Radiometric Dating Calculator: Age from Daughter/Parent Ratio, U-Pb, K-Ar, Rb-Sr and More
Age of a rock, mineral or sample from the daughter/parent ratio or the fraction of parent left, for U-238, U-235, Th-232, K-40, Rb-87, Sm-147, Lu-176, Re-187, C-14 or a custom half-life. Also works backwards from a known age, with uncertainty, a decay table and chart.
How it works
λ = ln 2 ÷ t½; from a ratio: t = (1 ÷ λ) × ln(1 + D*/P), with D* = measured daughter − initial daughter; K–Ar: t = (1 ÷ λ) × ln(1 + (λ ÷ λe) × Ar*/K); from the fraction left f: t = ln(1 ÷ f) ÷ λ; uncertainty: Δt = Δ(D/P) ÷ [λ × (1 + D/P)]
A radioactive parent isotope decays at a fixed rate, so the daughter atoms that build up beside the surviving parent atoms act as a clock. The clock starts when a mineral crystallises (or an organism dies, for carbon-14) and locks the atoms in. If D* is the number of daughter atoms made by decay and P the parent atoms left today, then D*/P = e^(λt) − 1, which gives the age t = ln(1 + D*/P) ÷ λ. Pick the isotope system and enter the measured daughter/parent atom ratio, or the percentage of parent still present. You can also go the other way and get the ratio a sample of a known age should show. Potassium-40 is a special case. Only about 10.5% of its decays give argon-40; the rest give calcium-40, which cannot be told apart from ordinary calcium. So the Ar/K ratio is scaled by λ/λe before taking the logarithm. Carbon-14 is dated from the fraction left, because its daughter (nitrogen-14) is everywhere. The decay constants are the values geochronologists use: the IUPAC-IUGS recommendations for U-238, Rb-87 and Sm-147, Jaffey et al. for U-235, and Steiger & Jäger for K-40. Real ages also need a correction for daughter atoms present at the start. Zircon U–Pb dating avoids this because zircon rejects lead when it forms; other systems use isochrons. The result also assumes a closed system, and a sample that lost argon or lead will read too young. Each method works best between about 1% and 10 half-lives.
Worked example
A zircon with Pb-206/U-238 = 0.2 and no initial lead. λ = 0.693147 ÷ 4.4683 × 10⁹ yr = 1.55125 × 10⁻¹⁰ per year. t = ln(1 + 0.2) ÷ λ = 0.18232 ÷ 1.55125 × 10⁻¹⁰ = 1.175 billion years. That is 0.263 half-lives, and 1 ÷ 1.2 = 83.33% of the original uranium-238 remains. If you add a ±0.002 uncertainty on the ratio under More options, the calculator shows ± 0.0107 billion years (about ±11 million years).
Sources: IUPAC-IUGS recommendation on the half-lives of Rb-87, Sm-147 and U-238 (Villa et al.) · Radiometric dating: age equation and isotope systems (Wikipedia) · Potassium-40 decay branches (Wikipedia) · Calculation of radiocarbon dates (Wikipedia)
Frequently asked questions
How do you calculate the age of a rock from a parent-daughter ratio?
Divide the radiogenic daughter atoms by the parent atoms left (D/P), add 1, take the natural logarithm, and divide by the decay constant λ = ln 2 ÷ half-life. For example, Pb-206/U-238 = 0.2 gives ln(1.2) ÷ 1.551 × 10⁻¹⁰ = 1.18 billion years.
How do we know there was no daughter at the start?
Some minerals exclude the daughter when they crystallise; zircon takes in uranium but almost no lead. Otherwise the isochron method uses several minerals from the same rock, plotted against a stable isotope of the daughter, to work out the starting amount. You can enter a known initial daughter amount under More options.
Why does K–Ar dating use 10.48% instead of the full decay?
Potassium-40 decays two ways. About 89.5% of decays become calcium-40 and about 10.5% become argon-40. Only the argon is measured, so the age equation scales the Ar/K ratio by λ/λe (5.543 ÷ 0.581 ≈ 9.54) to count every decay.
Why can carbon-14 not date dinosaur bones?
Its half-life is only 5,730 years. After about 50,000 years (roughly 9 half-lives) less than 0.2% of the original carbon-14 is left, too little to measure. Dinosaur ages come from uranium–lead or argon–argon dating of the volcanic ash layers above and below the fossils.
Which half-life of carbon-14 should I use?
The physical half-life is 5,730 ± 40 years. By convention, labs report a “conventional radiocarbon age” using the older Libby value of 5,568 years and then calibrate it with the IntCal20 curve. The calculator shows both.
How accurate is radiometric dating?
Modern U–Pb dates on zircon can reach about 0.1% precision, around ±1 million years on a billion-year-old rock. Accuracy depends on a closed system, the right initial-daughter correction and the decay constant. Measurements are checked by dating the same rock with two systems, such as U-238 and U-235.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.