Pearson’s r is 0.99632 — as close to perfect as a real measurement gets — and the concordance is 0.90035. The second method reads about 25% high, so the two move together beautifully and do not agree. The decomposition says exactly where the loss is: precision 0.99632, accuracy 0.90368, and their product is the concordance to the last digit.
20 pairs · moderate
CCC = 0.90035
Pearson's r on the same pairs is 0.99632 and the bias-correction factor is 0.90368. Their product is the concordance exactly — 0.99632 × 0.90368 = 0.90035 — which is what makes the two halves worth reading separately. The accuracy factor is doing the damage here: the two methods differ by -8.3650 on average and their standard deviations are in a ratio of 0.8048. The 95% interval is 0.82206 to 0.94523.
Concordance
0.90035
CI 0.8221 to 0.9452
Precision (r)
0.99632
how tightly they track
Accuracy (Cb)
0.90368
how close to the diagonal
Mean difference
-8.3650
SD ratio 0.8048
Where the agreement is lost
The decomposition of concordance into precision and accuracy
Component
Value
What it measures
Precision (r)
0.996317
how tightly the points hug some straight line
Accuracy (Cb)
0.903678
how close that line is to the 45-degree diagonal
Scale shift (v)
0.804760
ratio of the two standard deviations; 1 means the same spread
Location shift (u)
-0.407200
mean difference in pooled standard deviations; 0 means no offset
Concordance
0.900350
the product of the first two, exactly
A scale shift away from 1 and a location shift away from 0 are different problems with different fixes: a scale difference needs recalibration, an offset needs a constant correction. Cb collapses both into one number, and these two rows separate them again.
The line agreement is measured against
Measured against y = x Splits into precision and accuracy Interval on the transformed scale One number, no units
What this tool shows
On the shipped comparison, Pearson’s r is 0.99632 and Lin’s concordance is 0.90035. The two methods track each other almost perfectly and one of them reads about 25% high, so they do not agree. Concordance is exactly the product of the correlation and a bias-correction factor, and printing both halves says which of the two problems a comparison has — scatter, or a shift.
Lin’s concordance correlation coefficient, measured against the 45-degree line rather than a fitted one
The exact decomposition CCC = precision × accuracy, with both factors printed
Scale shift and location shift separated, because they need different corrections
A confidence interval on the inverse-hyperbolic-tangent scale, so it cannot leave (−1, 1)
A preset whose concordance has a closed-form value of exactly 33/35
Pearson’s r alongside, as the number this coefficient exists to replace
Against y = x Exact decomposition Bounded interval Shifts separated
One number, and no units. It cannot say how far apart two readings can be.
Updated 13 September 2026 · Works in any browser, no installation
Lin’s concordance correlation measures how far paired measurements fall from the 45-degree line, not from some fitted line. That is the whole difference from an ordinary correlation: a correlation is satisfied by any straight relationship, and concordance is satisfied only by equality. It reaches 1 when every point sits exactly on y = x, and it falls whenever the two methods differ in level, in scale, or simply scatter.
At a glance
Formula shown
CCC = 2·s_xy / (s²_x + s²_y + (x̄ − ȳ)²), using population moments. Equivalently CCC = r · Cb, where r is Pearson’s correlation and Cb = 2 / (v + 1/v + u²) with v = s_x/s_y the scale shift and u = (x̄ − ȳ)/√(s_x·s_y) the location shift. The two factors multiply to the coefficient exactly, which the verification suite asserts to zero difference — not to a tolerance — across 250 generated pairs.
Scenario support
Summarising a method comparison in one number for a paper or a submission, comparing several candidate instruments against a reference on the same scale, test-retest reliability on continuous measurements, and any situation where a reviewer has asked for a single agreement coefficient rather than a plot.
Educational estimate
Planning support from the values you enter — not professional advice.
r = 0.996, concordance = 0.900
The shipped scale preset separates the two ideas as cleanly as real data allows.
Pearson’s r is 0.99632. The points sit almost exactly on a straight line.
The concordance is 0.90035, because that line is not the diagonal — the second method reads about 25% high.
The decomposition names the culprit: precision 0.99632, accuracy 0.90368. Their product is the concordance to the last digit, which is an algebraic identity rather than a coincidence.
So the two factors answer different questions. Precision asks how tightly the points hug a line; accuracy asks how close that line is to equality. A low concordance with high precision is a calibration problem; with low precision it is a noise problem.
Scale shift and location shift need different fixes
The accuracy factor folds two distinct problems into one number, and the table on this page unfolds them again.
The scale shift v is the ratio of the two standard deviations. Away from 1 means one method spreads more than the other — a slope problem, fixed by recalibration.
The location shift u is the mean difference in pooled standard deviations. Away from 0 means a constant offset, fixed by subtracting it.
On the pure-shift preset v is exactly 1 and u is −0.34816. The methods have identical spread and differ only in level.
They can also cancel. A scale shift in one direction and a location shift in the other can produce an accuracy factor near 1 with both problems present, which is why the two rows are printed rather than only their combination.
A case with a closed-form answer
The second preset is on this page because its answer can be worked out by hand, which is a stronger check on an implementation than any published table.
x runs 10 to 100 in tens, and y is x + 10. The correlation is exactly 1 and the two standard deviations are identical, so v = 1.
The population variance of those ten values is 825, so u² = 100/825 = 4/33.
Which makes Cb = 2/(1 + 1 + 4/33) = 33/35, and since r = 1 the concordance is 33/35 = 0.942857142857… exactly.
The verification suite asserts that as an exact equality to 1e-15, not to a tolerance — which would catch a rounding error in the moments that a looser check would let through.
What one number cannot tell you
Concordance is a summary, and summaries lose the thing a method comparison usually needs.
It has no units. A concordance of 0.95 does not say how far apart two readings on the same subject can be, which is the question anyone deciding whether to swap instruments actually has.
A Bland-Altman analysis does. Its limits of agreement are in the units of the measurement and can be compared against a clinically acceptable difference.
Concordance also rises with the spread of the sample, exactly as a correlation does: measure a wider range of subjects and the coefficient improves with no change in either instrument.
So use it as the headline and the limits as the answer. Reporting a concordance alone is reporting a ratio where a difference was needed.
Why the interval is transformed
A concordance near 1 has a skewed sampling distribution, and a symmetric interval around it runs off the end of the scale.
The interval here is built on the inverse hyperbolic tangent of the coefficient and mapped back, so it can never leave (−1, 1).
Its standard error is Lin’s asymptotic formula, which includes terms for the location shift that vanish when the two methods have the same mean.
That formula is checked against simulation here rather than trusted: the suite compares it against a 4,000-draw simulation at three sample sizes and requires agreement within 12%.
It is asymptotic, so it is optimistic at small n. Below about twenty pairs the interval should be read as indicative, and the poor-agreement preset shows one running from −0.11 to 0.58 — wide enough to include no agreement at all.
Concordance and the intraclass correlation
The two coefficients are close relatives and are often reported interchangeably, which they are not quite.
Lin’s concordance and the two-way mixed ICC for absolute agreement are algebraically almost the same statistic when there are exactly two raters.
The difference is in the divisor: concordance uses population moments while the ICC comes from an ANOVA with sample moments, so they differ by a factor of about (n−1)/n and converge as n grows.
The ICC generalises to more than two raters; concordance is specifically a two-method coefficient.
Concordance decomposes and the ICC does not, which is the practical reason to prefer it for a two-method comparison: it says whether the problem is scatter or calibration.
Reporting a concordance
Four items, and the second is what makes the coefficient actionable rather than decorative.
Give the coefficient with its interval and n. The interval is asymptotic and widens sharply at small n.
Give the precision and accuracy factors. They say whether to fix the calibration or reduce the noise, and the single coefficient says neither.
Give the range of the measurements. Concordance rises with the spread of the sample, so a coefficient from a wide-ranging sample is not comparable with one from a narrow sample.
And pair it with limits of agreement. A dimensionless coefficient cannot be compared against a clinically acceptable difference; limits in the original units can.
Sources and methodology
References for the coefficient, its decomposition and its variance.
Method. The coefficient uses population moments, as Lin defined it, and the decomposition into precision and accuracy is computed from those same moments rather than derived from the coefficient — which is what lets the suite assert their product equals the coefficient to zero difference on 250 generated pairs, an exact equality rather than a tolerance. The scale and location shifts are printed separately because the accuracy factor combines two problems with different fixes. The confidence interval uses the corrected 2000 variance on the inverse-hyperbolic-tangent scale, so it cannot leave (−1, 1), and that variance is not taken on trust: the suite compares it against a 4,000-draw simulation at three sample sizes and configurations. It also asserts that the coefficient is symmetric in the two methods, that it never exceeds the correlation in magnitude, that rescaling both methods by the same factor leaves it unchanged, and that a pure shift of 10 on x = 10…100 gives exactly 33/35. That engine is verified on every change against 103 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Bland-AltmanLimits of agreement with confidence intervals on the limits themselves, a proportional-bias test and the correlation printed beside them for contrast.
Intraclass CorrelationAll six ICC forms from one subject-by-rater matrix, with the rater means that drive them apart: one 8x3 matrix gives ICC(1,1) = 0.1277 and ICC(3,1) = 0.9852.
Correlation CoefficientReports Pearson, Spearman and Kendall together with the scatter plot, and ships Anscombe's quartet built in — four datasets with an identical r of 0.816 that Spearman tells apart.
Passing-BablokRobust method-comparison regression with rank-based intervals, the symmetry shift reported, and the pairwise-slope distribution shown.
Gauge R&RANOVA gauge repeatability and reproducibility with both acceptance criteria, the operator-by-part interaction tested, and the full variance decomposition.
Cronbach's AlphaAlpha with alpha-if-item-dropped, item-total correlations and the mean inter-item correlation, plus the length table: at a mean inter-item correlation of 0.05, a 100-item scale still reports 0.8403.
An educational tool. Lin’s concordance is dimensionless, so it cannot say how far apart two readings can be on one subject — that requires limits of agreement in the units of the measurement. Like a correlation, it also rises with the spread of the sample, so a coefficient from a wide-ranging study is not comparable with one from a narrow one, and its confidence interval is asymptotic and optimistic at small n.