5,730
years BP
-3,780
0.5
1
0.00012097
1/year
5,730
years BP
-3,780
0.5
1
0.00012097
1/year
The Carbon-14 Dating Calculator estimates the age of organic materials using the radiocarbon method, one of the most important dating techniques in archaeology, geology, and environmental science. Developed by Willard Libby in 1949 (earning him the 1960 Nobel Prize in Chemistry), radiocarbon dating exploits the predictable decay of carbon-14 to determine when an organism died and stopped exchanging carbon with the atmosphere.
Carbon-14 is continuously produced in the upper atmosphere by cosmic ray neutron bombardment of nitrogen-14. Living organisms maintain a constant C-14/C-12 ratio through metabolic exchange. Upon death, C-14 decays with a half-life of 5,730 years without replenishment, and the remaining fraction reveals the elapsed time since death.
The age is calculated from the ratio of remaining C-14 to the original (atmospheric equilibrium) level:
$$t = -\frac{t_{1/2}}{\ln(2)} \cdot \ln\left(\frac{A}{A_0}\right) = -\frac{5730}{0.6931} \cdot \ln\left(\frac{A}{A_0}\right)$$
Equivalently, using the percent remaining:
$$t = -8267 \cdot \ln\left(\frac{\%\text{remaining}}{100}\right)$$
where 8,267 years is the mean life of C-14. The method assumes:
1. The atmospheric C-14/C-12 ratio has been constant (corrected via calibration curves for known variations)
2. The sample has been a closed system since death (no contamination)
3. The half-life is 5,730 ± 40 years (Cambridge half-life)
The practical dating range extends from about 300 to 50,000 years, limited by measurement precision at both extremes.
The Age represents the conventional radiocarbon age — the time elapsed since the organism died and stopped absorbing C-14. Age BP (Before Present) uses 1950 as the reference year, the standard convention in radiocarbon dating. Half-Lives Elapsed provides intuitive context: values near 1 indicate ~5,730 years, near 2 indicate ~11,460 years, etc. Note that this gives uncalibrated ages; for calendar-year accuracy, calibration curves (IntCal20) should be applied to account for historical atmospheric C-14 variations.
Inputs
Results
25% remaining corresponds to exactly 2 half-lives = 11,460 years, dating this sample to the end of the last Ice Age.
Inputs
Results
A sample retaining 53% of its C-14 dates to approximately 5,250 years ago, consistent with the Old Kingdom period of ancient Egypt.
Living organisms absorb C-14 from the atmosphere through photosynthesis (plants) or diet (animals), maintaining equilibrium with atmospheric levels. When the organism dies, C-14 intake stops and existing C-14 decays with a half-life of 5,730 years. By measuring the remaining C-14 fraction, we calculate how long ago the organism died.
The practical limit is approximately 50,000 years (about 8-9 half-lives), when less than 0.2% of the original C-14 remains. Beyond this, the signal becomes indistinguishable from background radiation. Accelerator Mass Spectrometry (AMS) has extended the range to about 50,000-60,000 years by directly counting C-14 atoms.
In radiocarbon dating, 'Present' is defined as the year 1950 CE. This convention was established because atmospheric nuclear testing after 1950 dramatically increased C-14 levels (the "bomb pulse"), making post-1950 atmospheric C-14 unreliable as a baseline. All radiocarbon ages BP reference this fixed point.
The atmospheric C-14/C-12 ratio has not been constant over time due to variations in cosmic ray intensity, solar activity, ocean circulation, and volcanic CO₂ emissions. Calibration curves (like IntCal20) convert raw radiocarbon ages to calendar years using independently dated reference materials such as tree rings and coral.
No. Carbon dating only works on materials that were once part of living organisms and are younger than ~50,000 years. Rocks and dinosaur fossils (millions of years old) contain no measurable C-14. Other radiometric methods (K-Ar, U-Pb, Rb-Sr) are used for geological timescales.
The Suess effect refers to the dilution of atmospheric C-14 by fossil fuel burning since the Industrial Revolution. Fossil fuels contain no C-14 (they are millions of years old), so burning them adds "dead" carbon to the atmosphere, decreasing the C-14/C-12 ratio. This must be accounted for in modern samples.
Atmospheric nuclear testing in the 1950s-1960s nearly doubled the atmospheric C-14 level. Since the 1963 test ban treaty, this excess has been declining as C-14 exchanges with oceans and biosphere. The bomb pulse is actually useful for dating recent biological materials (post-1950) and studying carbon cycling.
Modern AMS (Accelerator Mass Spectrometry) requires only 1-10 milligrams of carbon, equivalent to about 20-100 mg of organic material. Older decay-counting methods required several grams. AMS measures C-14/C-12 ratios directly by counting atoms rather than waiting for decays.
Any material containing organic carbon from a once-living source: wood, charcoal, bone, shell, seeds, peat, textiles, paper, parchment, leather, hair, coral, and some soils. The material must not have been contaminated with carbon from a different age (e.g., modern rootlets in ancient soil).
Measurement precision is typically ±20-100 years for samples younger than 10,000 years, increasing to ±several hundred years for older samples. The main sources of uncertainty are statistical counting error, calibration curve interpolation, and potential sample contamination. Proper pretreatment and multiple measurements improve accuracy.
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