Understand the physical quantity
What is Radioactive Decay and Half-Life?
Radiation measurement distinguishes activity, detected count rate, concentration, attenuation, absorbed dose, and equivalent dose. A conversion or screening relationship must preserve which physical quantity was actually entered.
Complete the exponential physical-decay workflow without hardcoded isotope data or separate thin reverse-calculation pages.
The relationship
Keep quantity and basis explicit
Activity follows A = A₀·2^(−t/T½) = A₀e^(−λt), where λ = ln(2)/T½. Reverse modes solve A₀, t, or T½. Integrated transformations over the interval equal A₀(1−e^(−λt))/λ using seconds because 1 Bq = 1 s⁻¹.
See the workflow
What the calculator is doing
1Entered physical quantity2Apply decay, detector, or geometry model3Reported activity, count, or dose quantity
Worked context
Read the output in context
An initial 1,000 Bq after two 10-day half-lives has 250 Bq remaining, 75% decayed, and about 9.35×10⁸ integrated transformations over the 20 days.
Interpret with care
Important boundary
This models one isolated physical exponential decay component. It does not include daughter ingrowth, decay chains, mixtures, biological clearance, effective half-life, production, detector response, dose, contamination, risk, or disposal decisions.
The result does not provide a safety limit, medical interpretation, personal-risk estimate, shielding approval, release decision, treatment plan, or regulatory authorization.
Browse Light & radiation for related physical quantities.
Quick guide
How to use this calculator
- Choose the physical radiation quantity and solve direction before entering measurements. Keep activity, count rate, absorbed dose, equivalent dose, time, distance, material attenuation, and detector efficiency separate.
- Enter isotope, detector, geometry, material, or field data only from an applicable measurement or authoritative record; these pages do not supply generic safety values or hidden presets.
- Use companion outputs to reconcile the arithmetic, then retain every stated boundary. A screening result is not authorization for exposure, handling, shielding, release, transport, treatment, or disposal.
Calculation method
How the radioactive decay and half-life calculator works
Complete the exponential physical-decay workflow without hardcoded isotope data or separate thin reverse-calculation pages.
Activity follows A = A₀·2^(−t/T½) = A₀e^(−λt), where λ = ln(2)/T½. Reverse modes solve A₀, t, or T½. Integrated transformations over the interval equal A₀(1−e^(−λt))/λ using seconds because 1 Bq = 1 s⁻¹.
Worked example
Radioactive Decay and Half-Life example
An initial 1,000 Bq after two 10-day half-lives has 250 Bq remaining, 75% decayed, and about 9.35×10⁸ integrated transformations over the 20 days.
Activity follows A = A₀·2^(−t/T½) = A₀e^(−λt), where λ = ln(2)/T½. Reverse modes solve A₀, t, or T½. Integrated transformations over the interval equal A₀(1−e^(−λt))/λ using seconds because 1 Bq = 1 s⁻¹.
Supported inputs
Precision and limits
Radiation boundary
This models one isolated physical exponential decay component. It does not include daughter ingrowth, decay chains, mixtures, biological clearance, effective half-life, production, detector response, dose, contamination, risk, or disposal decisions.
Units and precision
Calculations normalize compatible units once, retain working precision, and round only for display. Very small and large nonzero values use scientific notation; displayed precision cannot exceed the entered measurements or source data.
Decision boundary
This calculator does not provide a dose limit, regulatory threshold, medical interpretation, personal-risk estimate, radiation-protection program, or professional approval. Use applicable instruments, current authoritative data, and qualified radiation-protection expertise for consequential decisions.
Privacy
Entered values and results stay in this browser and are not sent to analytics or third parties.
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