Half-Life Calculator

Half-Life is the time required for a quantity to reduce to half its initial value. This concept applies to radioactive decay, chemical reactions, drug metabolism, and many other processes.

The exponential decay formula:

N(t) = N₀ × (1/2)^(t / t½)

Where:

• N(t) = remaining quantity after time t
• N₀ = initial quantity
• t = elapsed time
• t½ = half-life period

This calculator solves for three different unknowns:

1. Remaining quantity: Given initial amount, half-life, and elapsed time, calculate what remains
2. Elapsed time: Given initial and remaining amounts plus half-life, find how much time has passed
3. Half-life period: Given initial and remaining amounts plus elapsed time, determine the half-life

Rearranged formulas:

• Time elapsed: t = t½ × log(N₀/N) / log(2)
• Half-life: t½ = t × log(2) / log(N₀/N)

Real-world examples:

• Carbon-14 has a half-life of 5,730 years (used in archaeological dating)
• Iodine-131 has a half-life of 8.02 days (used in medical treatments)
• Caffeine in the human body has a half-life of about 5 hours
• Uranium-238 has a half-life of 4.47 billion years

After N half-lives, the fraction remaining is:

• 1 half-life: 50% remains
• 2 half-lives: 25% remains
• 3 half-lives: 12.5% remains
• 5 half-lives: 3.125% remains
• 10 half-lives: 0.098% remains (essentially gone)