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Half-Life Calculator

Calculate remaining radioactive material, find elapsed time, or determine the half-life of a substance from decay data.

Initial Amount (N₀)

Half-Life (t½)

Elapsed Time (t)

QUICK EXAMPLES

About Half-Life Calculator

Half-Life Calculator is a free scientific calculation tool that helps students, researchers, and engineers calculate remaining radioactive material, find elapsed time, or determine the half-life of a substance from decay data. Instead of looking up formulas and calculating by hand, enter your values and get instant, accurate results with clear explanations of the underlying science.

How to Use

Enter your known values Fill in the input fields with the values you have. The tool will calculate the unknowns.

Select units if applicable Choose the correct units for your calculation to ensure accurate results.

Review the solution Check the calculated result along with any formulas, steps, or diagrams shown.

Explore different values Change inputs to see how different values affect the outcome. Great for building scientific intuition.

🔒 Privacy note: All processing happens locally in your browser. Your data is never sent to any server.

Why Use Half-Life Calculator?

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Verified Formulas Half-Life Calculator implements standard scientific formulas from physics, chemistry, and mathematics textbooks. Results you can trust for homework, research, and engineering.

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Step-by-Step Solutions Where applicable, see not just the answer but the calculation steps. Perfect for learning and verifying your own work.

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Instant Computation Complex calculations that take minutes by hand are solved in milliseconds. Explore different scenarios and parameters quickly.

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Great for Students Whether you're in high school physics or graduate-level engineering, Half-Life Calculator helps you check your work and build intuition for the underlying concepts.

Frequently Asked Questions

Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation (alpha, beta, or gamma particles). The decay is random at the individual atom level but follows predictable statistical patterns for large samples, described by N(t) = N₀ × (1/2)^(t/t½).

Half-life (t½) is the time required for exactly half of a given quantity of a radioactive substance to decay. After one half-life, 50% remains. After two half-lives, 25% remains. After ten half-lives, less than 0.1% remains. Half-life is constant for each isotope regardless of temperature, pressure, or chemical state.

Half-lives span an enormous range: Carbon-14: 5,730 years (used in radiocarbon dating); Iodine-131: 8.02 days (used in medical imaging); Uranium-238: 4.5 billion years; Polonium-214: 0.000164 seconds; Radium-226: 1,600 years. Medical isotopes are chosen for appropriate half-lives — long enough to image, short enough to minimize patient exposure.