Half-Life & Decay Calculator

Solve the remaining quantity, initial mass, half-life duration, or decay constant of any substance.

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Select the variable you want to solve for, enter your known values (such as initial mass, time, and half-life), and view the decay working.

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A Helpful Guide to Half-Life and Exponential Decay

Half-life is the amount of time required for a quantity of a substance to decrease to exactly half of its initial value. This concept is most famous in nuclear physics, where it describes the decay of unstable radioactive atoms, but it is also used in chemistry, medicine, and biology. Understanding half-life helps scientists predict how long substances will remain active or trace the age of historical artifacts.

The Decay Mathematics

Half-life calculations utilize exponential formulas because decay happens at a rate proportional to the current quantity. In each half-life interval, the remaining amount drops by 50%. After one interval, you have 50% left; after two, you have 25%; after three, 12.5%, and so on.

These calculations require raising fractions to powers, which you can evaluate using our calculating exponential changes tool. To solve for the decay time when you know the initial and final quantities, you must use logarithmic formulas, which you can solve using our logarithmic math tools or our scientific calculator display tool.

Practical Decay Applications

Carbon Dating in Archeology: Researchers measure the remaining Carbon-14 (half-life of 5,730 years) in bones or wood to find the age of fossils.
Medical Treatment Dosages: Doctors use isotopes with short half-lives for diagnostic scans so the radiation clears the body quickly. You can check percentage drops using our calculating percentage shares tool.
Nuclear Waste Storage: Environmental engineers calculate how long toxic radioactive waste must be isolated before it is safe.
Pharmacology Clearances: Drug designers track the half-life of medications in the blood to determine correct dosing schedules, which you can average using our calculating averages tool.

The Decay Constant Explained

The decay constant (often represented by the Greek letter lambda) measures the probability of decay per unit of time. It is inversely related to half-life. A substance with a very short half-life decays rapidly, meaning it has a large decay constant.

By utilizing our solver, you can switch between half-life time and the decay constant. The calculator automatically handles the logarithmic conversions, letting you focus on analyzing the data rather than doing algebraic derivations.

Example of Carbon Decay

Suppose an archeologist finds a piece of ancient charcoal that contains exactly 25% of the Carbon-14 found in living trees.

Since the Carbon-14 level has dropped to 25%, we know it has undergone exactly two half-life intervals (100% to 50% is one, and 50% to 25% is two). Knowing the half-life of Carbon-14 is 5,730 years, we multiply the number of intervals by the half-life: 2 × 5,730 = 11,460 years. The charcoal is approximately 11,460 years old. This example illustrates how half-life acts as a natural geological clock.