Carbon Dating Calculator — Radiocarbon Age
Enter the percentage of original C-14 activity remaining in a sample and the accepted half-life to calculate its uncalibrated radiocarbon age in years before present (BP).
%
years
Uncalibrated radiocarbon age — calibrate with IntCal to get calendar years
- 1
Fraction remaining
50 ÷ 100 = 0.5 - 2
Decay constant λ
ln(2) ÷ 5,730 = 1.2097e-4 yr⁻¹λ = ln(2) / half-life — governs how fast C-14 disappears - 3
Estimated age
ln(1 ÷ 0.5) ÷ 1.2097e-4 = 5,730
How does this calculator work?
Age (years BP) = ln(1 / fraction_remaining) × t½ / ln(2). With the standard C-14 half-life of 5,730 years, 50% remaining → 5,730 yr BP (one half-life); 25% remaining → 11,460 yr BP (two half-lives). Raw dates are uncalibrated radiocarbon years; use IntCal for calendar-year conversion.
Formula
How this is calculated
Carbon-14 is a radioactive isotope produced continuously in the upper atmosphere and incorporated into living organisms through photosynthesis and the food chain. When an organism dies it stops exchanging carbon with its environment, and its C-14 decays exponentially with a conventional half-life of 5,730 years (the Cambridge half-life; the older Libby value of 5,568 years is still used in some laboratory protocols). Measuring the fraction of C-14 remaining relative to a modern standard lets researchers calculate how long ago the organism died.
The decay law is N(t) = N₀ × e^(−λt) where λ = ln(2)/t½. Rearranging for t gives the age formula: t = ln(N₀/N) / λ. Accelerator Mass Spectrometry (AMS) can detect C-14 fractions as low as 0.001% (roughly 50,000 years BP), though beyond about 40,000–45,000 years the remaining signal is dominated by contamination uncertainty.
The raw output is a conventional radiocarbon age in "years BP", anchored to 1950 CE by convention. Atmospheric C-14 concentrations have varied over millennia due to solar activity, geomagnetic field changes and ocean circulation, so raw radiocarbon ages must be calibrated against the IntCal calibration curve (maintained by the IntCal Working Group) to convert to calendar years. This calculator gives the uncalibrated conventional age only.
Frequently asked questions
Practical limits for standard AMS radiocarbon dating are around 45,000–50,000 years BP. Beyond this only about 0.3% of the original C-14 remains, and even trace modern-carbon contamination (as little as 0.1%) can distort the result by thousands of years.
C-14 dating only works on materials that were once alive (wood, charcoal, bone, shell, seeds). Fossils more than ~100,000 years old have had their organic carbon replaced by minerals. Geologists date rocks and older materials using long-lived isotope systems such as potassium-argon (K/Ar) or uranium-lead (U/Pb).
"BP" means Before Present, with "present" fixed at 1950 CE by international convention — chosen because that is before large-scale nuclear weapons testing began to inflate atmospheric C-14 levels. To convert to BCE/CE, subtract 1,950 from the BP age and treat positive values as BCE, negative as CE (before calibration).
TG we-Calculate Editorial Team. (2026). Carbon Dating Calculator — Radiocarbon Age [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/carbon-dating-calculator
TG we-Calculate Editorial Team. "Carbon Dating Calculator — Radiocarbon Age." TG we-Calculate. 2026. https://we-calculate.com/calculator/carbon-dating-calculator.
TG we-Calculate Editorial Team, "Carbon Dating Calculator — Radiocarbon Age," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/carbon-dating-calculator
@misc{wecalculate_carbon_dating_calculator, title = {Carbon Dating Calculator — Radiocarbon Age}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/carbon-dating-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?