Rubidium-strontium radiometric age calculator
An Rb-Sr isochron slope of 0.02 corresponds to about 1.395 billion years, a typical Precambrian granite age, using the Steiger and Jäger 1977 decay constant. Enter the fitted slope and read the 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
- Slope
- 0.02
- Decay constant
- 0 years
- Age (years)
- 1,394,551,218.04
- Age ma
- 1,394.55121804
- Age ga
- 1.394551218
A rubidium-strontium radiometric age calculator turns the slope of an 87Sr/86Sr versus 87Rb/86Sr isochron into the time since those minerals last shared a common strontium-isotope ratio. The isochron slope equals e to the lambda t minus one, so the age is the natural logarithm of one plus the slope, divided by the decay constant of rubidium-87. Enter the fitted slope; the tool applies the conventional Steiger and Jäger 1977 lambda of 1.42 times 10 to the minus 11 per year unless you override it, and returns the age in years, mega-annum, and giga-annum.
What the Rb-Sr isochron slope means and how age is recovered
Rubidium-87 decays to strontium-87 with a half-life of about forty-nine billion years, so the radiogenic 87Sr that accumulates in a closed mineral is a clock. Co-genetic minerals that began with the same initial 87Sr/86Sr but different rubidium-to-strontium ratios now plot as a straight line on a diagram of 87Sr/86Sr against 87Rb/86Sr. That line is the isochron.
Its intercept is the initial ratio; its slope m equals e to the lambda t minus one, where lambda is the decay constant of 87Rb and t is the time since the minerals last equilibrated. Rearrangement gives the textbook age t equals the natural logarithm of one plus m, divided by lambda. A zero slope is a zero-age isochron: no measurable ingrowth yet.
A positive slope is a finite age. A negative slope cannot be produced by closed-system decay of 87Rb, so this calculator refuses it rather than printing a negative number that a student might copy into a report. The conventional Steiger and Jäger 1977 International Union of Geological Sciences value lambda equals 1.42 times 10 to the minus 11 per year is the default, because most published tables and teaching problems still quote ages on that scale.
Ages are returned in years and in the mega-annum and giga-annum units geochronologists actually write on maps.
Where an Rb-Sr age helps, and its limits
Teaching labs and geochronology courses use a rubidium-strontium radiometric age calculator so students can check the last algebraic step of an isochron problem without mixing up mega-annum and giga-annum or forgetting that the argument of the logarithm is one plus the slope, not the slope itself. Research notebooks that already fit an isochron in a spreadsheet or a Python regression need a deterministic contract that pins t, lambda, and the half-life next to the slope for a methods table.
Content sites that want the query rubidium-strontium radiometric age calculator get a landing whose formula is the one every textbook prints. Keep the slope non-negative and, if you override lambda, keep it positive and in inverse years so the product lambda t is dimensionless. This page is not a York-fit isochron solver, not a potassium-argon or uranium-lead clock, and not a mixing-line interpreter: a negative slope here is treated as invalid input, not as a two-component mixture.
Prefer this capability when you already have m and only need t.
What you can do with it
Geochronology homework and lab reports
Enter the isochron slope from a textbook granite or meteorite problem and check that t = ln(1+m)/λ matches the expected mega-annum age before you write the methods paragraph.
Museum and outreach dating widgets
Embed the free browser calculator so visitors can turn a published isochron slope into a rock age without installing a geochronology package.
FAQ
How is the rubidium-strontium age computed from the isochron slope?
The isochron slope m equals e^{λt} − 1, so the age is t = ln(1 + m) / λ.
What happens if the isochron slope is negative?
A negative Rb-Sr slope would imply a negative radiometric age and cannot be produced by closed-system 87Rb decay, so it is not billed.
Which 87Rb decay constant does the calculator use?
By default it uses λ = 1.42 × 10^−11 a^−1 (Steiger and Jäger 1977, IUGS conventional).
Can I use a different decay constant?
Yes. The default is the Steiger and Jäger 1977 value of 1.42 × 10⁻¹¹ per year, but you can enter another positive constant when a paper follows Villa 2015 or a later recommendation. The result notes which convention was used.
Does the calculator fit the isochron for me?
No. It starts once you have the slope. Fit the line through your mineral pairs in your own spreadsheet or regression first, then enter that slope here to turn it into an age.
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-rb-sr \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"slope":0.02}'const res = await fetch("https://api.kit.forhosting.com/earth/radiometric-age-rb-sr", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"slope": 0.02
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/earth/radiometric-age-rb-sr",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"slope": 0.02
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/earth/radiometric-age-rb-sr", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"slope":0.02}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"slope":0.02}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/earth/radiometric-age-rb-sr", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"slope": 0.02
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "earth.radiometric_age_rb_sr",
"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
A negative slope is rejected with invalid_input because it would imply a negative age.
What the Rb-Sr isochron slope means and how age is recovered
You may pass a different decay_constant when a paper requires Villa 2015 or another recommendation; the response records which convention was used so the age is reproducible.
Input contract, response shape, and error behaviour
A zero or negative decay constant is rejected the same way, because the age formula divides by lambda. Example: slope 0.02 with the default lambda yields ln(1.02) divided by 1.42e-11, about 1.395 billion years, which is a typical Precambrian granite age. POST a JSON body with one required finite number, slope, the Rb-Sr isochron slope m. Aliases m, isochron_slope, and sr87_rb87_slope are accepted and mapped onto the same field. An optional decay_constant (aliases lambda, lambda_rb, lambda_rb87) overrides the default 1.42e-11 per year; it must be a finite positive number when supplied. Missing slope, a non-finite value, or a negative slope fails with invalid_input naming the field and is never billed. On success the body echoes the cleaned slope and the decay constant actually used, then publishes age_years, age_ma, age_ga, and half_life_years, plus convention set to steiger_jaeger_1977 or custom, method set to rb_sr_isochron_slope, formula set to t = ln(1 + m) / λ, and unit set to years. Pair this endpoint with your own isochron-fit code if you still have raw mineral pairs; this landing starts after the slope is already known. Successful API calls cost the published $0.002 base price with unit item; failed validation does not consume prepaid balance.
Where an Rb-Sr age API earns its keep, and what it is not
Round-trip checks are easy: recompute the natural log of one plus slope, divide by the echoed decay_constant, and confirm age_years matches within the same twelve-significant-digit rounding.
Integration use cases
Research notebooks after an isochron fit
Pipe a fitted Rb-Sr slope from a spreadsheet or York regression into the API and pin age_ma, lambda, and convention beside the plot so the age is reproducible.
Technical questions
What units are the ages returned in?
age_years is the elapsed time in years. age_ma is the same age in mega-annum (millions of years) and age_ga is giga-annum (billions of years). half_life_years is ln(2)/λ.
What does the rubidium-strontium radiometric age calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.