AHP Consistency Ratio (CR) Calculator
Validate mathematical rigor, calculate principal eigenvalue (λmax), priority vector weights (wi), consistency index (CI), and consistency ratio (CR).
1 Define Decision Criteria
Add between 2 to 10 criteria for pairwise matrix evaluation.
2 Pairwise Comparisons (Saaty 1–9 Scale)
Adjust relative importance sliders. Center (0) denotes equal priority (1:1).
3 AHP Consistency Analysis
Evaluates transitivity logic: if Criterion A > B and B > C, then A should > C.
Calculated Priority Vector (wi) Weights
Relative weighting allocated to each decision criterion.
AHP Mathematical Foundations
1. Pairwise Comparison Matrix (A)
For n criteria, an n × n pairwise matrix is built where each element aij represents the relative weight of criterion i over j, satisfying reciprocal symmetry: aji = 1 / aij and aii = 1.
2. Priority Vector / Row Averages (wi)
Column-normalize matrix A and compute the arithmetic row mean to calculate normalized priority weights:
3. Principal Eigenvalue (λmax)
Multiply original matrix A by priority vector w, divide row-wise by wi, and take the average:
4. Consistency Index (CI) & Consistency Ratio (CR)
Quantifies random departure from exact transitivity:
Where RI is Thomas L. Saaty's empirical Random Index based on sample size n. Matrices with CR ≤ 10% (0.10) are considered consistently reliable for operational decision-making.
Updated: 06/10/20206 Changes made: AHP Consistency Analysis added. Radar chart added. Comparison Matrix and Normalized Matrix are added.




