What formula does this calculator use?

It uses the standard radioactive decay law: A(t) = A₀ × e^(−λt), where A₀ is the initial activity, t is the elapsed time, and λ (the decay constant) = ln(2) / t½. This is exact for a pure radionuclide with no ingrowth from parent nuclides.

Does it account for daughter products?

No. This calculator models a single-nuclide simple exponential decay. If your nuclide produces radioactive daughters (e.g., Ra-226 → Rn-222 chain), you need a Bateman-equation solver. The result here is the parent activity only.

What is the decay constant λ?

The decay constant λ (lambda) is the probability of decay per unit time for a single nucleus. It is related to the half-life by λ = ln(2) / t½ ≈ 0.6931 / t½. A larger λ means faster decay.

What units can I use?

Activity: Bq, kBq, MBq, GBq, Ci, mCi, µCi, or nCi. Time: seconds, minutes, hours, days, years, or millennia. Mixed time units (e.g. half-life in years, elapsed in hours) are handled automatically by converting everything to seconds internally.

How many half-lives until activity is negligible?

After 7 half-lives, roughly 0.78% of the original activity remains; after 10, about 0.098%. For practical radiation protection, 7–10 half-lives is often used as the decay-in-storage criterion.

Is this accurate for very long elapsed times?

The formula is mathematically exact for any elapsed time, but for very large multiples of the half-life the remaining activity will be extremely small (effectively zero). Floating-point precision limits apply below about 10⁻¹⁵ of the initial activity.

Radioactive Contamination Decay Calculator

Enter initial activity, half-life, and elapsed time to calculate remaining contamination using A(t) = A₀ × e^(−λt).

Decay Inputs

Initial Activity (A₀)

Half-Life (t½)

Default: Cs-137 (30.17 years)

Elapsed Time (t)

Quick Presets

Results

Enter values above and click Calculate.

Remaining Activity A(t)

Becquerel (Bq)

Curie (Ci)

Remaining

Decayed

Half-lives

Decay constant λ: s⁻¹

Activity at Selected Intervals

Half-lives elapsed	Activity (Bq)	% Remaining

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Summary

This calculator applies the fundamental radioactive decay law A(t) = A₀ × e^(−λt), where λ = ln(2) / t½, to determine the remaining activity of a contaminated surface, sample, or source after a given time has elapsed. It accepts initial activity in Becquerel or Curie, half-life in any time unit, and elapsed time to output remaining activity along with the fraction decayed and number of half-lives elapsed. Useful for radiation protection planning, decontamination scheduling, and nuclear engineering coursework.

How it works

Enter the initial contamination activity and select the unit (Bq, kBq, MBq, GBq, Ci, mCi, µCi, or nCi).
Enter the nuclide half-life and choose the appropriate time unit (seconds through years).
Enter the elapsed time since the initial measurement, in any time unit.
Click Calculate — the tool computes λ = ln(2) / t½, then A(t) = A₀ × e^(−λt).
Results show remaining activity in Bq and Ci, percentage remaining, fraction decayed, and number of half-lives elapsed.
Use the time-series table to see activity at 0, 1, 2, 5, and 10 half-life intervals for trend reference.

Use cases

Determine when a contaminated area will decay to a safe re-entry level.
Schedule decontamination work based on projected activity drop.
Verify radioactive waste decay-in-storage timelines before disposal.
Calculate remaining activity in a calibration source at a given date.
Teaching the exponential decay law in nuclear engineering and health physics courses.
Quick sanity-check calculations before full Monte Carlo transport modeling.
Estimate when a short-lived medical isotope source will be depleted.
Assess ingested or inhaled contamination activity at a later time point.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu