How many half-lives does it take for a substance to fully decay?

In theory, a substance never reaches exactly zero since each half-life only removes half of what remains. In practice it's considered negligible after about 7 half-lives, when less than 1% of the original amount remains (0.5^7 ≈ 0.78%).

Can this calculator solve for the elapsed time instead of the remaining amount?

Yes, switch 'Solve for' to elapsed time and provide the initial amount, remaining amount and half-life. The calculator rearranges N(t) = N₀ × 0.5^(t ÷ half-life) to t = half-life × log₂(N₀ ÷ N(t)).

Half-Life Calculator

Calculate the remaining amount of a substance or the elapsed time using radioactive decay.

How this is calculated

N(t) = N₀ × 0.5^(t ÷ half-life)

Assumptions used in this calculation

Units must match: Elapsed time and half-life must be in the same time unit for the result to be meaningful.

About this calculator

The half-life calculator uses the exponential decay formula to find the remaining amount of a substance after a given time, or the elapsed time given a remaining amount.

Worked example

N₀=100, t=15, half-life=5

Result: 12.5 remaining (12.5%)

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Frequently asked questions

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Calculate the molecular weight of a chemical compound from its formula.

Half-Life Calculator

About this calculator

Frequently asked questions

How many half-lives does it take for a substance to fully decay?

Can this calculator solve for the elapsed time instead of the remaining amount?

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