How Carbon-14 Dating Works (and Its Limits)

In 1991 two hikers in the Alps found a body in melting ice. At first it was assumed to be a recent mountaineering accident. Radiocarbon dating showed the man, now known as Ötzi, had died more than 5,000 years ago. The same method has dated the Dead Sea Scrolls, cave paintings and countless archaeological sites. It works because of one radioactive isotope of carbon and its steady, predictable half-life.

Where carbon-14 comes from

Almost all carbon is carbon-12 (about 98.9%) with a little carbon-13 (about 1.1%). Both are stable. But high in the atmosphere, cosmic rays produce a steady trickle of neutrons, and when a neutron hits a nitrogen-14 atom it can knock out a proton and turn it into carbon-14:

¹⁴N + neutron → ¹⁴C + proton

Carbon-14 is radioactive. It slowly decays back to nitrogen-14 by beta decay, with a half-life of about 5,700 years. Production and decay balance out, so the atmosphere holds a small, roughly constant proportion of carbon-14 — about one atom in every trillion carbon atoms.

How it gets into living things

Carbon-14 reacts with oxygen to form carbon dioxide, just like ordinary carbon. Plants take in that CO₂ during photosynthesis, animals eat the plants, and so every living thing carries roughly the same ratio of carbon-14 to carbon-12 as the atmosphere around it.

When an organism dies, it stops taking in new carbon. From that moment the carbon-14 it contains decays and isn’t replaced. The ratio of ¹⁴C to ¹²C falls by half every 5,700 years or so. Measure how much is left, and you can work out how long ago it died.

A worked example

A piece of charcoal from an ancient hearth contains 30% of the carbon-14 found in living wood. How old is it?

Using the half-life formula rearranged for time:

t = t½ × log₂(N₀ ÷ N) t = 5,700 × log₂(100 ÷ 30) t = 5,700 × 1.737 t ≈ 9,900 years

As a rough check: one half-life leaves 50%, two leave 25%. 30% lies between, so the answer should be between 5,700 and 11,400 years — and it is.

Measuring it

Early radiocarbon labs counted the beta particles given off by a sample, which needed grams of material and days of counting. Today most dating uses accelerator mass spectrometry (AMS), which counts the carbon-14 atoms directly. It needs only milligrams — a single seed or a fragment of bone collagen — and is much faster.

The method was developed by Willard Libby and his colleagues in the late 1940s, and Libby received the 1960 Nobel Prize in Chemistry for it.

Why it only works back about 50,000 years

After about ten half-lives (57,000 years), less than 0.1% of the original carbon-14 remains. That’s so little that tiny amounts of modern contamination — a trace of modern carbon from handling or groundwater — overwhelm the signal. In practice radiocarbon dating is reliable up to around 50,000 years.

For older material, scientists use isotopes with much longer half-lives, such as potassium-40 (1.25 billion years) or uranium-238 (4.47 billion years). Those are used for rocks rather than organic remains. It’s a common misconception that carbon dating is used to date dinosaur fossils or the Earth itself — it can’t reach anywhere near that far.

Why dates need calibration

The simple calculation assumes the atmosphere always had the same proportion of carbon-14. It didn’t quite. Cosmic ray intensity, the Earth’s magnetic field and the carbon cycle have all varied. Two big human effects matter too:

• Burning fossil fuels adds carbon with no carbon-14 at all (it’s millions of years old), diluting the atmospheric level — the “Suess effect”.
• Atmospheric nuclear weapons tests in the 1950s and early 1960s nearly doubled atmospheric carbon-14 for a time — the “bomb pulse”.

So raw radiocarbon ages are converted to calendar ages using calibration curves, built from samples of known age like tree rings (counted year by year), lake sediments and corals. That’s why published dates often come as a range, such as “3350–3100 BC”.

There’s also a quirk of convention: radiocarbon labs still report “uncalibrated” ages using Libby’s original half-life of 5,568 years, and measure “before present” from the year 1950. Calibration takes care of both.

Quick answers

Can you carbon-date a rock or a metal tool? No. Only material that was once alive and took in carbon from the atmosphere — wood, charcoal, bone, shell, cloth, paper.

Can carbon dating date dinosaurs? No. Dinosaurs died out about 66 million years ago, more than a thousand times beyond the method’s range.

Why is the half-life sometimes given as 5,730 years? It’s an older measured value. The current evaluated half-life is about 5,700 years, which is what nuclear data tables — and our carbon isotope table — use.

Try it

The half-life calculator has carbon-14 built in: enter the percentage remaining and leave the time blank to get an (uncalibrated) age.