Half-Life Calculator

Calculate remaining amount after radioactive or chemical decay over time.

By Konstantin Iakovlev · Updated April 2026 · Source: Khan Academy

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

How much of a substance is left after a given stretch of time depends on its decay, and that question shows up across nuclear medicine, environmental science, and even the shelf-life of certain products. The half-life of Carbon-14 underpins archaeological dating, while iodine-131 decay drives decisions in medical treatment and waste handling well into 2026.

Behind the result is the half-life formula N(t) = N₀ * (1/2)^(t/T), in which N(t) is the amount remaining after time t, N₀ is the starting amount, and T is the half-life of the substance. This exponential model tracks how the quantity falls with each successive half-life, and the t/T exponent simply counts how many of those cycles have elapsed.

Time units have to match throughout: a half-life quoted in days requires the elapsed time in days as well. The model also assumes a constant decay rate, which holds reliably for radioactive isotopes but can shift with environmental conditions in chemical decay. Watch the distinction between the initial amount and the amount that has decayed, since mixing up the two is an easy way to answer the wrong question.

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.

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