How is the age actually calculated from the ratio slider?

The simulator rearranges the decay law to t equals minus the natural log of N over N-zero, divided by lambda, where lambda equals ln2 divided by the half-life of the selected method. Moving the Measured N over N-zero ratio slider changes N directly, and the readout recomputes the age instantly using this formula.

What is the concordia diagram and why does it only appear for U-Pb?

Uranium has two decay chains to lead (uranium-238 to lead-206 and uranium-235 to lead-207), so a zircon crystal gives two independent age estimates at once. Plotting lead-207/uranium-235 against lead-206/uranium-238 on the Wetherill curve lets concordant, undisturbed samples fall on the curve while lead-loss events push discordant samples off it.

Why does changing Initial ratio N0 shift the calculated age?

N0 represents how much of the isotope was present when the sample's clock started; the age formula divides the measured ratio by N0 before taking the logarithm, so assuming a different starting amount directly changes the derived age, exactly as it would for a real sample with inherited daughter isotope.

Home▸Palaeontology & Evolutionary Geology▸Isotope Dating

☢️ Isotope Dating

Explore radiometric dating methods: radiocarbon 14C, K-Ar, U-Pb, Rb-Sr. Visualize decay curves, calculate ages from isotope ratios, and explore concordia diagrams for U-Pb geochronology.

Palaeontology & Evolutionary Geology3DModerate60 FPS

About this simulation

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.

🔬 What it shows

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.

🎮 How to use

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.

💡 Did you know?

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.

Frequently asked questions

Why do the four methods have such different half-lives?

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.

How is the age calculated from the ratio slider?

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.

What does the uncertainty band on the decay plot represent?

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.

What is the concordia diagram, and why only for U-Pb?

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.

Why does changing Initial ratio N₀ shift the calculated age?

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.

Frequently Asked Questions

How does carbon-14 dating work?

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.

What is the half-life of an isotope?

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.

What is concordia dating and why is it used?

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.

Can radiometric dating be used on sedimentary rocks?

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.

How accurate is isotope dating?

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.

⚙ Under the hood

Explore radiometric dating methods — carbon-14, uranium-lead and potassium-argon — and how they reveal deep time.

isotope-datingradiocarbonpaleontologygeochronology

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install