Uranium-lead radiometric age calculator
A 206Pb/238U ratio of 0.1 gives an age of roughly 614 million years with the Steiger and Jäger 1977 decay constant. Enter the ratio measured on zircon, monazite or baddeleyite and read the closed-system age in years, Ma and Ga. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Pb206 u238
- 0.1
- Decay constant
- 0.0000000002
- Age (years)
- 614,408,894.79
- Age ma
- 614.40889479
- Age ga
- 0.6144088948
Uranium–lead dating is one of the most widely used radiometric clocks in geology because 238U decays to 206Pb with a well-measured half-life of about 4.47 billion years, long enough to date most crustal rocks and many meteorites. Given a radiogenic lead-206 to uranium-238 atomic ratio measured on a mineral such as zircon, monazite, or baddeleyite, the single-stage age follows a closed-form logarithm: t equals one over lambda times the natural log of one plus the daughter-to-parent ratio. This uranium-lead radiometric age calculator applies that identity with the conventional Steiger and Jäger 1977 decay constant for 238U, or with a lambda you supply when a paper uses a different convention. A negative 206Pb over 238U ratio is rejected as invalid input so pipelines never invent ages from impossible isotope data.
How the 206Pb/238U age is derived and what assumptions it carries
Start from the parent–daughter relationship for a closed system that begins with no radiogenic lead: the number of 206Pb atoms produced equals the number of 238U atoms that have decayed, so D equals P times the quantity e to the lambda t minus one. Rearrangement yields the classic age equation t equals one over lambda times the natural logarithm of one plus D over P.
Here D over P is the radiogenic 206Pb star to 238U atomic ratio after any common-lead correction you already applied offline; this capability does not estimate initial lead, does not run a discordia or Tera-Wasserburg regression, and does not couple the 235U–207Pb clock. It is the single-pair closed-form clock that textbooks, lab worksheets, and many first-pass scripts use when a mineral is assumed concordant or when only the uranium-238 chain is being taught.
Time is returned in years and also converted to mega-annum and giga-annum for map legends and abstract prose. Zero ratio yields zero age; large ratios approach multi-billion-year ages as the logarithm grows slowly. Negative ratios have no physical meaning for radiogenic daughter over parent and always fail validation before any logarithm is evaluated.
Where a uranium–lead age helps in real work
Undergraduate and graduate geochronology courses assign 206Pb over 238U age drills that convert measured isotope ratios into mega-annum answers; a single trusted oracle speeds homework keys and live demos without spreadsheet formula drift. Regional mapping teams and consulting geologists publish first-pass crystallization ages on map sheets when only a concordant 206Pb over 238U ratio is available from a contract lab. Planetary and meteorite short courses compare simple U–Pb ages against more complete multi-isotope reductions to teach why concordance matters.
Curriculum authors ranking for uranium lead radiometric age calculator want English landing copy and a live tool that matches the paid automation contract byte for byte.
What you can do with it
Classroom and exam answer keys
Convert a homework 206Pb/238U ratio into age in years, Ma, and Ga with the standard λ_238 so students and auto-graders share one closed-form ground truth.
Lab QC after common-lead correction
Sanity-check a corrected radiogenic 206Pb*/238U ratio from zircon or monazite before full multi-system or discordia modelling.
Map and notebook first-pass ages
Pin a deterministic U–Pb age string in mapping notebooks and LIMS exports when only the 238U–206Pb pair is being reported.
FAQ
What happens if the 206Pb/238U ratio is negative?
A negative daughter-to-parent ratio is non-physical for this clock and is never turned into an age.
Can I supply my own decay constant?
Omit it to use Steiger & Jäger 1977.
Does this correct for common lead or 207Pb/235U discordance?
No. You must supply an already-corrected 206Pb*/238U ratio if your method needs common-lead correction. Discordia, Tera–Wasserburg, and dual-clock concordance checks are out of scope.
What does the uranium–lead radiometric age calculator cost?
The browser tool is free and runs locally.
Can I enter a mass ratio instead of an atomic ratio?
No. The calculator expects the atomic ratio of radiogenic lead-206 to uranium-238 and does not convert mass ratios. Convert your data first, and apply any common-lead correction your method needs before entering it.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/earth/radiometric-age-u-pb \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pb206_u238":0.1}'const res = await fetch("https://api.kit.forhosting.com/earth/radiometric-age-u-pb", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pb206_u238": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/earth/radiometric-age-u-pb",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pb206_u238": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/earth/radiometric-age-u-pb", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pb206_u238":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pb206_u238":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/earth/radiometric-age-u-pb", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"pb206_u238": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "earth.radiometric_age_u_pb",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How the 206Pb/238U age is derived and what assumptions it carries
The default decay constant is 1.55125 times ten to the minus ten per year, the Steiger and Jäger 1977 value still printed beside countless zircon ages; if your protocol cites a later IUGS or laboratory-preferred lambda, pass it as decay_constant so the age stays consistent with your paper.
Input contract, response fields, defaults, and error behaviour
Example: a ratio of 0.1 with the default lambda yields roughly 614 million years. Example: a ratio of 1.0 yields roughly 4.47 billion years, near the 238U half-life scale. The calculator does not convert mass ratios to atomic ratios, does not apply U–Th–Pb discordance filters, and does not report uncertainty ellipses; those are separate workflows with different search intents. POST a JSON body with pb206_u238 as a required finite number: the 206Pb over 238U atomic ratio after you have corrected for common lead if your method requires it. Aliases ratio, pb_u, d_p, and daughter_parent are accepted so ad-hoc scripts can keep short field names. Optionally send decay_constant as a finite positive number in inverse years; aliases lambda, lambda_238, and lambda_u238 map to the same field. On success the body echoes cleaned pb206_u238 and decay_constant, reports age_years as the primary closed-form result, and also reports age_ma and age_ga as age_years divided by one million and one billion respectively. Fields method and formula document the algorithm as u_pb_206_238_closed_form and t equals one over lambda times ln of one plus 206Pb over 238U. Missing fields, non-finite values, non-positive custom lambda, and any negative daughter-to-parent ratio fail with invalid_input and are not billed.
Where a uranium–lead age API earns its keep in real work
Keep common-lead correction and error propagation in your own pipeline, call this endpoint for the deterministic closed-form core, and you get reproducible ages for teaching, QC, and lightweight automation without standing up a full geochronology suite.
Technical questions
What formula does this uranium–lead age calculator use?
The single-stage closed form t = (1/λ_238) · ln(1 + 206Pb/238U), where pb206_u238 is the radiogenic daughter-to-parent atomic ratio and λ_238 defaults to 1.55125×10⁻¹⁰ a⁻¹ (Steiger & Jäger 1977) unless you override decay_constant.