Half-life Calculator

First-order decay: radioactive isotopes, drugs leaving the body and many chemical reactions. Find the amount left, the starting amount, the time elapsed or the half-life.

KineticsRadioactivityExponential Decay

Inputs

Click Solve next to the quantity you want to find: it moves into the result below. Then fill in the other three. N₀ and N must use the same unit (grams, mol/L, %, counts…).

Input examples

Unit for N₀ and N

Initial amount N₀

Amount remaining N

Time elapsed t

Half-life t₁⁄₂

What is a Half-life?

In a first-order process the rate is proportional to how much is left. The result is exponential decay with a fixed half-life: every t₁⁄₂, half of what remains disappears — no matter how much you started with.

Radioactive nuclei decay this way, which makes them natural clocks for dating rocks and fossils. The same mathematics describes how fast medicines are cleared from the blood and how many reactions proceed.

1 t₁⁄₂50% left

3 t₁⁄₂12.5% left

10 t₁⁄₂about 0.1% left

k= ln 2 / t₁⁄₂

Live Graph

decay

amount remaining N(t)

each half-life

your time

Result

Enter the values above

Half-lives

Substance	t₁⁄₂	Use
Uranium-238	4.47×10⁹ y	dating rocks
Carbon-14	5730 y	dating fossils
Iodine-131	8.02 d	thyroid therapy
Technetium-99m	6.01 h	medical imaging
Caffeine (adult)	~5 h	pharmacology
N₂O₅ → NO₂ + O₂ (45 °C)	~23 min	reaction kinetics

Key Relations

Integrated Rate Law

Taking the logarithm turns the decay into a straight line: plotting ln N against t gives slope −k, the rate constant.

Example:

Counting Half-lives

For whole numbers of half-lives you can work it out in your head: 100% → 50% → 25% → 12.5%…

Example:

Radiocarbon Dating

Living things keep a constant ¹⁴C level. After death it decays, so the fraction left reveals the age — reliable up to about 50 000 years.

Example:

Sources & Verification

References

S. S. Zumdahl & S. A. Zumdahl, Chemistry, 10th ed., Cengage, 2018 — Ch. 12 (Chemical Kinetics: integrated rate laws) and Ch. 19 (The Nucleus: A Chemist’s View: kinetics of radioactive decay).