Free Half-Life Calculator Online
This free online half-life calculator computes remaining quantity, decay constant, and elapsed half-lives for any exponential decay process.
Decay Parameters
Remaining Quantity
Enter parameters above
How the Half-Life Calculator Works
The half-life calculator uses the exponential decay formula: N(t) = N&sub0; × (1/2)^(t/t½). Enter the initial quantity, half-life period, and elapsed time. The half-life calculator computes how much remains and the decay constant λ = ln(2)/t½.
For example, starting with 100g of a substance with a 5-year half-life, after 15 years: N = 100 × (0.5)³ = 12.5g remains. Three half-lives have passed. The half-life calculator shows the complete decay curve.
The half-life calculator also displays a decay chart showing how the quantity decreases over time. This visual representation helps you understand the exponential nature of decay — each half-life reduces the quantity by exactly half.
Half-Life Applications
In nuclear physics, half-life describes radioactive decay. Carbon-14 has a half-life of 5,730 years, used for dating organic materials. Uranium-238 has a half-life of 4.5 billion years. The half-life calculator works with any time scale.
In pharmacology, the half-life calculator helps determine drug dosing. If a medication has a 6-hour half-life, after 24 hours (4 half-lives) only 6.25% remains. This guides how often to take doses.
In chemistry, reaction half-lives tell you how fast reactants are consumed. The half-life calculator applies the same exponential decay formula regardless of the specific application.
Tips for Using the Half-Life Calculator
Match Time Units
Use the same time unit for half-life and elapsed time. The half-life calculator does not convert units.
Read the Decay Chart
The half-life calculator shows a decay curve. Notice how the curve flattens — each half-life removes less absolute quantity.
10 Half-Lives ≈ Gone
After 10 half-lives, less than 0.1% remains. The half-life calculator shows this convergence toward zero.
Decay Constant
λ = 0.693/t½ gives the per-unit-time probability of decay. The half-life calculator displays this alongside remaining quantity.
Frequently Asked Questions
More Math Calculators
Percentage Calculator
Calculate percentages, percent change, and percent of a number.
Percent Change Calculator
Calculate the percentage change between two values — increase or decrease.
Percentage Increase Calculator
Calculate the percentage increase from one value to another.
Fraction Calculator
Add, subtract, multiply, and divide fractions instantly.