Radiocarbon Dating Calculator (Carbon-14 Dating)

The age formula is t = -(t½ / ln2) x ln(N / N0), where N/N0 is the fraction of carbon-14 remaining, t½ is the half-life of carbon-14 (5730 years, or 5568 years in the older Libby convention), and ln is the natural logarithm. This comes directly from the general radioactive decay law N(t) = N0 e^(-λt), solved for t.

The modern, most accurate measured half-life of carbon-14 is 5730 years (sometimes called the Cambridge half-life). Many published archaeological dates instead use the older Libby half-life of 5568 years for historical consistency, since that was the value Willard Libby used when he developed the method in the 1940s.

For samples younger than about 50,000 years, radiocarbon dating is typically accurate to within a few decades to a few centuries, depending on sample quality and lab precision. Accuracy degrades for very old samples, since so little C-14 remains, and results are always reported with a statistical uncertainty range, plus they require calibration against known-age records for a precise calendar date.

Divide the percent modern carbon by 100 to get the fraction remaining, N/N0, then apply t = -(t½/ln2) x ln(N/N0). For example, a sample with 50% modern carbon remaining has age = -(5730/0.6931) x ln(0.5) = 5730 years, exactly one half-life, since 50% remaining is the definition of one half-life.

In practice, carbon-14 dating becomes unreliable beyond roughly 50,000 years (about 8.7 half-lives), because so few C-14 atoms remain that instrument background noise and contamination dominate the signal. Older materials require other radiometric methods, such as potassium-argon or uranium-series dating, which use isotopes with much longer half-lives.

Radiocarbon dating depends on an organism continuously exchanging carbon with the atmosphere while alive, plants absorb CO2 directly, and animals absorb it by eating plants or other animals, keeping their C-14 to C-12 ratio matched to the atmosphere. Once the organism dies, that exchange stops and the C-14 begins decaying without replacement, which is what makes the clock start. Inorganic materials like stone or metal never had this exchange process, so they cannot be dated this way.

Percent modern carbon is the sample's measured C-14 activity expressed as a percentage of a standardized modern reference activity (based on the year 1950). A pMC of 100% means the sample matches the modern reference exactly (essentially no C-14 decay has occurred), while a pMC of 50% means half of the original carbon-14 has decayed away, corresponding to exactly one half-life of elapsed time.

Yes, significantly. Even small amounts of younger carbon contamination (from handling, soil, or preservatives) can make a sample appear artificially younger, since it dilutes the old sample's low C-14 signal with modern-level C-14. Older carbon contamination has less effect since it typically has very little C-14 left to contribute. Modern labs use careful chemical pretreatment specifically to remove contaminants before measurement.

The assumption that atmospheric C-14 concentration has always been constant is only approximately true, it has fluctuated over millennia due to changes in cosmic ray intensity, the carbon cycle, and human fossil fuel burning. Calibration curves (like IntCal20), built from tree rings, corals, and other independently dated records, convert a raw radiocarbon age into a more accurate calendar-year age range. This calculator returns the simpler, uncalibrated radiocarbon age.

Common sample types include wood and charcoal, bone and collagen, shell, peat, seeds and other plant remains, and textiles, essentially anything that was once part of a living organism. Each sample type has its own best-practice pretreatment method in the lab to remove contamination before the C-14 activity is measured.

Divide the sample's measured activity by the modern reference activity (a typical reference value is about 13.56 disintegrations per minute per gram of carbon) to get the fraction remaining, then apply the same decay formula, t = -(t½/ln2) x ln(measured/reference). This is mathematically identical to the percent modern carbon method, just expressed with raw activity numbers instead of a percentage.