Input parameters

Isotopic system

Half-life

Adopted constant for the selected system

What do you want to estimate?

Input datum

Remaining ¹⁴C activity

Activity normalized to the model's initial value (0–100%)

0.01100

Results

Ideal model age

5.73

Total decay constant (λ)

1.210e-4

yr⁻¹

Half-lives elapsed

t½

Remaining parent isotope

Ideal parent-decay curve

t½ = 5730 years

Model age

5.73 ka (Thousand years)

Geochronologic unit

Holocene

Earth history

> 99.9%

elapsed by the modeled time

Cosmic history

> 99.9%

elapsed by the modeled time

Holocene

◀ 15 ka (Thousand years)Present ▶

Pleistocene

Holocene

15 ka (Thousand years)12 ka (Thousand years)9 ka (Thousand years)6 ka (Thousand years)3 ka (Thousand years)Present

▾ 5.73 ka (Thousand years)

Nearest reference events

Selected, non-exhaustive milestones; “~” marks an approximate age. Formal units follow the ICS 2026/06 chart.

Start of the Holocene11.7 ka (Thousand years)5.97 ka (Thousand years) before the modeled time

Early evidence of Homo sapiens~300 ka (Thousand years)~294.3 ka (Thousand years) before the modeled time

K-Pg mass extinction66 Ma (Million years)65.99 Ma (Million years) before the modeled time

Earliest unequivocal dinosaurs~233.2 Ma (Million years)~233.2 Ma (Million years) before the modeled time

Permian Extinction (Great Dying)251.9 Ma (Million years)251.9 Ma (Million years) before the modeled time

Fundamentals & Explanation

What is Radiometric Dating?

Radiometric dating is a geochronological technique used to determine the numerical age of rocks, minerals, and organic materials by measuring the ratio between a parent isotope (radioactive) and its daughter isotope (decay product). Unlike relative dating (stratigraphy, biostratigraphy), which only establishes chronological order, radiometric dating assigns numerical ages in years with quantifiable uncertainties.

Scope of this simulator: it solves an ideal, closed-system exponential model. Its outputs are model ages, not reportable dates: analytical blanks, standards, uncertainties, ¹⁴C calibration, isochrons, and U-Pb concordia are not included.

Radioactive Decay Law

In the geochronological model, each radionuclide decays with a characteristic constant that remains stable under ordinary geological conditions. This behavior was described by Rutherford and Soddy (1902) as a statistical law: each nucleus has a fixed probability λ of decaying per unit time, resulting in an exponential decrease of the population.

Exponential decay law

N(t) = N_0 \cdot e^{-\lambda t}

Where N₀ is the initial number of parent atoms, N(t) is the amount remaining after time t, and λ is the decay constant (probability of disintegration per unit time).

Important Note: The decay constant λ is an intrinsic property of the atomic nucleus, governed by the weak nuclear interaction (β decay) or the Coulomb barrier (α decay). It is stable, within the precision relevant to geochronology — a fundamental condition for the validity of every radiometric clock.

Half-Life (t½) and Decay Constant

The half-life is the time required for half of the radioactive atoms in a sample to decay. It is obtained by setting N(t½) = N₀/2 in the exponential law and solving:

Decay constant

\lambda = \frac{\ln 2}{t_{1/2}}

Half-life

t_{1/2} = \frac{\ln 2}{\lambda}

After 1 half-life, 50% of the parent remains; after 2, 25%; after 3, 12.5%, and so on. Beyond ~10 half-lives, less than 0.1% remains; practical usefulness depends on background, abundance, preparation, and analytical sensitivity.

Method A — Remaining Fraction

When the percentage of the original parent isotope remaining in the sample is known (typical in Carbon-14 dating, where the current activity is compared to the atmospheric one), the age is calculated by solving for t from the exponential law:

Age from remaining fraction

t = -\frac{1}{\lambda} \ln\!\left(\frac{P_{\%}}{100}\right)

In practice, ¹⁴C is measured by Accelerator Mass Spectrometry (AMS) or radiometric counting. This calculator uses the 5,730-year physical half-life; a conventional radiocarbon age uses Libby's 5,568-year half-life, is reported in BP (present = 1950), and is then calibrated with a curve such as IntCal20 to estimate calendar age.

Method B — Radiogenic Daughter/Parent Ratio (D*/P)

In this model, D* is only the accumulated radiogenic daughter after subtracting the daughter contribution present at formation. If b is the fraction of decays producing that daughter, the relation and its inverse are:

Age from D*/P ratio

\frac{D^*}{P}=b(e^{\lambda t}-1),\quad t=\frac{1}{\lambda}\ln\!\left(1+\frac{D^*/P}{b}\right)

Here b = 1 for the ideal U-Pb and Rb-Sr models, while b = 0.1048 for the ⁴⁰K branch that produces ⁴⁰Ar, following the Steiger and Jäger convention (1977; ref. [5]). Carter et al. (2020; ref. [6]) reassess the minor EC_ground channel; their revised constants are not the ones adopted by this simulator. U-Pb and Rb-Sr can be measured with TIMS or ICP-MS; K-Ar additionally requires noble-gas mass spectrometry. Each real method has its own corrections and quality controls.

Common Isotopic Systems

¹⁴C → ¹⁴N

t½ = 5,730 yr · β⁻ decay · Archaeology, paleoclimatology (up to ~50 ka)

²³⁸U → ²⁰⁶Pb

t½ = 4,468.3 Ma · α/β decay chain · Zircons, igneous rocks, age of the Earth

⁴⁰K → ⁴⁰Ar

Total t½ = 1,248 Ma · Branch to ⁴⁰Ar: b = 0.1048 · Basalts, micas, volcanic ashes

⁸⁷Rb → ⁸⁷Sr

t½ = 49,610 Ma · β⁻ decay · Granites, pegmatites, metamorphic rocks

Model Assumptions

Closed system: neither parent nor daughter entered or left the sample since its formation (crystallization, deposition, or death of the organism).
Stable decay constant:the model adopts recommended or conventional values and assumes λ remained constant throughout the sample's history.
Initial contribution resolved: D* represents only daughter produced by radioactive decay. The simulator assumes that any daughter contribution present at formation has already been subtracted; practice may require an isochron, common-Pb correction, or another system-specific strategy.
No contamination: the sample was not altered by weathering, metamorphism, or hydrothermal fluids after its formation.

Indicative ranges

C-14: ≤ 50 ka

K-Ar: ≥ 0.1 Ma

U-Pb: ≥ 1 Ma

Rb-Sr: ≥ 10 Ma

Earth: 4,540 ± 50 Ma

They depend on sample, preparation, and instrument.

Adopted constants

λ(¹⁴C) ≈ 1.21 × 10^-4 yr⁻¹

λ(²³⁸U) ≈ 1.55 × 10^-10 yr⁻¹

λ(⁴⁰K) ≈ 5.55 × 10^-10 yr⁻¹

λ(⁸⁷Rb) ≈ 1.397 × 10^-11 yr⁻¹

b(⁴⁰K→⁴⁰Ar) = 0.1048 (convention [5])

Essential sources

[1] Faure, G., & Mensing, T. M. (2005). Isotopes: Principles and Applications (3rd ed.). John Wiley & Sons.
[2] Stuiver, M., & Polach, H. A. (1977). Reporting of ¹⁴C Data. Radiocarbon, 19(3), 355–363. doi.org/10.1017/S0033822200003672
[3] Reimer, P. J. et al. (2020). The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP). Radiocarbon, 62(4), 725–757. doi.org/10.1017/RDC.2020.41
[4] IUPAC–IUGS (2022). Recommendations and status reports on half-lives of long-lived radionuclides used in geochronology. Pure and Applied Chemistry, 94(9), 1085–1092. doi.org/10.1515/pac-2021-1202
[5] Steiger, R. H., & Jäger, E. (1977). Subcommission on geochronology: Convention on the use of decay constants in geo- and cosmochronology. Earth and Planetary Science Letters, 36(3), 359–362. doi.org/10.1016/0012-821X(77)90060-7
[6] Carter, J. et al. (2020). Production of ⁴⁰Ar by an overlooked mode of ⁴⁰K decay with implications for K-Ar geochronology. Geochronology, 2, 355–365. doi.org/10.5194/gchron-2-355-2020