Calculate age and uncertainty from C-14 residual fraction in real time. Compare decay curves, error propagation, and other radiometric dating methods on interactive charts.
Measurement Parameters
Uncalibrated Radiocarbon Age
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± - yr
Results
Uncalibrated calendar estimate, BP 1950 base
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Fraction Decayed
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Number of Half-lives Elapsed
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Activity Ratio (A/A0)
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Decay Curve
Error Propagation
Dating Method Comparison
Decay
The curve shows C-14 remaining fraction. The red point marks the current sample.
Error
Age uncertainty grows as the remaining fraction gets small because delta t is proportional to delta f / f.
Methods
Different radiometric methods cover different age ranges. The marker shows the current sample age.
Key equations
N(t) = N0 exp(-lambda t) = N0 (1/2)^(t/T1/2)
t = -T1/2 / ln(2) * ln(N/N0)
delta t = T1/2 / ln(2) * delta f / f, where f = N/N0
Conversation About Radiocarbon Dating
Q
Where does carbon-14 come from, and why can it date once-living material?
A
Cosmic rays create carbon-14 in the upper atmosphere. Living organisms exchange carbon with the environment, but after death the exchange stops and C-14 decays with a 5,730-year half-life.
Q
Why is calibration needed if the decay equation is known?
A
The decay equation gives a radiocarbon age, not a fully calibrated calendar date. Atmospheric C-14 production varies with solar activity, geomagnetic field strength, and human nuclear testing, so calendar conversion uses measured calibration curves.
Q
Is this useful outside archaeology?
A
Yes. The same decay and uncertainty logic appears in radioactive tracers, bio-based carbon certification, waste safety assessment, and nuclear-material monitoring.
What This Simulator Calculates
This simulator converts a measured C-14 remaining fraction into an uncalibrated radiocarbon age. It also estimates age uncertainty from a percentage-point measurement error and visualizes the result on decay, uncertainty, and method-range charts.
Physical Model and Units
The input fraction is expressed in percent. A value of 50% means one half-life has elapsed. The measurement error slider is an absolute percentage-point error, so 50.0% with a 1.0%pt error means f = 0.500 +/- 0.010.
Engineering and Research Use
Use this page for quick checks of decay age, uncertainty scaling, and method selection. For publication-grade dating, combine the radiocarbon age with lab background correction, contamination control, reservoir correction, and calibration curves such as IntCal.
Common Pitfalls
A simple C-14 decay calculation is not the same as a calibrated calendar date. Very old samples, very small remaining fractions, and post-1950 samples require special handling.
Frequently Asked Questions
Why is the C-14 dating limit about 57,000 years?
57,000 years is about ten C-14 half-lives. After ten half-lives only about 0.1% remains, so contamination and detector background become comparable to the signal. In practice, about 50,000 years is often treated as the useful upper limit.
What is the difference between the Libby half-life and the true half-life?
Libby's original value was 5,568 years. The modern physical half-life is about 5,730 years. Archaeological reports may still use the Libby half-life for conventional radiocarbon ages, so the convention must be stated.
Why does this simulator show an uncalibrated calendar estimate?
Radiocarbon age is conventionally reported in years BP, where present is defined as 1950. Calendar calibration requires external curves such as IntCal. This simulator shows the uncalibrated BP estimate so the decay physics remains transparent.
How is the bomb peak from nuclear testing handled?
Atmospheric nuclear testing in the 1950s and 1960s sharply increased atmospheric C-14. Post-1950 samples need specialized bomb-curve calibration and should not be interpreted with a simple constant-atmosphere decay model.
What radiometric dating methods are used besides radiocarbon?
Different ranges require different methods: potassium-argon for volcanic rocks, uranium-lead for zircon and deep time, thorium-series for carbonates, fission-track dating, and luminescence dating for sediments.
Enter the measured C-14 fraction remaining as a decimal (0.0–1.0) in the field, or drag the slider to set residual activity percentage
Input measurement uncertainty as a percentage in the field, or adjust the slider for standard deviation range (typically 0.5–5% for AMS labs)
Click Calculate to compute radiometric age in years before present (BP) using the Libby half-life (5,730 years), display calibrated age range, and visualize decay curve with confidence intervals
Worked Example
A charcoal sample from an archaeological site shows C-14 remaining fraction of 0.42 with 2% measurement uncertainty. The simulator calculates age = 7,110 BP using λ = ln(2)/5730 = 1.209×10⁻⁴ year⁻¹. With 2σ error propagation, the 95% confidence interval spans ±240 years. Traditional decay curve shows exponential decline; overlay indicates systematic uncertainty from ion beam counting statistics and blank subtraction protocols typical of AMS facilities.
Practical Notes
Modern samples (>95% C-14 remaining) require accelerator mass spectrometry; conventional counting fails due to background noise exceeding signal in wood or bone
Samples below 0.1% residual activity approach detection limits (~50 kya); measurement error dominates and age becomes unreliable
Marine reservoir effect adds 400–800 years systematic offset for oceanographic samples; terrestrial and atmospheric corrections differ by region and calibration dataset (IntCal20 vs. SHCal20)
Cross-check results against stratigraphic context; anomalous ages often indicate contamination (rootlet intrusion, carbonaceous groundwater) rather than simulator error