Radiocarbon Dating Calculator - Carbon-14 Age of Organic Samples

What is carbon dating?

Have you ever wondered how archaeologists determined that the Maya civilization collapsed between the 8th and 9th centuries, or that Tutankhamun — also known as King Tut — ruled during the end of the 18th Dynasty? The answer lies in a technique called radiocarbon dating (also known as carbon dating or carbon-14 dating).

Carbon dating is a method used to determine the age of organic materials — more precisely, the time elapsed since the death of the plant or animal the material came from. It relies on measuring the amount of the radioactive carbon isotope ¹⁴C remaining in a sample and correlating it with the known half-life of carbon-14. The technique was developed in the 1940s by Prof. Willard F. Libby, who won a Nobel Prize for this discovery.

The three isotopes of carbon

Carbon has three naturally occurring isotopes:

• Carbon-12 (¹²C) — ~99% of all natural carbon; stable.
• Carbon-13 (¹³C) — ~1%; stable.
• Carbon-14 (¹⁴C) — about 1 part per trillion of ¹²C; radioactive.

¹⁴C decays into nitrogen-14 (¹⁴N) through beta decay with a half-life of 5,730 years (Cambridge value, the current international standard). An older value of 5,568 years — the original Libby half-life — is still used in some legacy reporting and is also available in our calculator.

How does carbon dating work?

Carbon-14 is continuously produced in the upper atmosphere when cosmic-ray neutrons collide with nitrogen-14 atoms. The resulting ¹⁴C quickly mixes with oxygen and circulates through the biosphere just like ordinary ¹²C. While a plant or animal is alive, it constantly absorbs new ¹⁴C through photosynthesis or diet, keeping its ¹⁴C/¹²C ratio roughly constant.

When an organism dies, it stops absorbing ¹⁴C. The ¹⁴C already in its tissues then begins to decay steadily, so the ratio falls over time. By comparing the measured activity (or percentage remaining) against the activity of modern living tissue, we can calculate precisely how long ago the organism died.

Basic principles of carbon-14 dating

The age formula is derived from the law of radioactive decay:

N(t) = N₀ × e^−λt

where λ = ln(2) / t_½

Rearranging to solve for age t:

t = t_½ × ln(N₀ / N) / ln(2)

• t — age of the sample (years BP, Before Present)
• t_½ — half-life of ¹⁴C: 5,730 yr (Cambridge) or 5,568 yr (Libby)
• N₀ — initial amount of ¹⁴C (modern reference activity)
• N — measured amount of ¹⁴C in the sample

The "Before Present" (BP) convention defines the reference year as 1950 CE, the year radiocarbon dating was standardized. Our calculator converts BP ages to calendar BCE/CE dates using the measurement year you enter.

American and metric input systems

Our calculator accepts three types of input, covering both metric (SI) and the traditional American system:

• Percentage remaining (%) — the most intuitive: 100% means freshly dead, 50% means one half-life has elapsed, etc.
• Specific activity in Bq/g (metric / SI) — Becquerels per gram of carbon. Modern wood has an activity of ~0.226 Bq/g.
• Specific activity in dpm/g (American traditional) — disintegrations per minute per gram. Modern wood: ~13.56 dpm/g. (1 Bq = 60 dpm)

You can also choose between the Cambridge half-life (5,730 yr) — the current international standard — and the original Libby half-life (5,568 yr), which is still cited in older American laboratory reports.

Examples of application

• Archaeology — dating wood, charcoal, bone, shells, fabric (Shroud of Turin, Dead Sea Scrolls).
• Geology & climate science — dating peat bogs, lake sediments, coral reefs, ice cores.
• Art authentication — distinguishing genuine Renaissance paintings from modern forgeries.
• Forensic science — estimating year of death in criminal investigations.
• Oceanography — studying ocean circulation rates using dissolved carbonate.

Practical range and limitations

Radiocarbon dating is reliable for samples up to about 50,000 years old (≈ 8–9 half-lives, leaving ~0.2% of the original ¹⁴C). Beyond this limit, the remaining activity is too close to background radiation for accurate measurement. For older materials, other radiometric methods (e.g., potassium-argon or uranium-lead) are used instead.

How to use the Radiocarbon Dating Calculator

1. Select input type — choose between C-14 percentage remaining, specific activity in Bq/g (metric), or specific activity in dpm/g (American traditional).
2. Enter the measured value — type the value from your lab report or textbook problem. Use the quick-example buttons to explore preset scenarios.
3. Choose the half-life system — Cambridge (5,730 yr, recommended) or Libby (5,568 yr, for compatibility with older laboratory data).
4. Set the measurement year — the year the sample was measured. This is used to convert the BP age to a calendar BCE/CE date (default: 2024).
5. Click "Calculate Age" — the results panel shows age in years BP, the equivalent calendar date, number of half-lives elapsed, and activity in both Bq/g and dpm/g.

Frequently asked questions

Why is the reference year 1950?

In 1950, radiocarbon dating was standardized internationally. All "Before Present" ages are counted from 1 January 1950. You can adjust the measurement year in our calculator to get an accurate calendar conversion for any year of analysis.

Is radiocarbon dating accurate?

For most purposes, yes. Calibration curves (IntCal20, SHCal20, Marine20) correct for historical fluctuations in atmospheric ¹⁴C caused by solar activity, ocean circulation, and volcanic eruptions, reducing uncertainties to ±20–40 years for recent samples.

Why does the calculator limit the activity to the modern value?

Any sample measured today cannot have more ¹⁴C than a freshly dead organism (~0.226 Bq/g or ~13.56 dpm/g). Values above this would indicate contamination or measurement error. The calculator alerts you if you enter an unrealistically high activity.

What is the difference between the Cambridge and Libby half-lives?

Libby originally measured a half-life of 5,568 years. Later precision measurements gave 5,730 ± 40 years (Cambridge). By convention, radiocarbon ages are still reported in "Libby years" in some databases, but the Cambridge value is used for calibration. Our calculator lets you use either.