5,730
years BP
5,566
years BP
5,897
years BP
50
%
1
half-lives
0.00012097
1/year
5,730
years BP
5,566
years BP
5,897
years BP
50
%
1
half-lives
0.00012097
1/year
The Carbon Dating Calculator estimates the age of organic materials by analyzing the remaining fraction of carbon-14 (¹⁴C) relative to the level found in living organisms. Radiocarbon dating, developed by Willard Libby in 1949 (for which he received the Nobel Prize in Chemistry in 1960), is the most widely used chronological method in archaeology and paleontology for dating materials up to approximately 50,000 years old.
The principle is elegant: cosmic rays continuously produce ¹⁴C in the upper atmosphere, which is incorporated into CO₂ and then into living organisms through photosynthesis and the food chain. While alive, organisms maintain a constant ratio of ¹⁴C to ¹²C. Upon death, ¹⁴C intake stops, and the existing ¹⁴C decays with a half-life of 5,730 years. By measuring the remaining ¹⁴C fraction, we can calculate the time since death.
The age formula is \(t = -\frac{t_{1/2}}{\ln 2} \ln\left(\frac{N}{N_0}\right)\), where \(N/N_0\) is the fraction of ¹⁴C remaining compared to a modern reference standard. A ratio of 0.5 corresponds to one half-life (5,730 years), 0.25 to two half-lives (11,460 years), and so on.
This calculator also accounts for measurement uncertainty, providing an age range that reflects the precision of the ¹⁴C measurement. Modern accelerator mass spectrometry (AMS) can measure ¹⁴C ratios with uncertainties as small as 0.3%, yielding age uncertainties of about ±30 years for recent samples.
Radiocarbon dating has revolutionized our understanding of human history, enabling precise chronologies for ancient civilizations, ice ages, megafauna extinctions, and early human migrations. It remains an indispensable tool in archaeology, geology, oceanography, and climate science.
Note that raw radiocarbon ages require calibration against tree-ring chronologies or other records because atmospheric ¹⁴C levels have not been perfectly constant over time. This calculator provides the conventional radiocarbon age; calibrated calendar ages may differ by up to several centuries.
The carbon-14 dating formula derives directly from the exponential decay law:
$$N(t) = N_0 \cdot e^{-\lambda t}$$
Solving for age \(t\):
$$t = -\frac{1}{\lambda} \ln\left(\frac{N}{N_0}\right) = -\frac{t_{1/2}}{\ln 2} \ln(R)$$
where \(R = N/N_0\) is the fraction of modern ¹⁴C remaining, \(t_{1/2} = 5730\) years, and \(\lambda = \ln 2 / t_{1/2} \approx 1.2097 \times 10^{-4}\) per year.
Uncertainty propagation: Age bounds are calculated using \(R \pm \sigma_R\):
$$t_{low} = -\frac{\ln(R + \sigma_R)}{\lambda}, \quad t_{high} = -\frac{\ln(R - \sigma_R)}{\lambda}$$
The age is reported in years BP (Before Present, where 'present' is conventionally defined as 1950 CE). A ratio of 1.0 means the sample is modern (zero age), while lower ratios indicate older samples. The practical limit of radiocarbon dating is about 50,000 years (ratio ~0.002), beyond which the remaining ¹⁴C is too small to measure reliably. The age range reflects measurement uncertainty only—additional uncertainty from ¹⁴C production variations requires calibration curves.
Inputs
Results
A sample with exactly 50% of its original ¹⁴C remaining is exactly one half-life old (5,730 years). With ±1% measurement uncertainty, the age range is approximately 5,614–5,849 years BP.
Inputs
Results
A bone with 10% ¹⁴C remaining dates to approximately 19,035 years BP, placing it in the Late Pleistocene near the Last Glacial Maximum.
The practical limit is about 50,000 years, corresponding to about 8.7 half-lives and a remaining ¹⁴C fraction of roughly 0.2%. Beyond this, the amount of ¹⁴C is too small to measure reliably even with AMS technology. For older materials, other radiometric methods like potassium-argon or uranium-lead dating are used.
The calculation assumes constant atmospheric ¹⁴C levels, but ¹⁴C production has varied over time due to changes in cosmic ray flux, solar activity, and Earth's magnetic field. Calibration curves (like IntCal20) based on tree rings, corals, and lake sediments convert raw radiocarbon ages to calendar ages. The difference can be several centuries.
Any material containing carbon that was once part of the biosphere: wood, charcoal, bone, shell, seeds, peat, soil organic matter, textiles, paper, and some carbonates. The material must not have been contaminated with carbon of a different age. Rocks, metals, and purely inorganic materials cannot be carbon dated.
BP stands for 'Before Present,' where 'present' is conventionally defined as the year 1950 CE. This convention was established because atmospheric nuclear weapons testing after 1950 dramatically altered ¹⁴C levels (the 'bomb spike'), making post-1950 as a reference unreliable. So 5730 years BP means 5730 years before 1950.
Traditional methods count beta particles from ¹⁴C decay, requiring large samples (grams) and long counting times. Accelerator Mass Spectrometry (AMS) directly counts ¹⁴C atoms by accelerating them through a particle accelerator, needing only milligrams of material and achieving much higher precision. AMS has largely replaced traditional counting.
Yes. Atmospheric nuclear testing in the 1950s-60s nearly doubled atmospheric ¹⁴C levels (the 'bomb peak'). This means post-1950 organic material has elevated ¹⁴C, making it easily distinguishable from pre-1950 material. The bomb peak is actually useful for dating recent materials (forensics, wine authentication) but complicates the standard dating framework.
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