HickLaw [fact] v1.0.0

Hick's Law (1952): the time required to make a decision grows logarithmically with the number of equally probable choices, approximately T = b · log2(n+1).

Decision time scales as approximately T = b · log2(n+1) where n is the number of equally probable, equally salient options — meaning each doubling of choices adds a constant unit of decision time, not a linear amount.

Confidence

proven

Applies To

• menu / navigation depth-vs-breadth decisions
• form field count + options-per-field
• command palette result count
• settings panel grouping

Quantitative

• Formula: T = b · log2(n + 1)
• Typical B: ≈ 150 ms per bit (varies by task / familiarity)
• Practical Implication: going from 4 to 8 options adds ~150 ms decision time, not 4× the time

Counter Conditions

• Not equally probable: when options have salience hierarchy (one obvious primary action), Hick's Law overstates the cost.
• Highly familiar options (often-used menu items) approach constant time — log scaling collapses.
• Visual / spatial chunking changes effective n (a grouped 3×3 grid behaves more like 3+3, not 9).
• Hick's Law concerns choice-reaction time only; complex decisions (cost-benefit) follow different curves.

HickLaw [fact] v1.0.0

Hick's Law (1952): the time required to make a decision grows logarithmically with the number of equally probable choices, approximately T = b · log2(n+1).

Decision time scales as approximately T = b · log2(n+1) where n is the number of equally probable, equally salient options — meaning each doubling of choices adds a constant unit of decision time, not a linear amount.

Confidence

proven

Applies To

• menu / navigation depth-vs-breadth decisions
• form field count + options-per-field
• command palette result count
• settings panel grouping

Quantitative

• Formula: T = b · log2(n + 1)
• Typical B: ≈ 150 ms per bit (varies by task / familiarity)
• Practical Implication: going from 4 to 8 options adds ~150 ms decision time, not 4× the time

Counter Conditions

• Not equally probable: when options have salience hierarchy (one obvious primary action), Hick's Law overstates the cost.
• Highly familiar options (often-used menu items) approach constant time — log scaling collapses.
• Visual / spatial chunking changes effective n (a grouped 3×3 grid behaves more like 3+3, not 9).
• Hick's Law concerns choice-reaction time only; complex decisions (cost-benefit) follow different curves.

Sources

Confidence

proven

Source

• W. E. Hick, 'On the rate of gain of information', Quarterly Journal of Experimental Psychology (1952)
• Hyman, R., 'Stimulus information as a determinant of reaction time', Journal of Experimental Psychology (1953)
• Card, Moran & Newell, 'The Psychology of Human-Computer Interaction' (1983)

Applies To

• menu / navigation depth-vs-breadth decisions
• form field count + options-per-field
• command palette result count
• settings panel grouping

Quantitative

• Formula: T = b · log2(n + 1)
• Typical B: ≈ 150 ms per bit (varies by task / familiarity)
• Practical Implication: going from 4 to 8 options adds ~150 ms decision time, not 4× the time

Counter Conditions

• Not equally probable: when options have salience hierarchy (one obvious primary action), Hick's Law overstates the cost.
• Highly familiar options (often-used menu items) approach constant time — log scaling collapses.
• Visual / spatial chunking changes effective n (a grouped 3×3 grid behaves more like 3+3, not 9).
• Hick's Law concerns choice-reaction time only; complex decisions (cost-benefit) follow different curves.