Introduction to Half-Life Calculator
Calculate radioactive half-life, remaining quantity, and decay time. Free physics and chemistry calculator.
Whether you are a student, a professional, or simply looking to understand the mechanics behind this computation, our comprehensive guide will walk you through the fundamental principles, the exact mathematical formula, and concrete examples of half-life calculator in action.
Detailed Explanation
How it Works & Explanation
Half-life is the time required for half of a radioactive substance to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on.
This calculator works for radioactive decay, pharmacokinetics (drug elimination), and any exponential decay process.
Healthy Tips & Guidelines
- Common half-lives: Carbon-14 = 5730 years, Uranium-238 = 4.5 billion years, Iodine-131 = 8 days.
- After 10 half-lives, less than 0.1% of the original substance remains.
- In medicine, drug half-life determines dosing frequency.
Common Mistakes to Avoid
- **Thinking decay is linear:** It's exponential — the rate slows down as less material remains.
- **Confusing half-life with mean lifetime:** Mean lifetime τ = t₁/₂ / ln(2) ≈ 1.443 × t₁/₂.
Math Formula
Mathematical Formula
N(t) = N 0 × (1 / 2)^t/t (1/2)This is the mathematical formula used to compute your results.
Tips & Best Practices
- Common half-lives: Carbon-14 = 5730 years, Uranium-238 = 4.5 billion years, Iodine-131 = 8 days.
- After 10 half-lives, less than 0.1% of the original substance remains.
- In medicine, drug half-life determines dosing frequency.
Common Mistakes to Avoid
- Thinking decay is linear: It's exponential — the rate slows down as less material remains.
- Confusing half-life with mean lifetime: Mean lifetime τ = t₁/₂ / ln(2) ≈ 1.443 × t₁/₂.
Step-by-Step Examples
Worked Examples
Standard Baseline Calculation
This is a baseline example showing how the Half-Life Calculator takes standard parameters and processes them through our local algorithm. You can execute this exact scenario in the interactive calculator.
Given Parameters
Decay ParametersStandard value
Expected Result
StatusCalculated instantly