Half-Life Calculator
Calculate the half-life of a substance from initial and final amounts over elapsed time. Free decay calculator with step-by-step results, decay curves, and breakdown tables.
About This Calculator
The Half-Life Calculator computes the half-life of a substance from its initial amount, final amount, and elapsed time using the exponential decay formula: t1/2 = t × ln(2) / ln(N0 / N). It is ideal for students, scientists, pharmacists, medical professionals, and anyone studying radioactive decay, drug metabolism, or any exponential decay process.
The calculator works by applying the radioactive decay law: N = N0 × (1/2)t / t1/2, which describes how a quantity decreases over time at a rate proportional to its current value. By rearranging this equation, we solve for the half-life. The calculator also derives the decay constant (λ = ln(2) / t1/2), representing decay probability per unit time, and the remaining fraction (N / N0). Results are displayed with an interactive decay curve showing the exponential decrease over time and a half-life step bar chart showing amounts at each half-life milestone.
How to use: Enter the initial amount of your substance, the amount remaining after some time, and the total elapsed time. The calculator instantly returns the half-life, decay constant, and remaining fraction. Use consistent units throughout â if time is in hours, the half-life will be in hours.
Regional Notes
Half-life is a universal physical and chemical constant that does not vary by geography. However, its applications vary by region:
- India: The Atomic Energy Regulatory Board (AERB) governs radioactive material handling. Half-life calculations are used in nuclear medicine at institutions like AIIMS and Tata Memorial Hospital, and in radiocarbon dating at the Birbal Sahni Institute.
- United States: The FDA uses drug half-life data for pharmaceutical approval and dosing guidelines. The CDC and NRC regulate radioactive substances. Half-life is widely applied in nuclear medicine (technetium-99m: 6 hours) and carbon dating.
- United Kingdom: The MHRA and NHS use pharmacokinetic half-life data for drug dosing schedules. The Environment Agency regulates radioactive waste based on half-life classifications (short-lived vs long-lived isotopes).
Frequently Asked Questions
What is half-life?
Half-life (t1/2) is the time required for a quantity to reduce to half its initial value. It is used in nuclear physics, chemistry, and pharmacology to describe exponential decay.
How do you calculate half-life?
t1/2 = t × ln(2) / ln(N0 / N), where N0 is initial amount, N is final amount, and t is elapsed time. From the decay law N = N0 × (1/2)t / t1/2.
What is the half-life of common isotopes?
Carbon-14: 5,730 years, Uranium-238: 4.47 billion years, Iodine-131: 8 days, Technetium-99m: 6 hours, Radon-222: 3.8 days.
What is the decay constant?
The decay constant λ = ln(2) / t1/2 represents decay probability per unit time. A shorter half-life means a larger decay constant.
How is half-life used in medicine?
Drug half-life determines dosing intervals. A shorter half-life requires more frequent dosing. Nuclear medicine uses half-life to plan imaging and therapy timing.
What is the difference between half-life and mean lifetime?
Half-life (t1/2) is the time for half the nuclei to decay. Mean lifetime (τ) is the average time a nucleus survives before decaying, and τ = t1/2 / ln(2). Mean lifetime is always about 44% longer than half-life.
Can half-life be used for non-radioactive substances?
Yes. Half-life applies to any exponential decay process, including drug metabolism in the body (pharmacokinetic half-life), chemical reaction rates, capacitor discharge in electronics, and elimination of environmental pollutants.
How accurate are half-life calculations?
Half-life calculations are mathematically exact when the decay follows an exponential model. Measurement accuracy depends on the precision of input data: initial amount, final amount, and elapsed time. For radioactive isotopes with long half-lives (e.g., Uranium-238: 4.5 billion years), values are derived from statistical analysis of large sample counts.