Radiocarbon Dating Calculator - Calculate C-14 Sample Age

A radiocarbon dating calculator estimates the age of an organic sample from the amount of carbon-14 it still contains. Carbon-14 is a radioactive form of carbon that decays at a fixed, known rate, so measuring how much is left reveals how long ago the source organism died.

What Is Radiocarbon Dating?

Radiocarbon dating, also called carbon-14 dating, finds the age of objects that contain carbon and were once part of a living thing. It works on wood, bone, shell, charcoal, textile fibers, and similar remains. It does not work directly on rock, metal, or pottery, since these were never part of a living carbon cycle.

The method was developed in the late 1940s by the American chemist Willard Libby, who received the 1960 Nobel Prize in Chemistry for the discovery.

How Carbon-14 Forms and Decays

Cosmic rays striking the upper atmosphere turn nitrogen atoms into carbon-14. This carbon-14 combines with oxygen to form carbon dioxide, which plants take in during photosynthesis. Animals eat the plants, so carbon-14 spreads through the food chain. While an organism is alive, it keeps absorbing fresh carbon, so its ratio of carbon-14 to ordinary carbon-12 stays close to the ratio found in the atmosphere.

Once the organism dies, it stops taking in new carbon. The carbon-14 already inside it keeps decaying into nitrogen, without being replaced. Half of it disappears every 5,730 years. This span is called the half-life of carbon-14.

The Radiocarbon Dating Formula

The calculator uses this formula:

t = −τ × ln(Nₜ / N₀)

• t is the age of the sample, in years
• τ (tau) is the mean lifetime of carbon-14: 8,267 years, found by dividing the half-life (5,730 years) by the natural logarithm of 2
• Nₜ is the amount of carbon-14 in the sample today
• N₀ is the amount of carbon-14 the organism had when it died
• ln is the natural logarithm

The ratio Nₜ / N₀ can be entered as a percentage of carbon-14 remaining, or as a ratio of the sample's current carbon-14/carbon-12 measurement to the ratio found in a living organism.

How to Calculate Radiocarbon Age: Example

Suppose a bone sample has 25% of its original carbon-14 left.

1. Convert the percentage to a fraction: 25% = 0.25
2. Take the natural logarithm: ln(0.25) ≈ −1.386
3. Multiply by −τ: t = −8,267 × (−1.386) ≈ 11,460 years

Because 25% is exactly one quarter, this checks out against the half-life directly: 25% remaining equals two half-lives, and 2 × 5,730 = 11,460 years.

The ratio method gives the same kind of answer. If a sample's current carbon-14/carbon-12 ratio is 0.5 and the initial (living-organism) ratio is 1.0, the ratio 0.5 ÷ 1.0 = 0.5 produces one half-life, or 5,730 years.

Reading the Calculator's Result

The calculator displays ages under 1,000 years as a whole number of years. For example, a sample with 90% of its carbon-14 remaining works out to about 871 years, shown as "871 years."

For ages of 1,000 years or more, the result switches to thousands of years with two decimal places. The 25%-remaining example above, 11,460 years, is shown as "11.46 thousand years."

Below the result, a chart plots the exponential decay curve from 0 to 50,000 years, with a marker at the 5,730-year half-life. The entered sample appears as a point on that curve, as long as its age falls within the 50,000-year window shown.

Valid Input Ranges

• Percentage of carbon-14 remaining: must be greater than 0 and no more than 100
• Current and initial carbon-14/carbon-12 ratio: both must be positive numbers, and the current ratio cannot be larger than the initial ratio

A value outside these ranges produces an error message instead of a result.

What Radiocarbon Dating Can and Cannot Date

Radiocarbon dating only works on material that was once alive and absorbed carbon from the atmosphere: wood, charcoal, bone, antler, shell, seeds, textile fibers, leather, and parchment. It cannot date rock, pottery, or metal directly. An organic residue on a pot, or charcoal found beside a stone tool, can sometimes stand in for dating the object itself.

The method works best on samples between roughly 300 and 50,000 years old. Below about 300 years, industrial pollution and nuclear weapons testing have disturbed the atmospheric carbon-14 record enough to make dates unreliable. Above about 50,000 years, less than a tenth of a percent of the original carbon-14 remains, too little to measure precisely even with sensitive laboratory equipment.

Sources of Error

Three problems most often throw off a radiocarbon date.

Contamination adds modern carbon to old material, making a sample look younger than it really is. Soil chemicals, conservation glue, and bacteria can all introduce it.

The reservoir effect makes some samples look older than they are. Marine shells and fish bones absorb carbon from ocean water that already contains old, "pre-aged" carbon, which can add several hundred to a couple of thousand years to the apparent age.

Calibration is needed because the amount of carbon-14 in the atmosphere has not stayed constant through history. Scientists correct raw radiocarbon ages into calendar years using calibration curves built from tree rings, corals, and lake sediments. This calculator reports the raw, uncalibrated age, not a calendar year.

A Brief History

Willard Libby and his colleagues at the University of Chicago developed radiocarbon dating after World War II. Libby proposed the method in 1946 and published the first radiocarbon dates in 1949. He won the Nobel Prize in Chemistry in 1960. The technique later gained the accelerator mass spectrometer, introduced in 1977, which counts carbon-14 atoms directly and needs a far smaller sample than the older counting methods.

Frequently Asked Questions

What is the oldest age radiocarbon dating can measure?

About 50,000 years. Beyond that point, too little carbon-14 remains in a sample to measure reliably.

Can radiocarbon dating date dinosaur fossils?

No. Dinosaurs went extinct around 66 million years ago, far past the roughly 50,000-year limit of the method. Fossilized bone has also lost its original carbon, replaced by minerals over millions of years.

Why does the formula use 8,267 instead of the 5,730-year half-life?

8,267 years is the mean lifetime of carbon-14, found by dividing the half-life by the natural logarithm of 2. The exponential decay equation needs the mean lifetime, not the half-life, to convert a ratio directly into an age.

Does radiocarbon dating give a calendar year?

No. It gives a raw radiocarbon age, which must be converted to a calendar year using a calibration curve, because atmospheric carbon-14 levels have varied over time.

Can radiocarbon dating be used on stone or metal objects?

No. It only works on material that once held living carbon. Stone and metal objects can sometimes be dated indirectly, through organic material found buried with them.

How accurate is radiocarbon dating?

Modern accelerator mass spectrometry can measure a sample's raw radiocarbon age to within about 20 to 50 years for material younger than 10,000 years. Accuracy decreases for older samples and depends heavily on how well the sample was preserved before testing.