What is a Bland-Altman plot and what does it show?

It plots each subject's difference between two methods (y-axis) against the mean of the two methods (x-axis). A horizontal line marks the average difference (bias) and two dashed lines mark the 95% limits of agreement. It shows the size and direction of disagreement, whether it is constant or grows with magnitude, and any outliers.

How do you calculate the 95% limits of agreement?

Take the differences d = A − B for each pair, find the mean difference (bias, d̄) and the sample standard deviation of the differences (s_d, using n−1). The limits of agreement are d̄ ± 1.96·s_d. About 95% of future differences are expected to lie within this range. Use 2.58 instead of 1.96 for 99% limits.

What does "bias" mean in a Bland-Altman analysis?

Bias is the mean difference between the two methods — the systematic offset. A bias of +2 mmHg means one method reads, on average, 2 mmHg higher than the other. Bias near zero means no consistent over- or under-reading, but it says nothing about the spread; that is what the limits of agreement capture.

Why shouldn't you use the correlation coefficient (r) to compare two methods?

Correlation measures whether two variables move together, not whether they agree. Two methods can have r = 0.99 while one reads consistently twice the other — perfectly correlated, completely disagreeing. r also rises with a wider measurement range. Bland and Altman built this method precisely to replace r for method comparison.

How do you interpret the limits of agreement — are the two methods "in agreement"?

Statistics alone cannot answer that. Decide, before collecting data, the largest difference that would still be clinically acceptable. If the limits of agreement fall inside that pre-set range, the methods agree well enough to be used interchangeably; if they fall outside it, they do not. The calculator gives the numbers; the clinical threshold is your call.

What are the confidence intervals for, and how are they found?

They show how precisely the bias and each limit are estimated from your sample. The bias uses SE = s_d/√n; each limit is less precise, with SE ≈ s_d·√(3/n). Both are multiplied by the Student-t value for n−1 degrees of freedom (Bland & Altman 1999). Wider intervals mean you need more pairs.

How many pairs of measurements do I need?

The maths works from 3 pairs, but the limits are then very uncertain — their confidence intervals are wide. Bland and Altman suggest around 100 subjects for stable limits; many method-comparison studies use 40–50. This tool accepts 3 or more so students can try it, but treat small-sample limits as indicative only.

When should I switch to percentage differences?

Use percentage mode when the disagreement grows with the size of the measurement — a common pattern where the scatter fans out from left to right on the plot. Percentage differences, 100·(A−B)/mean, often give a flat band where absolute differences do not, producing limits that apply across the whole measurement range.

Does my data leave my computer?

No. Every calculation — parsing, the mean, standard deviation, t-values and the plot — runs in your browser with JavaScript. Nothing is uploaded, logged or stored on a server, so patient or lab data stays on your device. You can disconnect from the internet after the page loads and it still works.

Statistics · Method comparison

Bland-Altman Limits of Agreement Calculator

Paste two columns of paired measurements and get the bias, the 95% limits of agreement, their confidence intervals and the Bland-Altman difference-vs-mean plot. Free, no signup, and every calculation runs in your browser — your data never leaves the page.

By Induwara Ashinsana— Executive Director, Ryzera TechnologiesUpdated Jul 10, 2026

Bland-Altman analysislimits of agreement

Bland & Altman 1986/1999

Method A values

10 values parsed

Method B values

10 values parsed

DataOne number per line, or comma-separated.

Difference

Agreement level

Scale

Units label (optional)

Bias (mean diff)

2.00

Lower limit (−1.96 SD)

-1.20

Upper limit (+1.96 SD)

5.20

SD of differences

1.63

n = 10 pairs

Bland-Altman plot

Estimates & 95% confidence intervals

Statistic	Estimate	95% CI
Bias (mean difference)	2.00	0.83 to 3.17
Upper limit of agreement (+1.96 SD)	5.20	3.18 to 7.22
Lower limit of agreement (−1.96 SD)	-1.20	-3.22 to 0.82
SD of differences	1.63	—
Sample size (n)	10	—
t critical (0.975, n−1)	2.262	—

Plain-language reading

On average, Method A reads 2.00 higher than Method B. About 95% of differences are expected to fall between -1.20 and 5.20 (the ±1.96 SD limits of agreement). Whether that spread is close enough is a clinical judgement, not a statistical one — compare the limits against a difference you decided was acceptable before collecting the data.

Method: Bland & Altman (Lancet 1986; Stat Methods Med Res 1999). Everything runs in your browser — your measurements never leave this page.

How it works

The Bland-Altman method answers a question correlation cannot: do two ways of measuring the same thing agree closely enough to be used interchangeably? It was introduced by J. Martin Bland and Douglas Altman in The Lancet in 1986 and is now the standard for method-comparison and device-validation studies. The calculator follows their original formulas exactly.

For n paired measurements, with each pair's difference dᵢ = Aᵢ − Bᵢ:

Bias (mean difference): d̄ = (Σ dᵢ) / n. This is the systematic offset between the methods.
Standard deviation of the differences: s_d = √( Σ(dᵢ − d̄)² / (n − 1) ), the sample SD with an n−1 denominator.
95% limits of agreement: d̄ ± 1.96·s_d. Roughly 95% of differences between the two methods are expected to fall inside this band. Use 2.58 for 99% limits.
Confidence interval for the bias: d̄ ± t·(s_d/√n), where t is the Student-t value at n−1 degrees of freedom.
Confidence interval for each limit: LoA ± t·s_d·√(3/n). A limit is estimated less precisely than the bias, so its interval is wider (Bland & Altman 1999).

The Student-t critical values are computed on the page from the regularized incomplete beta function and inverted by bisection, so no external statistics library is needed and any degrees of freedom are supported. As an internal check the standard deviation is also computed a second way — through the moment formula √((Σd² − n·d̄²)/(n−1)) — and both paths must agree. Percentage mode repeats every step on 100·(Aᵢ − Bᵢ)/((Aᵢ + Bᵢ)/2) to reveal proportional bias, where the disagreement grows with the size of the measurement. The limits are a prediction interval for a future difference — deciding whether that spread is acceptable is a clinical judgement made against a pre-specified threshold, not something the statistics decide for you.

Worked examples

Example 1 — pulse oximeter vs blood gas (n = 10)

Differences A−B: 2, 4, 0, 2, 4, 0, 2, 4, 0, 2
Bias d̄ = 20 / 10 = 2.00
Σ(dᵢ − d̄)² = 24 → s_d = √(24/9) = 1.63
95% LoA = 2.00 ± 1.96 × 1.63 = [−1.20, +5.20]
Bias 95% CI: t(0.975, 9) = 2.262, SE = 1.63/√10 = 0.516 → [0.83, 3.17]
Upper-limit 95% CI: SE_LoA = 1.63·√(3/10) = 0.894 → [3.18, 7.22]

Example 2 — smaller study (n = 5)

Differences: 1, 3, 2, 4, 5
Bias d̄ = 15 / 5 = 3.00
Σ(dᵢ − d̄)² = 10 → s_d = √(10/4) = 1.58
95% LoA = 3.00 ± 1.96 × 1.58 = [−0.10, +6.10]
Bias 95% CI: t(0.975, 4) = 2.776, SE = 1.58/√5 = 0.707 → [1.04, 4.96]
Wider limits than Example 1 — fewer pairs, larger t value.

Example 3 — identical methods (edge case, n = 3)

Method A: 5, 5, 5 Method B: 5, 5, 5
Every difference is 0 → bias = 0.00
s_d = 0 → 95% LoA = 0 ± 0 = [0.00, 0.00]
Every confidence interval is [0.00, 0.00] — no NaN, no error.
Perfect agreement: both methods return the same reading each time.

Frequently asked questions

Sources & references

Formulas are textbook-standard and vendor-neutral. They were last reconciled against the sources above, with both worked examples cross-checked in code, on 2026-07-10.

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