Intraclass Correlation Coefficient (ICC) Calculator

The intraclass correlation coefficient (ICC) measures how much of the total variation in a set of measurements comes from real differences between subjects rather than from disagreement between raters or repeat measurements. It is the standard way to report inter-rater and test–retest reliability for continuous data — goniometer angles, pain scores, questionnaire totals, timing measurements — and it is what journal reviewers ask for. This tool computes it in your browser and never uploads your data.

Given a complete matrix of n subjects (rows) by k raters (columns), the calculator runs a two-way analysis of variance without replication, following McGraw & Wong (1996). It first computes four sums of squares from the grand mean, the per-subject (row) means, and the per-rater (column) means:

• SS_R — between subjects: k · Σ(x̄ᵢ − x̄)²
• SS_C — between raters: n · Σ(x̄ⱼ − x̄)²
• SS_E — residual: SS_T − SS_R − SS_C
• SS_W — within subject (one-way): SS_T − SS_R

Dividing each by its degrees of freedom gives the four mean squares — BMS, JMS, EMS and WMS — that every ICC formula is built from. The six Shrout & Fleiss (1979) forms are then:

• ICC(1,1) = (BMS − WMS) / (BMS + (k−1)·WMS)
• ICC(2,1) = (BMS − EMS) / (BMS + (k−1)·EMS + (k/n)·(JMS − EMS))
• ICC(3,1) = (BMS − EMS) / (BMS + (k−1)·EMS)
• ICC(1,k) = (BMS − WMS) / BMS
• ICC(2,k) = (BMS − EMS) / (BMS + (JMS − EMS)/n)
• ICC(3,k) = (BMS − EMS) / BMS

The numbers in the first slot are the model (1 = one-way random, 2 = two-way random, 3 = two-way mixed) and the second slot is the unit(1 = a single rater, k = the average of all raters). Form 2 measures absolute agreement — it counts systematic rater bias as disagreement — while form 3 measures consistency and ignores that bias, which is why ICC(3,·) is always at least as large as ICC(2,·). To guard against arithmetic slips, the tool recomputes every form a second way, from independent variance components (McGraw & Wong, 1996, Table 1), and only shows the “cross-verified” badge when both methods agree to six decimals. Reliability bands (poor / moderate / good / excellent) follow Koo & Li (2016). If every subject has the same average rating there is no between-subject variance and the ICC is reported as undefined rather than a misleading zero.

• Shrout & Fleiss (1979) — Intraclass correlations: Uses in assessing rater reliability
• McGraw & Wong (1996) — Forming inferences about some intraclass correlation coefficients
• Koo & Li (2016) — A guideline of selecting and reporting ICCs for reliability research

Formulas and interpretation thresholds on this page were last cross-checked against these sources on 2026-07-10. The Shrout & Fleiss 6×4 dataset is used as the tool's regression test — the calculator reproduces every value in their Table 2.