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U-Pb concordia plot: Wetherill and Tera-Wasserburg diagrams, error ellipses, concordia age, discordia intercepts

Paste U-Pb isotope ratios with errors and correlations. Get Wetherill or Tera-Wasserburg concordia diagrams with 2σ error ellipses, the concordia age with its MSWD (Ludwig 1998), upper and lower discordia intercepts by York regression, the weighted mean ²⁰⁶Pb/²³⁸U age, and each analysis's three ages and discordance.

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  1. Ratios
  2. Concordia
  3. Intercepts
  4. Ages
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Analyses

Use radiogenic (common-Pb corrected) ratios. Decay constants λ238 = 1.55125 × 10⁻¹⁰ and λ235 = 9.8485 × 10⁻¹⁰ per year (Jaffey et al. 1971). The examples are made up.

Concordia diagram

Errors are 2σ from the analytical errors; decay-constant errors are not included. When the MSWD is above 1, the error also multiplied by √MSWD is given, for scatter beyond the stated errors. Untick an analysis below to leave it out of every calculation (it stays on the plot, grey).

Analyses and their ages

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What it does

Uranium-lead dating uses two clocks in one mineral: ²³⁸U decays to ²⁰⁶Pb and ²³⁵U decays to ²⁰⁷Pb at different rates. If a crystal (usually zircon) has stayed closed, both clocks agree and its two ratios plot on the concordia curve. Lead loss or mixing pulls analyses off the curve along a straight discordia line. This page:

  • Draws the Wetherill diagram (²⁰⁷Pb/²³⁵U against ²⁰⁶Pb/²³⁸U) or the Tera-Wasserburg diagram (²³⁸U/²⁰⁶Pb against ²⁰⁷Pb/²⁰⁶Pb), with each analysis as a 2σ (or 95 %) error ellipse that includes the error correlation.
  • Converts between the two kinds of ratios with their errors and correlation, so you can paste either.
  • Calculates the concordia age of a group of analyses (Ludwig 1998): their weighted mean point and the age on concordia that fits it best, with the MSWD of concordance, of equivalence and of both, and their probabilities.
  • Fits a discordia line by York regression (errors in both ratios and their correlation) and gives its upper and lower intercepts with concordia, with errors.
  • Gives the weighted mean ²⁰⁶Pb/²³⁸U age with MSWD, and each analysis’s ²⁰⁶Pb/²³⁸U, ²⁰⁷Pb/²³⁵U and ²⁰⁷Pb/²⁰⁶Pb ages and discordance.

How to use it

  1. Choose whether your ratios are Wetherill or Tera-Wasserburg, and how errors are given (2σ or 1σ, absolute or %).
  2. Paste one analysis per line: an optional label, the first ratio, its error, the second ratio, its error, and the error correlation (rho). Or open a CSV or Excel file.
  3. Choose the main result: discordia intercepts for a lead-loss line, the concordia age for a group of concordant grains, or the weighted mean ²⁰⁶Pb/²³⁸U age for young zircons.
  4. Untick analyses to leave them out (they stay grey on the plot). Download the table as CSV, or the report.

Worked example

The discordant example has eight made-up zircon analyses that mix 1850 Ma crystals with lead loss at 300 Ma. The York fit gives an upper intercept of 1852.4 ± 6.9 Ma and a lower intercept of 307 ± 13 Ma (2σ). The line’s MSWD is 0.59 (probability of fit 0.74), so the scatter is no more than the errors explain. A concordia age of these analyses would make no sense, and the page shows why: its MSWD of concordance is in the thousands. The concordant example (seven analyses near 420 Ma) gives a concordia age of 418.0 ± 2.4 Ma with an MSWD of concordance and equivalence of 0.69 (probability 0.77): the analyses agree with each other and with concordia.

Good to know

  • Use ratios corrected for common lead. In the Tera-Wasserburg diagram, uncorrected analyses spread towards the common-lead ²⁰⁷Pb/²⁰⁶Pb on the y axis.
  • The errors here are analytical only; decay-constant errors (which matter when comparing with other methods) are not added.
  • Isotope ratios of ²³⁸U/²³⁵U: 137.818 is the modern measured value; older work used 137.88. The choice shifts ²⁰⁷Pb/²⁰⁶Pb ages by about 1 Ma.

FAQ

Why do the concordia age and the weighted mean ²⁰⁶Pb/²³⁸U age differ? The concordia age also uses the ²⁰⁷Pb/²³⁵U ratio and the error correlation, so it is usually more precise.

What if the discordia line misses concordia? Then there is no intercept on that side: the analyses do not fit a simple two-component mixing.

Is my data sent anywhere? No. Everything is worked out on this page.

Where the numbers come from

  • Decay constants λ238 = 1.55125 × 10⁻¹⁰/yr and λ235 = 9.8485 × 10⁻¹⁰/yr (Jaffey et al. 1971, Physical Review C); ²³⁸U/²³⁵U = 137.818 (Hiess et al. 2012, Science) or 137.88 (Steiger and Jäger 1977). Physical constants.
  • Concordia age and its MSWDs of concordance and equivalence after Ludwig (1998, Geochimica et Cosmochimica Acta); York et al. (2004) regression for discordia; Wetherill (1956) and Tera and Wasserburg (1972) diagrams. Written by fibub from the equations and checked against an independent NumPy/SciPy implementation.
  • The example zircon analyses are made up by fibub.

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 2026-11-09.

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