What it does
Radioactive parents decay into daughters at a fixed rate, so a mineral is a clock: the more daughter it holds compared with the parent left, the older it is. For a parent with decay constant λ:
t = ln(1 + D*/P) / λ
D* is the radiogenic daughter, made by decay since the mineral formed, and P the parent left today. The tool has three parts.
- Age from a ratio: any decay system from a D*/P ratio, a K-Ar age from potassium content and radiogenic argon, or a ⁴⁰Ar/³⁹Ar age from a J factor set by a standard.
- Isochron: when samples started with some daughter already, plot daughter against parent, both divided by a stable isotope of the daughter. Samples of the same age fall on a line. Its slope gives the age and its intercept the starting ratio. The tool fits the line with York regression, which allows for errors in both x and y and their correlation, and reports the MSWD.
- U-Pb: the three ages from ²⁰⁶Pb/²³⁸U, ²⁰⁷Pb/²³⁵U and the ²⁰⁷Pb/²⁰⁶Pb ratio, and how concordant they are, plotted on a concordia diagram.
How to use it
- In Age from a ratio, pick the method. For a decay system, the decay constant fills in; change it if your lab uses another value. Enter the radiogenic daughter/parent atom ratio and its error.
- For K-Ar, enter potassium in weight percent and radiogenic ⁴⁰Ar in moles per gram.
- For ⁴⁰Ar/³⁹Ar, enter the standard’s age and measured ratio (which set J), the error on J, and the sample’s ratio.
- For an isochron, paste or open rows of x, σx, y, σy and, if you have it, the error correlation r. Say whether errors are absolute 1σ, percent 1σ, or absolute 2σ.
- For U-Pb, enter the radiogenic ratios after common-lead correction.
Reading the isochron
MSWD (mean square of weighted deviates) compares the scatter of points about the line with what their errors predict. Near 1 means the errors explain the scatter. Well below 1 suggests the errors are too generous. Well above 1, with a low probability of fit, means real geological scatter: the result is an “errorchron”, and the tool scales the age error by √MSWD.
Worked examples
All numbers here are made up for illustration.
- A Rb-Sr D/P ratio of 0.050 ± 0.0005* gives 3436 ± 34 Ma.
- K-Ar: 2.5 wt % K and 4.0 × 10⁻¹⁰ mol/g of radiogenic ⁴⁰Ar give ⁴⁰Ar*/⁴⁰K = 0.00536 and an age of 89.98 Ma.
- ⁴⁰Ar/³⁹Ar: a 28.2 Ma standard with a ratio of 12.0 gives J = 0.0013128. A sample ratio of 30.00 ± 0.05, with J known to 0.2 %, gives 69.69 ± 0.18 Ma.
- Isochron: the seven example whole-rock points give a Rb-Sr age of 1250.4 ± 3.1 Ma with initial ⁸⁷Sr/⁸⁶Sr = 0.703474 ± 0.000050 and MSWD 0.51.
- U-Pb: ²⁰⁶Pb/²³⁸U = 0.300 and ²⁰⁷Pb/²³⁵U = 4.80 give 1691 Ma and 1785 Ma. Their ²⁰⁷Pb/²⁰⁶Pb age is 1896 ± 14 Ma, so the grain is about 11 % discordant, a sign it lost lead.
Good to know
- Ages are only as good as their assumptions: a closed system since formation, a known or shared starting ratio, and no later disturbance.
- Decay constants differ slightly between conventions; for ⁸⁷Rb the newer value is about 1.6 % lower. State which you used.
- For radiocarbon dates, use the radiocarbon calibration tool, which corrects for changes in atmospheric ¹⁴C.
FAQ
Why is the ²⁰⁷Pb/²⁰⁶Pb age often the best for old zircons? Lead loss lowers both U-Pb ratios together, which barely changes their ratio. So the ²⁰⁷Pb/²⁰⁶Pb age resists lead loss.
Do I need the error correlation r? For Rb-Sr and Sm-Nd it is usually small, and leaving it at 0 is common. For U-Pb isochrons it can matter.
Where the numbers come from
- Age equation, isochron method and Wetherill concordia: standard geochronology, written from the equations.
- York regression with correlated errors: York and others (2004), American Journal of Physics; written from the published algorithm, no data copied.
- Decay constants: conventional values (²³⁸U and ²³⁵U, Jaffey and others 1971; ⁴⁰K and ⁸⁷Rb, Steiger and Jäger 1977, IUGS; ¹⁴⁷Sm, ¹⁷⁶Lu, ¹⁸⁷Re and ²³²Th as commonly used) and ²³⁸U/²³⁵U = 137.818. Physical constants, shown with their origin on the page.
- Example isochron and ratio data are made up by fibub; they are not measurements of any real rock.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.