Half-life math in one page
HalfLifeDB plots a simple exponential decay curve. It does not attempt to model absorption, distribution, multiple compartments, active metabolites, or non-linear elimination. The point is to make the shape of a half-life process easy to see.
The core equation
In a first-order model, the remaining fraction after time t is:
fraction remaining = (1/2)^(t / t½)
Where t½ is the half-life. If you start at 100%, after one half-life you are at 50%, after two half-lives you are at 25%, and so on.
Worked example
Suppose a substance has a half-life of 12 hours and it has been 18 hours since a single dose. The number of half-lives elapsed is 18/12 = 1.5. The remaining fraction is (1/2)^1.5 ≈ 0.353. In other words, about 35% of the starting amount remains in this simplified model.
Why this is not a “time to zero” calculator
Exponential decay approaches zero but does not hit zero at a specific timestamp. In practice, labs and instruments have detection thresholds, and biological systems have background noise. HalfLifeDB intentionally avoids giving “time to clear” numbers. The more useful educational framing is: decay is fast at first and then slows.
Common pitfalls
- Confusing half-life with duration. Subjective effects can fade earlier or later than elimination.
- Assuming one number fits everyone. Half-life depends on population, dose, route, and many variables.
- Ignoring repeated dosing. Re-dosing changes the curve via accumulation and overlapping decay.
- Treating the curve as blood levels. The site plots a relative amount in a simplified model, not a measured concentration.
Where the equation comes from
First-order elimination assumes the rate of change is proportional to the amount present. That yields an exponential function. Half-life is a convenient way to express the constant of proportionality.