Concordance correlation coefficient calculator
Two identical series from 1 to 5 give a concordance coefficient of 1, but shift or rescale one of them and it drops below 1 while Pearson's r stays at 1. Use it to check whether two instruments really agree. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- X
- 1, 2, 3, 4, 5
- Y
- 1, 2, 3, 4, 5
- N
- 5
- Ccc
- 1
- Mean x
- 3
- Mean y
- 3
This concordance correlation coefficient calculator computes Lin’s CCC between two equal-length lists of numbers. Unlike Pearson’s r, which only scores linear association, CCC asks whether the points sit near the line y equals x: high precision and high accuracy together. You get the paired sample size n, the coefficient CCC, Pearson r when both series vary, the means of x and y, the 1/n variances and covariance, Lin’s bias-correction factor, and the mean difference. Classic checks include identical series one through five on both axes, which yields perfect concordance CCC equals one, and a perfectly correlated but scaled or shifted y, which keeps r near one while CCC falls below one. The engine uses a deterministic two-pass algorithm only: no network calls, no random sampling, and no date-dependent shortcuts.
What Lin's coefficient measures and what you get
Lin’s concordance correlation coefficient combines precision and accuracy into a single number that answers a practical question: how well do two paired measurements agree if perfect agreement means every pair lands on the identity line y equals x. Pearson’s product-moment correlation can report r equals one when y is a scaled or shifted version of x, yet those pairs systematically miss the identity line; CCC penalizes that location or scale bias through the squared mean difference and the separate variance terms in the denominator.
After the means of x and y are known, the engine forms 1/n variance and covariance moments, then returns CCC as twice the covariance over the sum of the two variances plus the squared mean difference. A value near plus one means the series move together and sit near the identity line; a value near zero or negative means disagreement is large relative to the joint spread. The equal-length rule is intentional: unequal lists would invent pairings that are not in the data.
Where concordance correlation fits in labs, study, and product work
Students meet CCC when a biostatistics unit contrasts correlation with agreement, when a methods lab compares two assays or two instruments on the same samples, or when they need a clean check against a calculator that only prints Pearson r and hides systematic bias. Teachers can pre-generate answer keys for modest paired series without trusting opaque apps that drop pairs on missing cells or switch silently between n and n minus one moment conventions.
Developers call the same contract from scripts to seed deterministic test vectors, to validate sensor-fusion pipelines that require measurements to land near the identity line, or to satisfy data-quality gates that flag pairs whose CCC collapses when one channel gains a scale factor. Analysts use CCC next to Bland–Altman plots and residual summaries: a large Pearson r with a modest CCC is a classic signal that association is strong but agreement is not.
Product and operations teams watch concordance between two latency probes, two pricing engines, or two recommender scores to catch silent drift that a pure correlation dashboard would miss. Pair it with the Pearson correlation tool when you only need linear association, and with linear regression when you need slope and intercept rather than an identity-line agreement score.
What you can do with it
Assay and instrument agreement
Compare two lab methods or sensors on paired samples and report Lin’s CCC next to means, variances, and mean difference.
Homework and method-comparison labs
Verify textbook CCC examples where Pearson r stays high but scale or offset bias pulls concordance below one.
FAQ
What does the concordance correlation coefficient calculator cost?
It is free in your browser on this page.
How is Lin’s CCC different from Pearson’s r?
Pearson’s r measures linear association only. Lin’s CCC also penalizes location and scale bias relative to the identity line y = x, so agreement can be low even when r is near 1.
Which moment divisor does the calculator use?
Lin’s original form with divisor n for variances and covariance (not Bessel’s n − 1). The response formula string documents that convention.
What happens when both series are identical constants?
If every pair shares the same constant value, CCC is defined as 1 (perfect agreement). If both series are constant but at different levels, CCC is 0.
Why must both lists have the same length?
Because each position pairs one measurement from the first list with one from the second. Unequal lists would invent pairings that are not in the data, so they are rejected rather than padded or trimmed.
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/stat/concordance-correlation \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"x":[1,2,3,4,5],"y":[1.1,2,2.9,4.2,5]}'const res = await fetch("https://api.kit.forhosting.com/stat/concordance-correlation", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"x": [
1,
2,
3,
4,
5
],
"y": [
1.1,
2,
2.9,
4.2,
5
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/concordance-correlation",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"x": [
1,
2,
3,
4,
5
],
"y": [
1.1,
2,
2.9,
4.2,
5
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/concordance-correlation", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"x":[1,2,3,4,5],"y":[1.1,2,2.9,4.2,5]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"x":[1,2,3,4,5],"y":[1.1,2,2.9,4.2,5]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/concordance-correlation", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"x": [
1,
2,
3,
4,
5
],
"y": [
1.1,
2,
2.9,
4.2,
5
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.concordance_correlation",
"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.
Limits
max_n | 10000 |
max_abs | 1000000000000000 |
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
What Lin’s CCC measures and what the response contains
This calculator always returns a fixed shape: n, ccc, pearson_r when defined, mean_x, mean_y, var_x, var_y, cov, bias_correction when defined, mean_diff, a short formula string, and the published maximum length so clients can validate before they send a batch. There is no approximate Monte Carlo path presented as truth and no silent padding when the lists differ: the engine either finishes the two-pass arithmetic inside the supported length and magnitude limits or rejects the input with invalid_input. Rejected cases include a missing x or y field, empty lists, fewer than two pairs, non-finite entries such as Infinity or NaN, non-numeric tokens, unequal series lengths, and arrays longer than the published maximum.
How x and y are read and how the two-pass algorithm stays stable
Each element is parsed as a finite decimal; optional leading signs and scientific notation are allowed, while empty tokens, bare letters, and non-numeric objects fail with a field index in the message so a bad cell does not become a silent zero. When both series are constant and the means match, numerator and denominator are zero and the engine returns CCC equals one for perfect agreement on a shared constant. Returning the intermediate moments makes it easy to audit a homework answer or to wire the same numbers into a spreadsheet that uses Lin’s formula. The preferred fields are x and y, each an array of finite numbers of equal length, but aliases a and values_x and series_x for the first series and b and values_y and series_y for the second are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. A single comma-separated or whitespace-separated string of numbers is also accepted for each field when a form posts plain text instead of JSON arrays. The engine enforces a hard maximum of ten thousand pairs and a per-value magnitude ceiling so memory and latency stay inside a predictable budget on the free browser path and on the edge Worker. Computation is the classic Lin two-pass method: first the means of x and y, then the 1/n residual sums for var_x, var_y, and cov, then CCC as twice the covariance over var_x plus var_y plus the squared mean difference. When both series vary, Pearson r and Lin’s accuracy factor bias_correction are returned alongside CCC so you can see how much of the drop from one comes from precision versus location or scale bias. Pair the free browser run on this page with the priced API when you need the identical concordance result inside an automated pipeline without re-implementing Lin’s formula yourself.
Where concordance correlation fits in labs, study, and product work
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic CI fixtures
Generate reproducible CCC values for unit tests and data-quality gates without hand-maintaining bivariate tables.
Technical questions
Why must x and y have the same length?
CCC is defined on paired observations. Unequal lengths would invent or drop pairs, so the tool rejects them with invalid_input.