the sample started at the 1950 level. Calibration curves built from tree rings of known age (IntCal) map raw ages to true calendar ages — sometimes shifting them by centuries, occasionally offering two calendar ranges where the curve wiggles. The decay physics on this page is exact; the atmosphere’s history is the correction.

What materials can be carbon dated?

Anything once alive that stopped exchanging carbon at death: wood and charcoal, bone (the collagen fraction), seeds and grain, linen and wool cloth, leather, paper, and shell (with reservoir corrections). It cannot date stone, metal, glass or fired pottery directly — archaeologists date those by associated organics and by other methods (thermoluminescence for ceramics). It also cannot date anything that never took up atmospheric carbon, which is why claims of carbon-dating rocks or dinosaur fossils are category errors.

Why did the Turin Shroud date to the medieval period?

Three independent laboratories in 1988 measured the shroud’s linen ¹⁴C and converged on the flax having been harvested in roughly 1260–1390 CE — the fabric’s carbon had only been decaying for ~700 years, not 2,000. The result used the same decay law as this calculator (with accelerator mass spectrometry counting individual ¹⁴C atoms), plus calibration and inter-lab replication. Debate continues about sampling location and possible medieval repair sections, which is itself a lesson: the logarithm is never the weak point of a date — the sample’s biography is.

What is the Libby half-life vs the Cambridge half-life?

Libby’s original 5,568 years (the “Libby half-life”) turned out ~3% short of the refined physical value, 5,730 ± 40 years (the “Cambridge half-life”). Rather than orphan four decades of published dates, the field kept reporting conventional ages on 5,568 and let the calibration curves absorb the difference. This calculator uses the physical 5,730, so its raw ages run about 3% older than a lab’s conventional BP for the same sample — a definitional offset, not a disagreement about the sample.

Is this radiocarbon dating calculator free?

Yes — free, instant, no sign-up. Enter the percent of carbon-14 remaining for the age in years BP and an approximate calendar year.