Reaction Time Estimator Formula

Understand the math behind the reaction time estimator. Each variable explained with a worked example.

Formulas Used

Estimated Reaction Time

estimated_rt = max(base_rt + sleep_penalty - caffeine_benefit + fatigue_penalty, 150)

Age-Based Baseline

baseline_rt = base_rt

Total Adjustment

total_adjustment = sleep_penalty - caffeine_benefit + fatigue_penalty

Variables

VariableDescriptionDefault
ageAge(years)30
sleep_hoursSleep Last Night(hours)7
caffeine_mgCaffeine Today(mg)100
hours_awakeHours Awake(hours)8
base_rtDerived value= 200 + max(age - 25, 0) * 1.5calculated
sleep_penaltyDerived value= max(7 - sleep_hours, 0) * 15calculated
caffeine_benefitDerived value= min(caffeine_mg * 0.05, 20)calculated
fatigue_penaltyDerived value= max(hours_awake - 14, 0) * 10calculated

How It Works

Reaction Time Estimation

Average visual reaction time is about 200-250 ms for young adults.

Factors Affecting Reaction Time

| Factor | Effect | |---|---| | Age | +1.5 ms per year above 25 | | Sleep loss | +15 ms per hour below 7 | | Caffeine | Up to -20 ms improvement | | Fatigue (>14h awake) | +10 ms per hour |

Practical Impact

At 60 mph, each 100 ms adds about 8.8 feet of stopping distance.

Worked Example

A 30-year-old, 7 hours sleep, 100 mg caffeine, 8 hours awake.

age = 30sleep_hours = 7caffeine_mg = 100hours_awake = 8
  1. 01Base RT = 200 + (30 - 25) x 1.5 = 207.5 ms
  2. 02Sleep penalty = 0 (7 hours is adequate)
  3. 03Caffeine benefit = 100 x 0.05 = -5 ms
  4. 04Fatigue = 0 (8 < 14)
  5. 05Total = 207.5 - 5 = 203 ms

Ready to run the numbers?

Open Reaction Time Estimator