About this Half-Life Calculator
Half-life is the time required for a quantity to reduce to half of its initial value. This concept is widely used in nuclear physics to describe radioactive decay, in chemistry for reaction rates, and in medicine to determine how long a drug stays in the body.
Who this calculator is for
- Students learning exponential decay in chemistry, physics, or pharmacology.
- Lab and classroom users estimating how much of a substance remains after a given time.
- Anyone modeling repeated halving behavior with a constant half-life.
When to use it
- Estimate radioactive decay after a known number of years or hours.
- Check how much drug remains after several dosing intervals.
- Compare how quickly different substances decay when their half-lives differ.
How to use this calculator
- Enter the Initial Quantity of the substance.
- Enter the Half-Life period (how long it takes to halve).
- Enter the Elapsed Time.
- The result shows the Remaining Amount.
Key assumptions
- Initial quantity, elapsed time, and half-life are finite values.
- Half-life must be greater than zero, and elapsed time cannot be negative.
- The model assumes constant exponential decay across the full time period.
Accuracy and testing
Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.
How this calculator works
The formula for half-life decay is exponential:
N(t) = N₀ × (1/2)^(t / t½)
* N(t): Remaining quantity
* N₀: Initial quantity
* t: Elapsed time
* t½: Half-life period
Inputs explained
Initial Quantity
The amount of substance at time zero (e.g., grams, atoms, concentration).
Half-Life
The time it takes for the substance to decrease by 50%.
Elapsed Time
The total duration of the decay process. Must use the same time unit as Half-Life.
Understanding your results
The Remaining Amount approaches zero but theoretically never reaches it. After 10 half-lives, less than 0.1% of the original substance remains.
Example scenarios
Carbon Dating
Initial 100g. Half-life 5,730 years. Time 5,730 years. Remaining: 50g.
Medicine
Dose 500mg. Half-life 2 hours. Time 6 hours (3 half-lives). Remaining: 62.5mg.
Key Features
- Exponential Decay Logic
- Scientific Precision
- Universal Units
Tips & Best Practices
- Ensure Time and Half-Life are in the same units (e.g., both in years or both in hours).
- In pharmacology, it typically takes 5.5 half-lives for a drug to be considered effectively cleared from the plasma.
Glossary of Terms
- Decay Constant (λ)
- The probability of decay per unit time. Related to half-life by λ = ln(2) / t½.
- Exponential Decay
- A process where the quantity decreases at a rate proportional to its current value.