Radiocarbon Dating Calculator
Enter the carbon-14 measurement from your sample to get the conventional radiocarbon age in years Before Present (BP) and a 1-sigma uncertainty range. Choose between percent modern carbon (pMC), remaining fraction, or activity ratio as your input mode. Switch between the Libby (5,568 yr) and Cambridge (5,730 yr) half-life conventions, or use reverse mode to find what fraction remains at a known age. A live decay chart shows where your sample sits on the C-14 curve.
How radiocarbon dating works
Radiocarbon dating exploits the fact that living organisms continuously exchange carbon with the atmosphere, maintaining a fixed ratio of radioactive carbon-14 (C-14) to stable carbon-12. When an organism dies, this exchange stops and the C-14 begins to decay at a known rate, with a half-life of 5,730 years (Cambridge value). By measuring how much C-14 remains relative to the original amount, scientists can calculate how long ago the organism died. The technique was developed by Willard Libby in 1949 and earned him the Nobel Prize in Chemistry in 1960. It is the most widely used method for dating organic materials younger than about 50,000 years, from archaeological charcoal and bone to ancient textiles and wood.
The decay equation and half-life conventions
The core formula is N = N0 times e^(-lambda times t), where N is the remaining C-14, N0 is the original amount, lambda is the decay constant equal to ln(2) divided by the half-life, and t is time elapsed. Rearranged to solve for age: t = -(half-life / ln(2)) times ln(N/N0). Two half-life values are in use. The Libby value of 5,568 years comes from the original 1949 measurements and is used by most laboratories for conventional age reporting, ensuring comparability across decades of published dates. The Cambridge value of 5,730 years is the physically correct modern measurement. Calibration curves such as IntCal20 internally correct for this difference when producing calendar dates, so the choice of convention matters mainly for matching older publications.
Input modes: pMC, fraction, and activity ratio
Laboratory results can be expressed in several ways. Percent modern carbon (pMC) compares the sample to a 1950 oxalic acid standard: 100 pMC means the sample has the same C-14 concentration as the standard. A pMC above 100 indicates a post-bomb sample, where atmospheric C-14 spiked after 1950s nuclear weapons testing, making conventional dating inapplicable. Remaining fraction (N/N0) is the same quantity as a decimal (divide pMC by 100). Activity ratio (A/A0) compares the specific radioactivity of the sample to the standard and is numerically equivalent to the fraction for dating purposes. This calculator accepts all three formats, converts them to a fraction internally, and then applies the decay equation.
Uncertainty, calibration, and practical limits
The age output here is a conventional radiocarbon age, not a calibrated calendar date. Atmospheric C-14 concentration has varied over time due to changes in solar activity, ocean circulation, and other factors, so a raw BP age does not map linearly onto the calendar. Calibration curves such as IntCal20 (terrestrial) and Marine20 (marine) produced by the IntCal Working Group correct for these fluctuations. Software such as OxCal or Calib converts a conventional radiocarbon age plus its uncertainty into a calibrated calendar date range at 68% or 95% confidence. The practical upper dating limit is about 50,000 to 55,000 years BP, beyond which too little C-14 remains for reliable measurement. Marine and freshwater samples require a reservoir correction, typically about 400 years for average marine environments, because aquatic systems exchange carbon more slowly with the atmosphere.
Carbon-14 remaining vs. approximate age
| pMC remaining | Half-lives elapsed | Age (years BP) | Geological context |
|---|---|---|---|
| 100 | 0.00 | 0 | Modern (1950 CE reference) |
| 75 | 0.42 | 2,400 | Late Bronze Age |
| 50 | 1.00 | 5,730 | Early Neolithic (one half-life) |
| 25 | 2.00 | 11,460 | Last glacial maximum (two half-lives) |
| 12.5 | 3.00 | 17,190 | Late Pleistocene (three half-lives) |
| 6.25 | 4.00 | 22,920 | Last glacial period (four half-lives) |
| 3.13 | 5.00 | 28,650 | Middle upper Paleolithic |
| 1.56 | 6.00 | 34,380 | Early upper Paleolithic |
| 0.78 | 7.00 | 40,110 | Near practical limit |
| 0.20 | 8.97 | 51,400 | Beyond conventional C-14 range |
Based on the Cambridge half-life of 5,730 years. Actual ages vary with half-life convention and calibration.
Frequently asked questions
What does "years BP" mean in radiocarbon dating?
BP stands for Before Present, but Present is fixed at 1950, the year Willard Libby standardized the method. So 5,000 BP means 5,000 years before 1950, approximately 3050 BCE on the calendar. This fixed reference avoids the confusion of a shifting present year and is used by all radiocarbon laboratories worldwide.
What is the half-life of carbon-14?
The accepted modern (Cambridge) half-life is 5,730 years. The original value measured by Willard Libby in 1949 was 5,568 years. Most radiocarbon laboratories still report conventional ages using the Libby value for historical comparability across published literature, even though 5,730 years is physically more accurate. Calibration curves account for the true half-life when producing calendar dates.
How far back can radiocarbon dating reach?
The practical upper limit is roughly 50,000 to 55,000 years BP. Beyond that, fewer than 0.2% of the original C-14 remains, which is too little to measure reliably with most instruments even with accelerator mass spectrometry (AMS). For older materials, other radiometric methods such as potassium-argon, uranium-lead, or thermoluminescence are used instead.
What is pMC and how do I interpret it?
pMC stands for percent modern carbon. It expresses how much C-14 a sample contains relative to a 1950 standard. A value of 50 pMC means the sample retains half the original C-14 concentration, equivalent to one half-life of decay (about 5,730 years old). Values above 100 pMC indicate post-bomb contamination from 1950s nuclear testing; those samples cannot be dated by conventional radiocarbon methods.
What is the difference between a conventional radiocarbon age and a calibrated calendar date?
A conventional radiocarbon age (in years BP) is calculated directly from the decay equation, assuming atmospheric C-14 has been constant. A calibrated calendar date corrects for documented variations in atmospheric C-14 over time using curves like IntCal20. Calibration often produces a range of calendar years rather than a single date and can shift the midpoint by hundreds or even a few thousand years. Always use calibrated dates for publication; the raw BP age is mainly used for interlaboratory comparison.
What is the reservoir effect and when does it matter?
The reservoir effect occurs when an organism absorbs carbon from a source with a different C-14 concentration than the contemporary atmosphere. Marine organisms absorb carbon from seawater, which equilibrates with the atmosphere on a timescale of hundreds to thousands of years, making them appear older than they are by a global average of about 400 years. Freshwater systems can have much larger offsets. Reservoir corrections must be applied before or during calibration to get accurate dates from marine, estuarine, or freshwater samples.