Exponential Decay Calculator

A = A₀ · e^(-kt). Compute remaining quantity, half-life, or decay constant.

Inputs

Result

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How to use this calculator

  • Enter the initial amount, decay constant k, and elapsed time t.
  • Read the remaining amount and half-life.

About this calculator

Exponential decay: A = A₀e^(-kt), with k > 0. Models radioactive decay, drug clearance, capacitor discharge, and any process where the decay rate is proportional to the remaining amount. Half-life — time for half to decay — equals ln(2)/k regardless of starting amount.

Frequently asked

How is k related to half-life?+
t½ = ln(2)/k ≈ 0.693/k. So if you know t½, k = ln(2)/t½.
Why is half-life independent of starting amount?+
Because each half-life period reduces the quantity by half regardless of where you start. After 2 half-lives, ¼ remains; after 3, ⅛.
What's a real-world example?+
Carbon-14 has half-life ~5,730 years. So an organism that died 11,460 years ago has ¼ of its original C-14 remaining.
Is decay always exponential?+
No — depends on physics. First-order kinetics (radioactive decay, single-substrate enzymes) gives exponential. Higher-order kinetics give different curves.
Can the calculator handle drug clearance?+
Yes — enter dose, elimination rate constant, and time. The fraction-remaining shows percentage of original dose still in body.

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