Half-Life Remaining Amount Calculator Formula
Understand the math behind the half-life remaining amount calculator. Each variable explained with a worked example.
Formulas Used
Amount Remaining
remaining = initial_amount * pow(0.5, num_half_lives)Percent Remaining
pct_remaining = pow(0.5, num_half_lives) * 100Amount Decayed
amount_decayed = initial_amount * (1 - pow(0.5, num_half_lives))Variables
| Variable | Description | Default |
|---|---|---|
initial_amount | Initial Amount | 100 |
num_half_lives | Number of Half-Lives Elapsed | 5 |
How It Works
Remaining After n Half-Lives
Each half-life reduces the remaining amount by half. After n half-lives, the fraction remaining is (1/2)^n.
Formula
N = N0 × (1/2)^n
This applies to radioactive decay, drug elimination, chemical degradation, and any first-order process.
Worked Example
Starting with 100 grams, after 5 half-lives.
- 01Remaining = 100 × (0.5)^5
- 02Remaining = 100 × 0.03125 = 3.125 grams
- 03Only 3.125% remains after 5 half-lives
Frequently Asked Questions
How many half-lives until less than 1% remains?
After 7 half-lives: (0.5)^7 = 0.78% remains. So 7 half-lives reduces the amount to less than 1% of the original.
Does this work for drug elimination?
Yes. Drugs eliminated by first-order kinetics follow the same math. A drug with a 4-hour half-life is essentially gone after 5-7 half-lives (20-28 hours).
Can n be a fraction?
Yes. After 2.5 half-lives, the remaining fraction is (0.5)^2.5 = 0.177 = 17.7%. The formula works for any non-negative value of n.
Ready to run the numbers?
Open Half-Life Remaining Amount Calculator