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)=N0e−λt=N0(12)t/t1/2N(t)=N_0e^{-\lambda t}=N_0\left(\frac12\right)^{t/t_{1/2}} and activity is A=λNA=\lambda N. For a daughter nuclide starting from zero, N2(t)=λ1N0λ2−λ1(e−λ1t−e−λ2t)N_2(t)=\frac{\lambda_1N_0}{\lambda_2-\lambda_1}\left(e^{-\lambda_1 t}-e^{-\lambda_2 t}\right) when λ1≠λ2\lambda_1\ne\lambda_2.

Notation used in the formulas: RR = Remaining Quantity; x1x_{1} = Initial Quantity; x2x_{2} = Decay Input; x3x_{3} = Half-Life; x4x_{4} = Decay Constant λ; x5x_{5} = Elapsed Time; x6x_{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.

Reference Book

University Physics with Modern Physics

Hugh D. Young and Roger A. Freedman · Pearson

A common undergraduate physics text covering mechanics, electricity, waves, energy, and introductory modern physics.

View Book

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.

Related Calculators

Radioactive Decay Calculator: Formula & Use Cases | MCPCalc