Radiometric Age Calculator (Uranium–Lead, Potassium–Argon, Rubidium–Strontium)
Age of a rock or mineral from the ratio of daughter to parent atoms for the uranium–lead, potassium–argon and rubidium–strontium clocks, with the share of the parent isotope left.
Results
The dashed line marks the value you entered.
What this tool does
Each radioactive parent turns into its daughter at a fixed rate, so the daughter-to-parent ratio is a clock: t = ln(1 + D ÷ P) ÷ λ. Uranium-238 has a half-life of 4.47 billion years — close to the age of the Earth — which is why a ratio near 1 means an age near 4.5 billion years. Potassium-40 decays to argon-40 in only about 10 % of cases, which the tool allows for. The method assumes the sample started with no daughter atoms and has stayed closed since; real dating labs test those assumptions with isochrons and several clocks.
Formula
t = ln(1 + D ÷ P) ÷ λ (for K–Ar: t = ln[1 + (λ ÷ λ_e) × Ar ÷ K] ÷ λ)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sy | Decay system | — |
rr | Daughter atoms per parent atom in the sample today | — |
MA | Age of the rock | Ma |
YR | Age in years | yr |
HL | Half-life of the parent isotope | Gyr |
PL | Parent isotope still left | % |
NH | Half-lives elapsed | — |
Worked example
- Decay system1
- Daughter atoms per parent atom in the sample today0.5
- Age of the rock2613.80 Ma
- Age in years2,613,796,023 yr
- Half-life of the parent isotope4.468 Gyr
- Parent isotope still left66.67 %
- Half-lives elapsed0.585
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.