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Free online half-life calculator for radioactive decay, drug elimination, and exponential decay. Calculate remaining quantity, time elapsed, and half-life with detailed step-by-step solutions.
Can be in any unit (grams, mg, atoms, etc.)
Half-life is a fundamental concept in nuclear physics, chemistry, and pharmacology that describes the time required for a quantity to reduce to half of its initial value through exponential decay. Whether you're studying radioactive isotopes, drug metabolism, or any process involving exponential decay, understanding half-life is essential.
The term "half-life" was first introduced by Ernest Rutherford in 1907 while studying radioactive decay. It's denoted by t½ or t1/2 and represents a constant characteristic of each decaying substance. Importantly, the half-life doesn't depend on how much of the substance you start with - it's an intrinsic property.
For example, if you have 100 grams of a radioactive substance with a 5-hour half-life, after 5 hours you'll have 50 grams. After another 5 hours (10 hours total), you'll have 25 grams. After 15 hours, 12.5 grams remain, and so on. The substance never completely disappears but becomes negligibly small over time.
Where:
Where:
Use this formula when you know the initial amount, remaining amount, and time elapsed, but need to find the half-life.
Choose what you want to calculate: remaining amount, time elapsed, half-life, or initial amount. The calculator will adjust the input fields accordingly.
Input the values you know. For example, if calculating remaining amount, enter initial amount, half-life, and time elapsed. Select appropriate time units (seconds, hours, days, years, etc.).
Press the Calculate button to get your result. The calculator will show the answer along with decay constant, percentage remaining, and percentage decayed.
Scroll down to see the detailed step-by-step solution showing all formulas, substitutions, and calculations. This helps you understand the process and verify the result.
Problem: A sample contains 200g of Iodine-131 (half-life = 8 days). How much remains after 24 days?
Solution:
N(t) = N₀ × (1/2)^(t/t½)
N(24) = 200 × (1/2)^(24/8)
N(24) = 200 × (1/2)³
N(24) = 200 × 0.125
N(24) = 25 grams
Answer: 25 grams remain after 24 days (12.5% of original)
Problem: A patient receives 400mg of a drug with 6-hour half-life. How much remains after 15 hours?
Solution:
N(t) = N₀ × (1/2)^(t/t½)
N(15) = 400 × (1/2)^(15/6)
N(15) = 400 × (1/2)^2.5
N(15) = 400 × 0.1768
N(15) = 70.7 mg
Answer: Approximately 70.7mg remains after 15 hours (17.68% of original dose)
Problem: An artifact has 25% of its original Carbon-14. How old is it? (C-14 half-life = 5,730 years)
Solution:
25% = 100% × (1/2)^(t/5730)
0.25 = (1/2)^(t/5730)
log(0.25) = (t/5730) × log(0.5)
t = 5730 × log(0.25) / log(0.5)
t = 5730 × 2
t = 11,460 years
Answer: The artifact is approximately 11,460 years old (2 half-lives have passed)
Problem: A substance decreases from 80g to 20g in 12 hours. What is its half-life?
Solution:
t½ = t / (log(N₀/N) / log(2))
t½ = 12 / (log(80/20) / log(2))
t½ = 12 / (log(4) / log(2))
t½ = 12 / 2
t½ = 6 hours
Answer: The half-life is 6 hours (2 half-lives occurred in 12 hours)
Unlike basic calculators, we offer 4 calculation modes: find remaining amount, time elapsed, half-life, or initial amount. Most competitors only calculate one direction.
Every calculation includes complete step-by-step working with formulas, substitutions, and explanations. Perfect for students learning the concept.
Automatically calculates and displays the decay constant (λ) for each problem - a feature missing from most online calculators.
Convert between seconds, minutes, hours, days, weeks, months, and years. No manual conversion needed - we handle it automatically.
Works perfectly on desktop, tablet, and mobile devices. Calculate half-life anywhere, anytime with a beautiful, intuitive interface.
Comprehensive guides, real-world examples, common isotope reference table, and detailed FAQs. Learn while you calculate.
Shows both percentage remaining and percentage decayed for every calculation - helping you visualize the decay process better.
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Comprehensive database of radioactive isotopes and their half-lives. Official U.S. government reference for nuclear decay data used by scientists worldwide.
Visit NIST (External Authority) →United Nations agency and global authority on nuclear science, providing international standards and verified data for radioactive decay measurements.
Visit IAEA (External Authority) →Official U.S. government source for pharmacokinetics data and drug half-life information for all FDA-approved medications.
Visit FDA (External Authority) →Leading academic research facility at University of Oxford specializing in carbon-14 dating methodology and half-life applications in archaeology.
Visit Oxford (Academic Authority) →Non-profit educational platform with peer-reviewed content on half-life, exponential decay, and nuclear chemistry concepts.
Visit Khan Academy (Educational Resource) →