Half Life Calculator

How to Use the Half-Life Calculator

1. Select calculation type: Choose what you want to calculate: remaining amount, elapsed time, half-life period, or decay constant.
2. Enter known values: Fill in the input fields with your known values. Select appropriate units for each quantity.
3. Calculate: Click the calculate button to solve for the unknown variable using exponential decay formulas.
4. View results: See the calculated value and a visual decay timeline showing how the substance decays over multiple half-lives.

What is Half-Life?

Half-life is the time required for half of a radioactive substance to decay. It's a fundamental property of each radioactive isotope and remains constant regardless of the initial amount. After one half-life, 50% remains; after two half-lives, 25% remains; after three half-lives, 12.5% remains, and so on. This exponential decay pattern is characteristic of all radioactive processes. For calculations involving radioactive material amounts, use our Molar Mass Calculator.

The concept of half-life was discovered by Ernest Rutherford in 1907 while studying radioactive decay. Half-life is used to measure the rate of radioactive decay, which follows first-order kinetics. Unlike chemical reactions, radioactive decay is not affected by temperature, pressure, or chemical environment because it involves nuclear processes rather than chemical bonds.

Half-Life Formulas

Basic decay equation: N(t) = N₀ × (½)^(t/t½) where N(t) is the amount remaining at time t, N₀ is the initial amount, and t½ is the half-life.

Exponential form: N(t) = N₀ × e^(-λt) where λ is the decay constant.

Decay constant: λ = ln(2) / t½ = 0.693 / t½ relates the decay constant to half-life.

Half-life from decay constant: t½ = ln(2) / λ = 0.693 / λ

Number of half-lives: n = t / t½ where n is the number of half-lives elapsed.

Fraction remaining: N(t)/N₀ = (½)^n after n half-lives.

Common Radioactive Isotopes

Carbon-14: Half-life of 5,730 years. Used in radiocarbon dating to determine the age of organic materials up to 50,000 years old. Our Stoichiometry Calculator can help with decay product calculations.

Uranium-238: Half-life of 4.468 billion years. Used to date rocks and the age of Earth. Decays to lead-206 through a series of intermediate isotopes.

Iodine-131: Half-life of 8.02 days. Used in medical treatments for thyroid conditions and as a medical tracer.

Cobalt-60: Half-life of 5.27 years. Used in radiation therapy for cancer treatment and food irradiation.

Plutonium-239: Half-life of 24,110 years. Used in nuclear weapons and reactors. Its long half-life makes nuclear waste disposal challenging.

Applications of Half-Life

Half-life calculations are essential in radiometric dating, allowing scientists to determine the age of rocks, fossils, and archaeological artifacts. In nuclear medicine, half-life determines how long radioactive tracers remain in the body and how frequently doses must be administered. Nuclear power plants use half-life data to manage fuel cycles and radioactive waste. Environmental scientists monitor radioactive contamination using half-life calculations to predict when areas will be safe. Pharmacology applies half-life concepts to drug metabolism, determining dosing schedules for medications. For solution preparation with radioactive materials, see our Dilution Calculator.

Types of Radioactive Decay

Alpha decay: Emission of a helium nucleus (2 protons, 2 neutrons). Reduces atomic number by 2 and mass number by 4. Stopped by paper or skin.

Beta decay: Emission of an electron or positron when a neutron converts to a proton or vice versa. Changes atomic number by 1. Stopped by aluminum foil.

Gamma decay: Emission of high-energy photons. No change in atomic or mass number. Requires lead shielding to stop.

Positron emission: Emission of a positron (anti-electron). Converts a proton to a neutron, decreasing atomic number by 1.

Electron capture: Nucleus absorbs an inner orbital electron, converting a proton to a neutron.

Activity and Decay Rate

Activity measures the number of decays per unit time, expressed in becquerels (Bq) where 1 Bq = 1 decay per second, or curies (Ci) where 1 Ci = 3.7 × 10¹⁰ Bq. The activity equation is A(t) = λN(t) where A is activity, λ is the decay constant, and N is the number of atoms. Activity also decreases exponentially with the same half-life as the substance: A(t) = A₀ × e^(-λt). Initial activity A₀ depends on the amount of radioactive material and its decay constant.