MCPCalc

Radioactive Decay Calculator

Compute parent decay, activity, elapsed half-lives, and an optional two-isotope daughter chain.

Scratchpad (not saved)

What This Calculator Does

This calculator models exponential decay from either a half-life or a decay constant, then optionally adds a single daughter isotope in a two-stage chain. It is intended for straightforward radioactive-decay estimates rather than a full nuclide database.

It combines Initial Quantity, Decay Input, Half-Life, Decay Constant λ to estimate Remaining Quantity, Activity, Elapsed Half-Lives.

Formula & Method

Core equations: Parent decay is N(t)=N_0e^{-lambda t}=N_0left( rac12 ight)^{t/t_{1/2}} and activity is A=lambda N. For a daughter nuclide starting from zero, N_2(t)= rac{lambda_1N_0}{lambda_2-lambda_1}left(e^{-lambda_1 t}-e^{-lambda_2 t} ight) when lambda_1 elambda_2.

Notation used in the formulas: R = Remaining Quantity; x_{1} = Initial Quantity; x_{2} = Decay Input; x_{3} = Half-Life; x_{4} = Decay Constant λ; x_{5} = Elapsed Time; x_{6} = Daughter Half-Life.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it for isotope inventory estimates, laboratory decay timing, or any setting where you need a parent remainder, current activity, and a simple daughter build-up approximation.

Inputs Used

  • Initial Quantity: Used directly in the calculation.
  • Decay Input: Used directly in the calculation.
  • Half-Life: Used directly in the calculation.
  • Decay Constant λ: Used directly in the calculation.
  • Elapsed Time: Used directly in the calculation.
  • Daughter Half-Life: Used directly in the calculation.
  • Two-Isotope Chain: Used directly in the calculation.

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