Navigation Depth & Click Distance Calculator
Calculate the average click distance, maximum depth, and navigation efficiency of a website or application structure using tree-based metrics.
Formulas Used
Minimum Depth (balanced b-ary tree to hold N pages):
d_min = ⌈ log(N·(b−1)+1) / log(b) ⌉ − 1
Average Click Distance (weighted mean depth in balanced tree):
avg_d = Σ(k·bᵏ, k=1..d) / Σ(bᵏ, k=0..d)
Closed form numerator: b·(1 − (d+1)·bᵈ + d·bᵈ⁺¹) / (b−1)²
Pages Reachable within Max Depth:
C(d_max) = (b^(d_max+1) − 1) / (b − 1)
Navigation Efficiency Score (0–100):
efficiency = 100 · (1 − avg_d / (d_max+1)) · compliance_factor
where compliance_factor = 1 if d_min ≤ d_max, else max(0, 1 − (d_min−d_max)/d_max)
Recommended Branching Factor:
b_rec = ⌈ N^(1/d_max) ⌉
Assumptions & References
- The site/app structure is modelled as a balanced b-ary tree rooted at the homepage.
- All pages at the same depth are assumed equally likely to be visited (uniform distribution).
- Click distance is measured from the root (homepage); internal links between sibling pages are not counted.
- The 3-click rule (Nielsen, 2000) suggests key content should be reachable in ≤ 3 clicks; a max depth of 3–4 is generally recommended.
- Research by Zaphiris (2000) shows average click distance is a strong predictor of user navigation success.
- Branching factors of 5–9 align with Miller's Law (7 ± 2 items in working memory) for menu design.
- For b = 1 (linear chain), formulas reduce to a simple linked list model.
- Reference: Rosenfeld, L. & Morville, P. — Information Architecture for the World Wide Web, O'Reilly.