Half Life Calculator
Calculate the remaining amount after radioactive decay or drug metabolism, find an unknown half-life, or model multi-dose drug accumulation.
About the Half Life Calculator
A half-life is the time it takes for exactly half of a substance to decay, be eliminated, or transform. The concept applies equally to radioactive isotopes decaying in nuclear physics, drugs being metabolised and eliminated by the body, chemical reactions, and any exponential decay process. After one half-life, 50% remains. After two half-lives, 25% remains. After ten half-lives, less than 0.1% remains.
The mathematical formula governing half-life decay is N(t) = N₀ × (½)^(t/t½), where N(t) is the remaining amount at time t, N₀ is the initial amount, and t½ is the half-life. This is an exponential decay function. Our calculator lets you compute the remaining amount for any elapsed time, find an unknown half-life from before/after measurements, or model how a drug accumulates in the body across multiple doses.
Half-life has critical practical applications in medicine (dosing intervals for medications), pharmacokinetics (understanding how long a drug stays in your system), nuclear medicine (radiation safety and treatment planning), archaeology (carbon-14 dating), environmental science (pollutant persistence), and food safety (microbial reduction by heat treatment). The same mathematics applies in all these contexts.
Half-Life of Drugs and Medication
In pharmacokinetics, the biological half-life of a drug is the time required for the concentration in plasma to decrease by half. This determines dosing frequency — drugs with short half-lives (like ibuprofen at ~2 hours) require more frequent dosing, while drugs with long half-lives (like fluoxetine/Prozac at ~4 days) only need to be taken once daily and take weeks to reach steady state. After approximately 5 half-lives, a drug is considered fully eliminated from the body (about 97% cleared).
The relationship between half-life and dosing interval affects drug accumulation. If you take a drug every 6 hours and its half-life is 6 hours, the drug accumulates to a steady-state concentration of approximately double the single dose. Use the Drug Dosing mode in our calculator to model how medication levels build up over successive doses — this is the same calculation pharmacists use to determine loading doses and maintenance dosing schedules.
Radioactive Decay and Carbon Dating
Radioactive decay follows the same exponential half-life equation. Carbon-14 (¹⁴C), used in archaeological dating, has a half-life of approximately 5,730 years. By measuring the ratio of ¹⁴C to ¹²C in an organic sample and comparing it to the known atmospheric ratio, scientists can calculate how many half-lives have elapsed since the organism died — and thus its age. Objects up to about 50,000 years old can be dated with this method.
For nuclear medicine and radiation safety, knowing the half-life of isotopes determines how long materials remain hazardous. Iodine-131 (used in thyroid treatment) has a half-life of 8 days — it becomes essentially safe within 10 half-lives (~80 days). Caesium-137 from nuclear accidents has a half-life of 30 years, meaning contaminated areas remain hazardous for centuries. Uranium-238 has a half-life of 4.47 billion years — roughly the age of the Earth.