Calculate the radiocarbon age of an organic sample from its remaining C-14 percentage or measured activity. Instantly get age in years, half-lives elapsed, and the decay constant — based on the standard 5,730-year half-life.
✓ Verified: NIST & Radiocarbon Journal standard decay equation — April 2026
Choose how your C-14 measurement is expressed
Cambridge half-life is the current standard
100% = modern living tissue; 50% = ~1 half-life (~5,730 yrs)Enter a percentage between 0.001 and 100.
Enter a valid activity value.
Standard = 13.56 dpm/g (Oxalic Acid I)Enter a valid modern standard value.
0.5 = 50% remaining = ~5,730 years oldEnter a decimal fraction between 0.00001 and 1.
Estimated Age
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⚠️ Disclaimer: This calculator provides a theoretical estimate based on the standard radioactive decay equation. Real radiocarbon dating requires AMS laboratory measurement, calibration against a reference curve (IntCal23), and professional interpretation. Do not use this tool for scientific, archaeological, or forensic reporting.
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Sources & Methodology
🛡️Formula uses the standard radioactive decay equation as documented by NIST and the journal Radiocarbon. Half-life values are from the IUPAC/NIST reference database.
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NIST Reference on Constants, Units, and Uncertainty
Carbon-14 decay constants and half-life values. physics.nist.gov
📖
Radiocarbon Journal — Stuiver & Polach (1977)
The foundational paper defining reporting conventions for radiocarbon dates, including the use of 5,568 (Libby) vs 5,730 (Cambridge) half-lives.
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IntCal23 Calibration Curve (Reimer et al., 2020)
The international standard calibration curve used to convert raw radiocarbon ages to calendar ages. cambridge.org/radiocarbon
Formula: t = -(t½ / ln 2) × ln(N/N₀)
Where: t = age in years | t½ = half-life (5,730 yr) | N/N₀ = fraction of C-14 remaining
Equivalently: t = -8,267 × ln(fraction remaining)
Decay constant: λ = ln(2) / 5730 = 0.00012097 yr⁻¹
t = -8267 × ln(N/N0)
Example: 75% C-14 remaining → N/N0 = 0.75 t = -8267 × ln(0.75) = -8267 × (-0.2877) = 2,378 years old
How Carbon Dating Works: The Science Behind the Calculator
Radiocarbon dating — also called carbon-14 dating or simply carbon dating — is a radiometric technique used to estimate the age of organic materials up to about 50,000 years old. It was developed by Willard Libby in 1949, for which he received the Nobel Prize in Chemistry in 1960.
The technique is based on a simple physical principle: all living organisms continuously exchange carbon with the environment, maintaining a constant ratio of the radioactive isotope carbon-14 (C-14 or ¹⁴C) to the stable isotope carbon-12 (¹²C). When an organism dies, this exchange stops and the C-14 begins to decay at a predictable rate — halving every 5,730 years. By measuring how much C-14 remains, scientists can calculate when the organism died.
The Radioactive Decay Equation
The mathematical foundation is the standard first-order radioactive decay law. The key variables are the fraction of C-14 remaining (N/N₀), the half-life (t½ = 5,730 years), and the unknown age (t). Rearranging the decay equation gives: t = -(t½ / ln 2) × ln(N/N₀), which simplifies to t = -8,267 × ln(fraction remaining).
N(t) = N₀ × e^(-λt) → t = -8267 × ln(N/N₀)
λ (decay constant) = ln(2)/5730 = 0.00012097 yr⁻¹ | Mean lifetime = 1/λ = 8,267 yr
Carbon Dating Age Ranges and Half-Lives
C-14 Remaining (%)
Half-Lives Elapsed
Approx Age (Cambridge)
Typical Context
100%
0
Modern (0 yrs)
Living tissue / recent
75%
0.42
~2,378 yrs
Iron Age / Classical antiquity
50%
1.00
~5,730 yrs
Early Bronze Age / Neolithic
25%
2.00
~11,460 yrs
End of last Ice Age
10%
3.32
~19,035 yrs
Upper Paleolithic
1%
6.64
~38,069 yrs
Early modern humans in Europe
0.2%
8.97
~51,400 yrs
Near practical limit of C-14 dating
Libby vs Cambridge Half-Life: Which to Use?
There are two half-life values in common use. The Libby half-life (5,568 years) was the original value used by Willard Libby and is still used in some older literature and by convention in conventional radiocarbon age reporting for historical comparability. The Cambridge half-life (5,730 years) is the more accurate modern value determined by physical measurement. Most contemporary labs use the Cambridge value for calculations but may still report conventional ages using the Libby value — always check which your source uses.
💡 Important: This calculator gives a raw radiocarbon age. To convert this to a true calendar age, you must calibrate against the IntCal23 calibration curve, which accounts for fluctuations in atmospheric C-14 over time. A raw age of 3,000 BP (before present) may correspond to a calibrated calendar age of 3,150–3,350 BCE depending on the calibration plateau.
What Carbon Dating Cannot Do
Carbon dating is limited to organic materials that were once alive. It cannot be used on rocks, ceramics, metals, or glass. It is also unreliable for very recent samples (post-1950) due to atmospheric bomb-pulse carbon from nuclear testing, and for very old samples (beyond ~50,000 years) where remaining C-14 is below detection limits. For geological timescales, potassium-argon, uranium-lead, or uranium-thorium dating are used instead.
Frequently Asked Questions
Carbon dating works because all living organisms continuously absorb carbon-14 from the atmosphere. When an organism dies, it stops absorbing C-14 and the existing C-14 decays at a known rate with a half-life of 5,730 years. By measuring how much C-14 remains compared to the original amount, scientists calculate how long ago the organism died.
The carbon dating formula is: t = -(t½ / ln 2) × ln(N/N₀), where t is age, t½ is the half-life (5,730 years), N₀ is the original C-14 amount, and N is the current amount. This simplifies to t = -8,267 × ln(fraction remaining). For example, 75% remaining gives t = -8267 × ln(0.75) = 2,378 years.
Carbon dating is accurate to within plus or minus 40 years for recent samples and up to plus or minus 200-300 years for older ones when calibrated against IntCal23. The technique is reliable for organic materials up to about 50,000 years old. Calibration using dendrochronology (tree rings) and other proxies has significantly refined accuracy since the 1980s.
The accepted half-life of carbon-14 is 5,730 years (the Cambridge half-life). The original Libby half-life of 5,568 years is still used in some older literature and conventional reporting for historical comparability. This means every 5,730 years, half of the C-14 in a sample has decayed into nitrogen-14.
Carbon dating is generally limited to materials less than 50,000 to 60,000 years old. After about 8-9 half-lives, the remaining C-14 is less than 0.2% of the original — too little for accurate AMS measurement. For older materials, other methods like potassium-argon or uranium-lead dating are used.
No. Carbon dating only works on organic materials that were once living — wood, charcoal, bone, shell, peat, seeds, and similar materials. Rocks and minerals do not contain atmospheric C-14. For geological dating of rocks, scientists use potassium-argon, uranium-lead, or rubidium-strontium methods instead.
Percent modern carbon (pMC) expresses C-14 concentration relative to a 1950 reference standard. A pMC of 100 means the sample has the same C-14 concentration as the 1950 atmosphere. A pMC of 50 means 50% remains, corresponding to roughly one half-life (5,730 years) of age.
1950 is used because nuclear weapons testing after that date significantly altered atmospheric C-14 levels (the bomb effect). By using 1950 as the baseline, radiocarbon dates remain comparable regardless of when they were measured. Dates are expressed as BP (Before Present) where Present means 1950.
The decay constant (lambda) for carbon-14 is ln(2) / 5730 = 0.000120968 per year, or approximately 1.21 × 10⁻⁴ per year. This means 0.01210% of any C-14 sample decays each year. The mean lifetime of a C-14 atom is 1/lambda = 8,267 years.
Carbon dating can be applied to wood and charcoal, bone and teeth (using collagen), shells and coral, seeds and plant material, peat and organic sediment, leather and ancient textiles, and any other once-living organic material. The sample must be old enough to show measurable decay but young enough to still have detectable C-14.