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Half-Life Calculator ⚛️

Calculate radioactive decay using the half-life formula:

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Half-Life Calculator Guide & Information

Learn how radioactive decay works, why half-life is important, and view real-world examples.

What is Half-Life?

Half-life is the time required for a substance to decay to half of its original amount. It is commonly used in physics, chemistry, archaeology, and medicine.

How This Calculator Works

The tool uses the decay formula N(t) = N₀ (1/2)^(t / t₀.₅) and automatically converts units like minutes, hours, days, and years for accurate calculations.

Why Unit Conversion Matters

Half-life and elapsed time may be in different units. The calculator converts everything to seconds internally to ensure correct decay calculations.

Where Half-Life Is Used

Half-life calculations are used in radioactive decay, radiocarbon dating, nuclear medicine, battery discharge rates, and chemical reactions.

What The Steps Show

Each step explains the formula with LaTeX, including unit conversion, number of half-lives, decay factor, and remaining amount calculations.

Frequently Asked Questions

What does N(t) represent?
N(t) is the remaining amount of substance after a certain time t has passed.
Can I use any unit for half-life?
Yes. You can choose seconds, minutes, hours, days, or years. The calculator converts everything automatically.
Why does decay never reach zero?
Radioactive decay is exponential. The quantity gets extremely small but mathematically never becomes exactly zero.
What if my input is too large or small?
The calculator uses scientific notation for values like 2.4 × 10⁻⁶ or 8.9 × 10⁸ so results remain clean and readable.
Is half-life only for radioactive elements?
No. Half-life is used in medicine (drug elimination), battery discharge, chemical reactions, and more.

Example Calculations

Example 1: Carbon-14 Dating
Initial: 100 g, Half-Life: 5730 years, Time: 11460 years
Remaining: 25 g (since 2 half-lives passed)
Example 2: Iodine-131 (Medical Use)
Initial: 50 mg, Half-Life: 8 days, Time: 16 days
Remaining: 12.5 mg (2 half-lives elapsed)
Example 3: Drug Clearance
Initial: 200 mg, Half-Life: 3 hours, Time: 9 hours
Remaining: 25 mg

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