A half-life is the time it takes for half of a radioactive substance to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%; and so on.

What formula does this calculator use?

N(t) = N₀ × (1/2)^(t / t½), where N₀ is the initial quantity, t is elapsed time, and t½ is the half-life. Rearranging gives t = t½ × log(N/N₀) / log(0.5).

What units can I use?

Any consistent unit works — seconds, minutes, hours, days, or years — as long as the elapsed time and half-life share the same unit. The tool lets you pick the unit from a dropdown.

What is the decay constant?

The decay constant λ (lambda) equals ln(2) / t½. It represents the probability per unit time that a nucleus will decay. A higher λ means faster decay.

Can I use this for Carbon-14 dating?

Yes. Carbon-14 has a half-life of about 5,730 years. Enter 5730 as the half-life in years, set the initial amount to 100%, enter the remaining percentage, and calculate elapsed time.

Does this work for non-radioactive exponential decay?

Yes. Any process that follows exponential decay (drug concentration, bacterial die-off, capacitor discharge) can be modeled here by entering the appropriate half-life value.

Half Life Calculator

Find the remaining quantity of a radioactive substance after decay, or calculate how long it takes to reach a given amount.

Half-Life Calculator

Initial Quantity (N₀)

Any unit: grams, moles, atoms, %, Bq…

Half-Life (t½)

Unit

Elapsed Time (t)

Must use the same unit as the half-life above.

Common Isotopes

Enter values and click Calculate to see results.

Remaining Quantity

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Decay Constant (λ)

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Half-Lives Elapsed

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Fraction Remaining

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Decay Table

Half-Lives (n)	Elapsed Time	Remaining Qty	% Remaining

Summary

This half-life calculator uses the standard radioactive decay formula N(t) = N₀ × (1/2)^(t/t½) to compute how much of a substance remains after a given time, or how long ago a sample had a higher activity. It also derives the decay constant λ = ln(2) / t½. Results are instant and fully client-side.

How it works

Choose a calculation mode: remaining quantity, elapsed time, or number of half-lives.
Enter the initial quantity and the half-life period (with units).
For remaining quantity mode, enter the elapsed time.
For elapsed time mode, enter the final remaining quantity.
Click Calculate to see the result, decay constant, and a decay table.

Use cases

Determine how much Carbon-14 remains in an archaeological sample.
Calculate residual radioactivity of a medical isotope (e.g., Iodine-131).
Verify nuclear waste decay timelines for safety planning.
Solve physics and chemistry homework problems on radioactive decay.
Understand exponential decay behavior in classroom demonstrations.
Check how many half-lives have elapsed between two measured quantities.
Compute the decay constant for a given isotope.
Estimate when a radioactive source falls below a safe activity threshold.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu