Half-Life Calculator

Calculate remaining amount after radioactive or chemical decay over time.
Solve For

Remaining

12.5000

Time

15.00

Decay Details

Remaining12.5000
Decayed87.5000
% Remaining12.50%
Half-lives elapsed3.00

Use the Half-Life Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

Our Half-Life Calculator helps you determine the remaining quantity of a substance after a specific period, considering its radioactive or chemical decay. This is crucial for fields like nuclear medicine, environmental science, and even understanding the shelf-life of certain products. For instance, knowing the half-life of Carbon-14 is vital for archaeological dating, and understanding iodine-131 decay is critical in medical treatments and waste management in 2026.

The calculation relies on the fundamental half-life formula: N(t) = N₀ * (1/2)^(t/T), where N(t) is the remaining amount after time t, N₀ is the initial amount, and T is the half-life of the substance. This exponential decay model accurately predicts the diminishing quantity as each half-life period passes. The 't/T' exponent represents how many half-life cycles have occurred.

When using this calculator, ensure you're consistent with your time units; if the half-life is in days, your elapsed time should also be in days. Be aware that this model assumes a constant decay rate, which is generally true for radioactive isotopes but can be influenced by environmental factors for chemical decay. A common mistake is confusing initial amount with the amount decayed, so always double-check what you're trying to find.

Example: Radioactive Iodine-131 in a Medical Setting

  1. 1 A patient receives 100 MBq (Megabecquerels) of Iodine-131 for thyroid treatment. The half-life of Iodine-131 is approximately 8.02 days. We want to know how much Iodine-131 remains in the patient's system after 24.06 days.
  2. 2 Using the formula: N(t) = N₀ * (1/2)^(t/T). Here, N₀ = 100 MBq, t = 24.06 days, and T = 8.02 days. First, calculate the number of half-lives: 24.06 / 8.02 = 3. Now, N(t) = 100 MBq * (1/2)^3.
  3. 3 After 24.06 days, approximately 12.5 MBq of Iodine-131 would remain in the patient's system.
  4. 4 This remaining activity is important for monitoring radiation exposure, determining when follow-up treatments are safe, and ensuring proper disposal of biological waste. In 2026, hospitals carefully track these levels for patient safety and regulatory compliance.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

How do you calculate remaining amount after half-lives?
Remaining amount = initial amount x (1/2)^(time/half-life). After 3 half-lives, 12.5% remains (1/2³ = 1/8). After 10 half-lives, less than 0.1% remains.
What does half-life mean in simple terms?
Half-life is the time it takes for exactly half of a substance to decay or break down. After one half-life, 50% remains. After two half-lives, 25% remains. After three, 12.5% remains, and so on.
How is half-life used in medicine?
Drug half-life determines dosing frequency. A drug with a 4-hour half-life may need to be taken every 4-8 hours to maintain therapeutic levels. After 5 half-lives (about 97% eliminated), the drug is essentially cleared from your system.

You might also need

Percentage Calculator

Calculate percentages three ways: what is X% of Y, X is what % of Y, and percentage change from X to Y.

Fraction Calculator

Add, subtract, multiply, and divide fractions. Results shown as fraction, mixed number, and decimal.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation (population and sample) from a data set.