Radiocarbon Dating Calculator

Nuclear Physics, Isotopic Decay & Radiocarbon Chronometry Metrology

Radiocarbon dating measures the exponential beta decay of unstable Carbon-14 into Nitrogen-14:

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• Radioactive Decay & Radiocarbon Age Formulas**:

N(t) = N_0 · e^-λ t = N_0 · ( (1) / (2) )^t / t_1/2

λ = ( 2) / (t_1/2) = (0.693147) / (5,730 years) = 1.20968 × 10^-4 yr^-1

Radiocarbon Age (Years BP) = -((N(t) / N_0)) / (λ) = -() / (1.20968 × 10^-4)

Half-Lives Elapsed (n) = Aget_1/2

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• Calendar Conversion**:

Calendar Year = 1950 - Age (BP)

If Calendar Year < 0 |Calendar Year| + 1 BCE

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• Standard Chronological Benchmarks (5,730 Yr Half-Life)**:

• Dead Sea Scrolls (77.5% C-14): 2,107 Years BP (158 BCE | Iron Age)

• Exact 1 Half-Life (50.0% C-14): 5,730 Years BP (3781 BCE | Bronze Age)

• Bronze Age Artifact (35.0% C-14): 8,679 Years BP (6730 BCE | Neolithic)

• Pleistocene Mammoth (12.5% C-14): 17,190 Years BP (15241 BCE | Ice Age)

How to Use This Calculator

Enter your Remaining Carbon-14 (% of Modern Sample) (e.g. 35.0 in % C-14), Carbon-14 Half-Life Standard — choose from Cambridge True Physical Half-Life (5,730 ± 40 Years), Libby Standard (5,568 Years - Conventional Radiocarbon BP Reporting), and Archaeological Artifact Benchmark — choose from Custom Sample Activity, Bronze Age Artifact (35.0% C-14 remaining) → 8,679 Years BP (6730 BCE), Dead Sea Scrolls (~77.5% C-14 remaining) → 2,107 Years BP (158 BCE). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Age formula: t = -ln(N/N0) / lambda

Historical Calendar Date (1950 AD = 0 BP reference)

Worked Example

An archaeologist testing a wooden spear tip finds it contains 35.0% of modern C-14 activity, calculating its raw radiocarbon age as 8,679 years BP (6730 BCE), confirming it dates directly to the early Neolithic transition.

Understanding Your Result

Scientific calculations require careful attention to significant figures and units. Your result is only as precise as your least precise input — expressing the result with more significant figures than the inputs implies false precision. For laboratory or regulatory work, verify which measurement standard applies (SI, ASTM, ISO) and whether temperature, pressure, or concentration conditions affect the formula. Cross-reference results against published reference values for your specific material or compound.