Radioactive activity decreases according to a fixed mathematical law for each isotope. The arithmetic is straightforward: start with a calibration activity and date, apply the isotope half-life, and calculate the activity at another date or the date a lower target prompt is reached. The hard part is not the equation. The hard part is knowing whether the input is the right source record and whether the output is suitable for the intended record, survey, transport, waste, medical, or field-safety decision.
This guide treats decay correction as a pre-review calculation. It explains the equation, the half-life data sources, source-certificate boundaries, target-activity caveats, and the gaps that remain before a value can be used in official source records, dose-rate calculations, shipment records, transport/waste decisions, or radiation work planning.
The Decay Equation
Radioactive decay is a first-order process: the number of atoms that decay per unit time is proportional to the number of atoms present. This gives an exponential decrease in activity over time:
A(t) = A&sub0; × (1/2)^(t / t½)
Where A(t) is the activity at time t, A&sub0; is the initial activity at the reference (calibration) date, t is the elapsed time, and t½ is the half-life. The equation can also be written using the decay constant λ: A(t) = A&sub0; × e^(-λt), where λ = ln(2) / t½ = 0.693 / t½.
Both forms are mathematically equivalent. The half-life form is more intuitive for quick estimates: after one half-life, half remains; after two half-lives, one quarter remains; after ten half-lives, about one thousandth remains. The exponential form is more convenient for calculating decay constants and for working with computer programs.
An important property: the decay rate is independent of temperature, pressure, chemical state, and all other external conditions. A Cs-137 source decays at the same rate whether it is in a laboratory, buried underground, or orbiting in space. This is why the half-life is a true physical constant for each isotope, not an approximation.
A(t) = A&sub0; × (1/2)^(t / t½)
Equivalent form: A(t) = A&sub0; × e^(-0.693 × t / t½)
After n half-lives, the remaining fraction is (1/2)^n. After 10 half-lives, about 0.1% of the original activity remains.
Radioactive Decay Calculator
Calculate current source activity from original calibrated activity and elapsed time using the decay equation. Find when a source reaches a target activity for replacement or disposal planning.
Half-Life Data for Common Industrial Isotopes
Half-life rows should be treated as source pointers, not as source-certificate verification. The app includes local rows for Ir-192, Se-75, Co-60, Cs-137, Am-241, and Ra-226. NNDC NuDat and IAEA LiveChart are appropriate source pointers for evaluated nuclear data review, but the final activity basis still depends on the source certificate, source serial number, calibration date and time, isotope identity, manufacturer record, license conditions, and procedure context.
- Shorter-lived rows: Ir-192 and Se-75 can change enough over weeks or months that calibration-date and evaluation-date accuracy matter.
- Longer-lived rows: Co-60, Cs-137, Am-241, and Ra-226 may change slowly compared with daily operations, but transfer, possession, security, disposal, and survey requirements still dominate source-management decisions.
- Unsupported rows: If the isotope is not listed, use a current accepted data source and the controlling procedure; do not force the app to stand in for a medical, waste, or transport system.
The same equation can be correct while the source-management conclusion is still wrong. Verify the isotope row, source record, calibration time, license condition, survey basis, and intended use before carrying the number into any record or field decision.
Target-Activity Prompts
The reverse equation answers a narrow math question: how many days until a lower activity prompt is reached?
t = t½ × log2(A&sub0; / A(target))
That answer is useful for a review conversation, but it does not decide whether a source should be replaced, shipped, transferred, stored, disposed, or used in a job. A target activity may come from a manufacturer exposure table, instrument performance criterion, radiography procedure, procurement plan, waste program, or local administrative prompt. Each one has different authority and evidence requirements.
Before using a target-date prompt, confirm the current source certificate, source serial number, device rating, procedure, manufacturer support, inventory record, leak-test status, survey basis, license conditions, and qualified review path.
A target-date prompt can support planning, but final source exchange, ordering, shipment, and installation timing belongs in the licensee procedure, manufacturer/source supplier process, and RSO or qualified reviewer workflow.
Decay-in-Storage Programs
Decay-in-storage is a regulated program decision, not an automatic result of a half-life count. The decay equation can show how much activity remains after a selected number of half-lives, but it cannot decide whether a material is eligible for the facility program, whether the storage period is adequate, whether survey results meet the procedure, or whether a release/disposal path is authorized.
For any decay-in-storage review, check the current license, Agreement State or NRC requirements, procedure, isotope form, container/source condition, survey instrument, background method, documentation, and final disposition rules. Long-lived sealed sources usually require manufacturer, authorized-recipient, waste-broker, or regulator involvement rather than a calculator-driven disposal path.
Never use the decay equation alone as release or disposal evidence. Survey method, instrument calibration, background comparison, records, license conditions, and qualified review control whether a material can leave radioactive-material controls.
Source Record Boundaries
Source records are controlled documents. A decay calculator can help check the arithmetic used in a record, but it is not the record itself and it cannot verify source identity, source serial number, device model, possession authorization, leak-test status, inventory count, NSTS reporting, or financial-assurance obligations.
For regulated source tracking, start with the current license and procedure. Then reconcile the source certificate, manufacturer/source supplier information, source/device records, physical inventory, leak-test records, survey records, transfer/disposal records, and any NRC or Agreement State reporting requirements. If industrial radiography rules or other program-specific regulations apply, those requirements must be reviewed directly.
Keep the distinction clear: the app can reproduce decay arithmetic from entered prompts, while the licensee record controls source identity, source custody, leak-test status, inventory evidence, transfer/disposal evidence, and regulatory reporting.
Transport, Transfer, and Waste Boundaries
Transport, transfer, and waste questions depend on more than activity decay. Package type, source form, A1/A2 or exemption-threshold context, contamination, transport index, labels, placards, emergency response information, authorized recipient status, transfer documentation, disposal facility acceptance, and license conditions all matter.
10 CFR 20.2001 and 10 CFR 30.41 are source pointers for disposal and byproduct-material transfer context, while 49 CFR 173 Subpart I is a source pointer for Class 7 radioactive-material transport context. A decay number can be one input to those reviews, but the calculator cannot determine the legal path, final classification, or authorization.
For source end-of-life planning, gather the source certificate, source/device records, license conditions, supplier/manufacturer return information, authorized-recipient documentation, waste-broker acceptance criteria, DOT packaging/shipping basis, survey records, and RSO/regulatory review before acting.