Half-Life Calculator
This half-life calculator estimates the time required for a quantity to reduce to half its initial amount during exponential decay. It's commonly used in biology to describe decay of populations, clearance of substances, or degradation of biomolecules.
How it works
For first-order (exponential) decay, the relationship between the initial amount A0, the amount A after time t, and the half-life t_half is:
A = A0 * 2^(-t / t_half)Rearranging to solve for half-life when A0, A, and t are known:
t_half = -t * ln(2) / ln(A / A0)Use this calculator by entering the initial amount, the observed remaining amount after a known time period, and the time period itself. The result is the half-life in the same units as the time input (seconds, minutes, hours, etc.).
Example
Suppose a bacterial population decreases from 100 units to 25 units over 20 hours. Enter A0 = 100, A = 25, t = 20. The calculator will compute:
t_half = -20 * ln(2) / ln(25 / 100) = 10 hours
Interpretation and notes
- Inputs must be positive numbers. Final amount must be less than initial amount for decay.
- The half-life returned has the same time units as the Time Period you provide.
- This calculation assumes first-order kinetics (exponential decay). It does not apply to non-exponential decay without modification.
Frequently Asked Questions
What if the final amount is greater than or equal to the initial amount?
The formula assumes decay (final < initial). If final >= initial, the half-life for decay is not defined; you may be observing growth or measurement error.
Can I use different units (seconds, minutes, hours)?
Yes. The calculator returns the half-life in the same units as the Time Period you enter. Ensure consistency when interpreting results.
Is this valid for all biological processes?
This tool is valid for processes that follow first-order kinetics (exponential decay). Some biological systems follow more complex dynamics; use appropriate models in those cases.
References
Common textbooks on biochemistry and pharmacokinetics cover half-life and exponential decay models in detail. For applied microbiology, consult primary literature for process-specific kinetics.