Half-Life Calculator

Welcome to our Half-Life Calculator. Whether you're a scientist, student, or curious mind, this tool helps you accurately determine decay rates for various substances. From radioactive isotopes to pharmacokinetics, our calculator provides precise results for your research and educational needs.

Key Features:

Understanding half-life is crucial in fields like nuclear physics, medicine, and environmental science. Our calculator simplifies complex decay calculations, allowing you to focus on interpreting results and advancing your research. Simply input your data, choose your preferred time unit, and let our tool do the heavy lifting.

Understanding Half-Life

Half-life is the time required for a quantity to reduce to half of its initial value. This concept is widely applicable in various scientific disciplines:

Our calculator empowers you to explore these phenomena with ease and precision, supporting both academic and professional endeavors in science and research.

How to Use the Half-Life Calculator: A Comprehensive Guide

Step-by-Step Instructions

  1. Enter the initial amount of the substance.
  2. Input the half-life of the substance.
  3. Specify the time elapsed since the initial measurement.
  4. Select the appropriate time unit (seconds, minutes, hours, days, or years).
  5. Click the "Calculate" button to get your results.

Tips for Accuracy

  • Use consistent units for half-life and time elapsed.
  • For very long or short half-lives, consider using scientific notation.
  • Double-check your input values for accuracy.

Mathematical Examples

Problem: A sample of radioactive iodine-131 has an initial amount of 100 mg and a half-life of 8 days. How much remains after 24 days?

Solution:

  • Initial amount: 100 mg
  • Half-life: 8 days
  • Time elapsed: 24 days
  • Number of half-lives: 24 / 8 = 3
  • Remaining amount: 100 * (0.5)^3 = 12.5 mg

Result: 12.5 mg of iodine-131 remains after 24 days.

Problem: A drug has a half-life of 4 hours in the human body. If a patient takes a 200 mg dose, how much of the drug remains in their system after 10 hours?

Solution:

  • Initial amount: 200 mg
  • Half-life: 4 hours
  • Time elapsed: 10 hours
  • Number of half-lives: 10 / 4 = 2.5
  • Remaining amount: 200 * (0.5)^2.5 ≈ 53.033 mg

Result: Approximately 53.033 mg of the drug remains in the patient's system after 10 hours.

Problem: An archaeological sample contains 25% of its original carbon-14. The half-life of carbon-14 is 5,730 years. How old is the sample?

Solution:

  • Initial amount: 100% (normalized)
  • Current amount: 25%
  • Half-life: 5,730 years
  • Use the formula: t = (ln(25/100) / ln(0.5)) * 5,730
  • t ≈ 11,460 years

Result: The archaeological sample is approximately 11,460 years old.