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Half-Life Calculator

Calculate the remaining amount of a substance, initial quantity, or elapsed time based on half-life.

Units (e.g., grams)
Units (e.g., grams)
Time Unit (e.g., years)
Time Unit (e.g., years)
N(t) = N0 12t/T
Result
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Units

Enter the three known variables and click Calculate to solve for the missing variable.

Understanding Half-Life

Half-life ($T$) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay, or how long stable atoms remain. However, the concept can also describe other types of decay, whether exponential or not.

The Half-Life Formula

The formula relating the remaining amount to the initial quantity is:

N(t) = N0 12t/T

Where:

How to Use the Half-Life Calculator

This tool simplifies the complex logarithmic calculations required to determine decay rates. Follow these steps:

  1. Select the variable you wish to solve for from the dropdown menu (e.g., Remaining Amount, Time, or Half-Life).
  2. Enter the known values into the input fields. The field for the variable you are solving for will be disabled automatically.
  3. Click the "Calculate" button to instantly view the result and the formula used.

Practical Calculation Example

Let's say you have a 100-gram sample of a radioactive isotope. The half-life of this isotope is known to be 10 years. You want to know how much of the substance will remain after 20 years.

Step 1: Identify the variables: $N_0 = 100$, $T = 10$, $t = 20$.

Step 2: Determine the number of half-lives elapsed: $20 \text{ years} / 10 \text{ years/half-life} = 2 \text{ half-lives}$.

Step 3: Calculate the remaining amount. Since two half-lives have passed, the quantity is halved twice: $100 \to 50 \to 25$.

Result: 25 grams remain. You can verify this using our calculator by entering the initial quantity, time, and half-life.

Frequently Asked Questions (FAQ)

Is the half-life of a substance constant?

Yes, under standard conditions, the half-life of a radioactive isotope is a constant property. It does not depend on the amount of substance present, the temperature, or pressure. This makes it a highly reliable "clock" for dating ancient objects.

Can half-life be used for non-radioactive things?

Yes. While most famous in physics, the term is borrowed in pharmacology to describe how long a drug stays in the body, and in chemistry to describe the rate of certain chemical reactions. In these contexts, it refers to the time it takes for the concentration of a substance to drop by half.

What happens after multiple half-lives?

After one half-life, 50% remains. After two half-lives, 25% remains. After three, 12.5% remains. Theoretically, the substance never fully reaches zero, but after about 10 half-lives, less than 0.1% of the original substance remains, which is often considered negligible.

Common Applications