Half-Life Calculator

Determine how much material remains after any number of half-lives with exponential decay assumptions.

Units cancel; use grams, counts, moles, etc.

Half-lives elapsed

2.4

Remaining amount

18.9465

Fraction remaining

0.1895

How to Use This Calculator

1

Define the initial quantity

Measure or specify the starting amount of substance before decay begins.

2

Enter half-life

Use time units appropriate for the isotope or first-order process (seconds, minutes, years, etc.).

3

Provide elapsed time

Use the same time units as the half-life to maintain consistency.

4

Interpret the results

Review how much material remains and the fraction relative to the initial amount.

Formula

N = N0 * (1/2)^(t / t1/2)

N0 is the initial amount, t elapsed time, t1/2 the half-life. The ratio N/N0 equals (1/2)^(number of half-lives).

Example

For N0 = 100 g, t1/2 = 5 years, t = 12 years: half-lives = 2.4, fraction = (1/2)^2.4 about 0.19, remaining about 19 g.

Full Description

Half-life calculations apply to nuclear decay, pharmacokinetics, and any first-order decay process. The amount decreases exponentially with time.

Knowing half-lives helps forecast safe handling periods, dosing intervals, and residual concentrations in environmental studies.

Frequently Asked Questions

Is the decay assumed first order?

Yes. The half-life model assumes exponential decay with a constant half-life.

Can the half-life change over time?

Not for true first-order processes. If it changes, use a more detailed kinetic model.

What units should I use?

Any time unit works as long as the half-life and elapsed time units match.

Can I compute elapsed time given a target amount?

This tool focuses on forward calculation. Rearranging the formula or using logarithms lets you solve for time.

Does this handle growth processes?

No. For growth with doubling times, use a similar formula with base 2 but reverse the exponent sign.