Caffeine Calculator

def caffeine_remaining(initial_mg: float, elapsed_hours: float, half_life_hours: float = 5.5) -> float:
    """
    Calculate remaining caffeine using half-life decay formula.
    C(t) = C0 * (0.5)^(t / t½)
    Default half-life: 5.5 hours (adult average).
    """
    return initial_mg * (0.5 ** (elapsed_hours / half_life_hours))

def hours_until_threshold(initial_mg: float, threshold_mg: float, half_life: float = 5.5) -> float:
    """
    Calculate hours until caffeine drops below threshold.
    t = t½ * log2(C0 / threshold)
    """
    import math
    if threshold_mg <= 0 or initial_mg <= threshold_mg:
        return 0.0
    return half_life * math.log2(initial_mg / threshold_mg)

# Example: Morning coffee at 07:00
initial_mg = 200  # large drip coffee
half_life   = 5.5

print("Caffeine decay after a 200 mg coffee:")
print(f"{'Time':>8}  {'Remaining (mg)':>16}  {'% Left':>8}")
print("-" * 38)
for h in range(0, 14):
    remaining = caffeine_remaining(initial_mg, h, half_life)
    pct = remaining / initial_mg * 100
    print(f"{h:>7}h  {remaining:>14.1f}  {pct:>7.1f}%")

# Bedtime estimate
bedtime_h = hours_until_threshold(initial_mg, 25)  # <25 mg feels negligible
print(f"\nTime until <25 mg remains: {bedtime_h:.1f} hours after intake")