Updated Physics & Decay

Half-Life Calculator

Calculate remaining quantity, time to decay, and half-life for exponential decay processes. Includes an activity mode for radioactive decay in Bq or Ci.

Remaining Quantity Time to Decay Half-Life Solver Activity Mode

All-in-One Half-Life Calculator

Select a mode to compute remaining quantity, time, half-life, or radioactive activity based on exponential decay.

Decay law: Q = Q₀ × (1/2)t / T₁/₂. Valid for exponential decay processes.

Time to reach Q: t = T₁/₂ × log(Q / Q₀) / log(1/2), where log is natural or base 10 consistently.

Solving for half-life from known initial and remaining quantity over a measured time interval.

Radioactive activity decays with the same exponential law as quantity: A = A₀ × (1/2)t / T₁/₂.

Half-Life Calculator – Remaining Quantity, Time to Decay, and Half-Life

This Half-Life Calculator helps you solve common exponential decay problems in physics, chemistry, nuclear medicine, and radiology. You can compute how much of a substance remains after a given time, how long it takes to decay to a certain level, or what the half-life is based on experimental data.

Half-Life and Exponential Decay

Half-life is the time required for a quantity to decrease to half of its original value. Many processes follow exponential decay, including radioactive decay, some pharmacokinetic drug models, and certain chemical reactions.

The general decay law is:

Q = Q₀ × (1/2)t / T₁/₂

where Q is the remaining quantity, Q₀ is the initial quantity, t is the elapsed time, and T₁/₂ is the half-life.

Time to Decay to a Target Amount

If you know the half-life and want to find how long it takes to decay from Q₀ to Q, you can rearrange the equation:

t = T₁/₂ × \frac{\log(Q / Q₀)}{\log(1/2)}

This is useful when you want to know how long it takes for a radioactive sample or drug concentration to fall below a certain threshold.

Solving for Half-Life from Measurements

If you measure a quantity Q₀ at time 0 and Q at time t, you can estimate the half-life:

T₁/₂ = t × \frac{\log(1/2)}{\log(Q / Q₀)}

This is often used in laboratory experiments to determine the half-life of unstable isotopes or to approximate biological half-lives.

Activity in Radioactive Decay

Radioactive decay is often expressed as activity, measured in becquerels (Bq) or curies (Ci). Activity decays with the same half-life as the underlying nuclei, so the same formulas apply:

  • A = A₀ × (1/2)t / T₁/₂
  • Fraction remaining = A / A₀
  • Percentage remaining = 100 × A / A₀

Important Notes

  • This calculator assumes ideal exponential decay with a constant half-life.
  • Real-world systems may have multiple phases or non-ideal behavior.
  • For medical or safety-critical decisions, always consult a qualified professional.

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