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

Name: Radioactive Contamination Decay Calculator
Availability: InStock
Author: Nham Vu

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

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

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: 2026-07-24 · Reviewed by Nham Vu