This tool models the exponential decay law N(t) = N₀·e−λt that underlies every radiometric clock, letting you switch between four real isotope pairs — carbon-14, potassium-argon, uranium-lead and rubidium-strontium — each using its published half-life. Moving the measured ratio slider shifts a marker along the decay curve and, for uranium-lead, onto a live Wetherill concordia diagram used to spot lead loss in zircon crystals.
The plot overlays all four decay curves on a shared half-life axis, with your selected isotope highlighted. A yellow marker and crosshairs mark your measured N/N₀ ratio, with a shaded band for the chosen measurement uncertainty.
Choose ¹⁴C, K-Ar, U-Pb or Rb-Sr with the radio buttons. Drag Measured N/N₀ ratio (0.001–0.999), edit Initial ratio N₀ (default 1.000), and set Measurement uncertainty (0.1–10%). Click Calculate Age to refresh the readouts and, for U-Pb, the concordia plot.
Uranium-238's half-life of 4.47 billion years is almost exactly the age of the Earth, which is why U-Pb dating of ancient zircon and meteorites pins Earth's age at 4.54 billion years.
Each isotope decays at a fixed rate: ¹⁴C's 5,730 years suits organic material to about 50,000 years, K-Ar's 1.25 billion years suits volcanic rock, U-Pb's 4.47 billion years suits the oldest rocks, and Rb-Sr's 48.8 billion years suits ancient crust. A method works well within roughly one to ten half-lives of the true age.
The simulator rearranges the decay law to t = −ln(N/N₀)/λ, with λ = ln2/t½ from the selected half-life. Moving the ratio slider changes N directly, and the readout recomputes age instantly.
It re-runs the age formula at the ratio nudged up and down by your Measurement uncertainty percentage, then shades the region between the two resulting ages, reported as the ± uncertainty in the stats panel.
Uranium has two decay chains to lead (²³⁸U→²⁰⁶Pb and ²³⁵U→²⁰⁷Pb), giving two age estimates at once. Plotting ²⁰⁷Pb/²³⁵U against ²⁰⁶Pb/²³⁸U on the Wetherill curve keeps concordant samples on the curve while lead loss pushes discordant samples off it.
N₀ is how much isotope was present when the clock started; the formula divides the measured ratio by N₀ before the logarithm, so a different starting amount directly changes the derived age, as it would for a real sample with inherited daughter isotope.
Isotope dating (radiometric dating) is a family of methods for determining the age of rocks, fossils, and archaeological materials by measuring the radioactive decay of unstable isotopes into stable daughter products. Each radioactive isotope decays at a fixed rate characterised by its half-life — the time for half of the parent atoms to decay. By measuring the ratio of parent to daughter atoms in a sample, the elapsed time since the system closed (no further exchange with the environment) can be calculated.
Different isotope systems are suited to different time ranges and materials: carbon-14 (half-life 5,730 years) dates organic material up to ~50,000 years; potassium-40/argon-40 (half-life 1.25 billion years) dates volcanic rocks from thousands to billions of years; uranium-238/lead-206 (half-life 4.47 billion years) and uranium-235/lead-207 date the oldest rocks and meteorites; rubidium-87/strontium-87 dates ancient continental crust. Concordia diagrams plot U-Pb data to identify and correct for lead loss.
Radiometric dating has determined the age of the Earth at 4.54 billion years (from meteorite dating) and provided the absolute timescale for the geological record, converting relative stratigraphic sequences into dated events. The methods are self-consistent across different isotope systems and cross-validated against astronomical dating, dendrochronology, and ice cores. Rigorous contamination control and blank corrections are essential for accurate measurements, particularly for carbon-14 dating of small or old samples.
Cosmic ray interactions in the upper atmosphere continuously produce carbon-14, which enters the carbon cycle and is incorporated into all living organisms at a roughly constant ratio to stable carbon-12. When an organism dies, it stops exchanging carbon; its C-14 decays with a half-life of 5,730 years. Measuring the remaining C-14 fraction by accelerator mass spectrometry gives the time since death, calibrated against the tree-ring record (IntCal curve) to correct for past atmospheric C-14 variations.
The half-life is the time required for exactly half of the radioactive parent atoms in a sample to decay into daughter products. It is a fixed property of each isotope, independent of temperature, pressure, or chemical environment. After n half-lives, the fraction of parent remaining is (1/2)^n, enabling exponential decay equations to convert measured ratios into ages.
Concordia dating plots U-Pb dates from the two uranium decay chains (²³⁸U→²⁰⁶Pb and ²³⁵U→²⁰⁷Pb) simultaneously. If a sample has remained closed since crystallisation, both systems give the same age — a point on the concordia curve. Samples that lost lead (discordant) plot off the curve; a line through discordant points intersects the concordia at the crystallisation age and the lead-loss event age.
Sedimentary rocks are generally difficult to date directly because they consist of eroded detritus from older rocks. Instead, geologists date associated volcanic ash layers (tephra) interbedded with sediments, or date authigenic minerals (glauconite, phosphate) that formed at the time of deposition. Fossils in sedimentary sequences are constrained by the dates of surrounding dated volcanic layers.
Precision depends on the isotope system, sample quality, and analytical method. Modern U-Pb zircon dating by high-precision TIMS (thermal ionisation mass spectrometry) achieves precisions of ±0.1% or better — dating billion-year-old rocks to within a million years. Carbon-14 dates carry uncertainties of ±20–200 years for well-preserved samples, depending on sample size and calibration curve resolution.