Half-Life Calculator
Use this half-life calculator to find how much of a substance remains, how much you started with, how long it took or the half-life itself. Pick an isotope like carbon-14 or a substance like caffeine, and get a decay chart, half-life table and step-by-step working.
- Solve for any variable
- 17 isotope and drug presets
- Decay chart and table
- Free, private, no sign-up
Use any consistent amount: mass, activity, number of atoms or a percentage. Time units can differ between half-life and elapsed time.
Remaining amount
25 g
Decay curve
How the amount falls over time. Dashed lines mark each half-life.
Half-life table
How much is left after each half-life for these values.
| Half-lives | Time | Amount left | Percent left |
|---|
A half-life calculator that solves everything
Most half-life tools solve one thing and hide the math. This one solves any of the four values and shows each step.
Solve for any variable
Find the remaining amount, the initial amount, the time elapsed or the half-life from the other three values.
Built-in presets
Carbon-14, uranium-238, iodine-131, cobalt-60, caffeine and more, with accurate half-life values filled in for you.
Interactive decay curve
A clean chart plots the exponential decay curve and marks every half-life and your result.
Half-life table
See the amount and percentage left after 1, 2, 3 and up to 10 half-lives, with real times.
Step-by-step working
Every answer shows the formula with your numbers substituted, ideal for homework and exams.
Mixed time units
Enter the half-life in years and the time in days, or any mix of seconds, minutes, hours, days and years.
How to use the half-life calculator
Answers update as you type.
- Choose what to findTap Remaining, Initial, Time or Half-life. That field becomes the answer.
- Pick a substance (optional)Select an isotope or drug to fill in its half-life, or leave it on Custom.
- Enter the known valuesAdd the other three values and pick units for time and amount.
- Read the answer and workingSee the result, percent remaining, decay constant, mean lifetime and the formula.
- Explore the chart and tableCheck how the amount falls with each half-life, then copy or share your result.
Half-life formula and how to calculate it
Half-life is the time it takes for half of a substance to decay or be eliminated. After one half-life, 50% remains. After two, 25% remains, and so on. Because each half-life removes half of what is left, the amount never quite reaches zero, which is called exponential decay.
Worked example: carbon-14 dating
- Initial amount
- 100 g
- Half-life of carbon-14
- 5,730 years
- Time elapsed
- 11,460 years
- Half-lives elapsed
- 11,460 / 5,730 = 2
- Remaining
- 100 × (1/2)² = 25 g
Worked example: caffeine
You drink a coffee with 200 mg of caffeine at 8 am. With an average half-life of 5 hours, by 8 pm (12 hours later) about 200 × (1/2)2.4 ≈ 38 mg is still in your body. That is why afternoon coffee can affect sleep; check your bedtime with the sleep calculator.
How much is left after each half-life
| Half-lives | Remaining | Decayed |
|---|---|---|
| 1 | 50% | 50% |
| 2 | 25% | 75% |
| 3 | 12.5% | 87.5% |
| 4 | 6.25% | 93.75% |
| 5 | 3.125% | 96.875% |
| 6 | 1.5625% | 98.4375% |
| 7 | 0.7813% | 99.2188% |
| 8 | 0.3906% | 99.6094% |
| 9 | 0.1953% | 99.8047% |
| 10 | 0.0977% | 99.9023% |
In medicine, a drug is usually considered almost fully eliminated after 4 to 5 half-lives, when about 94 to 97% has gone.
Half-lives of common isotopes and substances
| Substance | Half-life | Known for |
|---|---|---|
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Uranium-238 | 4.468 billion years | Dating rocks and the age of the Earth |
| Uranium-235 | 704 million years | Nuclear reactor fuel |
| Potassium-40 | 1.248 billion years | Potassium-argon dating |
| Plutonium-239 | 24,110 years | Reactors and nuclear weapons |
| Radium-226 | 1,600 years | Historic luminous paint |
| Cesium-137 | 30.08 years | Fallout from nuclear accidents |
| Strontium-90 | 28.8 years | Fallout that builds up in bone |
| Tritium (hydrogen-3) | 12.32 years | Glowing exit signs and gun sights |
| Cobalt-60 | 5.27 years | Radiotherapy and sterilization |
| Polonium-210 | 138.4 days | Strong alpha emitter |
| Iodine-131 | 8.02 days | Thyroid treatment |
| Radon-222 | 3.82 days | Indoor radon gas |
| Technetium-99m | 6.01 hours | Medical imaging scans |
| Fluorine-18 | 109.7 minutes | PET scans |
| Caffeine (average adult) | 5 hours | Coffee, tea and energy drinks |
| Nicotine | 2 hours | Tobacco and vaping |
Not everything follows a half-life. Alcohol, for example, is cleared at a roughly constant rate rather than exponentially, which is why the BAC calculator uses a different method. For very large or small numbers, the scientific notation calculator can help.
Who uses a half-life calculator?
Half-life shows up in more places than you might expect.
Students. Check chemistry and physics homework with clear, step-by-step working.
Teachers. Demonstrate exponential decay with a live chart and table.
Archaeology fans. Explore how carbon-14 dating estimates the age of ancient remains.
Health and pharmacy. Understand how long caffeine or a medication stays in the body.
Nuclear medicine and safety. Estimate how quickly tracers and isotopes lose their activity.
Curious minds. See why uranium lasts billions of years while some isotopes vanish in minutes.
Half-life calculator FAQs
Quick answers about half-life, decay and the formula.
Half-life is the time it takes for half of a substance to decay or be removed. After one half-life 50% remains, after two 25% remains, and so on. For example, carbon-14 has a half-life of 5,730 years.
Use t½ = t × ln 2 / ln(N₀ / N), where t is the time elapsed, N₀ the starting amount and N the amount left. For example, if 80 g decays to 10 g in 30 days, that is three halvings, so the half-life is 10 days.
After 3 half-lives, 12.5% of the original amount remains. After 5 half-lives about 3.1% remains, and after 10 half-lives less than 0.1% is left.
In healthy adults, caffeine has an average half-life of about 5 hours, ranging from roughly 1.5 to 9.5 hours. Pregnancy and some medications make it last longer, while smoking shortens it. After about five half-lives, roughly a day, most of it is gone.
In practice, no. Radioactive half-lives stay constant regardless of temperature, pressure or how much material you have. Drug half-lives are different and can vary from person to person.
Living things take in carbon-14 while alive. After death it decays with a half-life of 5,730 years, so measuring how much is left reveals the age. A sample with 25% of its original carbon-14 is about 11,460 years old. The method works up to about 50,000 years.
The decay constant (λ) is the probability of decay per unit time, and equals ln 2 divided by the half-life. The mean lifetime (τ) is 1/λ, about 1.443 times the half-life. All three describe the same decay rate in different ways.
Mathematically, exponential decay never reaches zero. In reality a sample has a finite number of atoms or molecules, so it effectively runs out. After 10 half-lives, less than 0.1% of the original remains.
Solve any half-life problem in seconds
Pick what you want to find, enter the other values and get the answer, the working, a decay chart and a half-life table.
For education and general information. Half-lives of drugs such as caffeine vary between people with age, pregnancy, medications and liver function. Do not use this tool to make medical or radiation safety decisions.