Half-Life Calculator
Inputs
Enter initial amount, half-life, and time to calculate remaining quantity.
What is Half-Life?
Half-life (T½) is the time required for a quantity to reduce to half its initial value. It is most commonly associated with radioactive decay, but also applies to drug metabolism, chemical reactions, and other exponential decay processes.
For example, Carbon-14 has a half-life of ~5,730 years. This means that after 5,730 years, half of a sample of C-14 will have decayed into Nitrogen-14.
The Half-Life Formula
The remaining amount after time t is given by:
N(t) = N₀ × (½)^(t/T)- N(t) = Amount remaining after time t
- N₀ = Initial amount
- t = Time elapsed
- T = Half-life period
Examples
Example 1: Carbon-14 Dating
A fossil has 25% of its original C-14. How old is it?
- Half-life = 5730 years
- If N(t)/N₀ = 0.25 = (½)², then t/T = 2
- t = 2 × 5730 = 11,460 years old
Example 2: Drug Metabolism
A drug has a half-life of 4 hours. How much remains after 12 hours?
- t/T = 12/4 = 3 half-lives
- N(t) = N₀ × (½)³ = N₀ × 0.125
- 12.5% of the drug remains
Frequently Asked Questions
Does half-life change based on conditions?
For radioactive decay, half-life is constant and unaffected by temperature or pressure. For chemical reactions, it can vary.
What is the decay constant (λ)?
λ = ln(2) / T. It represents the probability of decay per unit time.