Solve for exponential decay over time
Half-Life Calculator – Calculate Radioactive Decay Instantly
Understanding how a substance decays over time is important in fields like physics, chemistry, medicine, biology, archaeology, and nuclear science. Whether you’re studying radioactive isotopes, calculating medication decay, or completing a science assignment, our Half-Life Calculator makes the process quick and easy.
Simply enter the initial amount, remaining amount, and elapsed time, and our free Half-Life Calculator will instantly calculate the half-life of the substance—saving you time and eliminating complicated formulas.
What Is Half-Life?
Half-life is the amount of time it takes for half of a radioactive substance or material to decay.
For example:
- 100 grams become 50 grams after one half-life.
- 50 grams become 25 grams after another half-life.
- 25 grams become 12.5 grams after the next half-life.
No matter how much material you start with, the time required to reduce it by half always remains the same.
Half-life is commonly used in:
- Radioactive decay
- Nuclear physics
- Medical imaging
- Cancer treatment
- Pharmacology
- Carbon dating
- Environmental science
Why Use Our Half-Life Calculator?
Our Half-Life Calculator helps you calculate radioactive decay quickly and accurately.
⚡ Instant Results
Calculate half-life in seconds without solving logarithmic equations manually.
🎓 Perfect for Students
Great for homework, laboratory experiments, and learning radioactive decay concepts.
🔬 Useful for Scientists
Quickly estimate decay rates for isotopes, pharmaceuticals, and other substances.
✔ Accurate Calculations
Our calculator uses the standard scientific half-life formula to ensure reliable results.
Half-Life Formula
The formula used by our Half-Life Calculator is:
Half-Life = (Elapsed Time × ln(2)) ÷ ln(Initial Amount ÷ Remaining Amount)
Where:
- t½ = Half-life
- t = Total elapsed time
- N₀ = Initial amount
- Nₜ = Remaining amount after time t
This formula is widely used in chemistry, nuclear physics, and medical research.
Example Calculation
Imagine you begin with:
- Initial Amount = 100 mg
- Remaining Amount = 12.5 mg
- Elapsed Time = 50 hours
Step 1:
100 ÷ 12.5 = 8
Step 2:
Apply the values to the formula.
Step 3:
The calculated half-life is approximately:
16.67 hours
Our Half-Life Calculator performs these calculations instantly for you.
Decay Constant Formula
Scientists also use the decay constant (λ) to measure how quickly a radioactive material decays.
Formula:
λ = ln(2) ÷ Half-Life
A larger decay constant means the material decays more quickly.
Mean Lifetime Formula
The mean lifetime represents the average lifespan of a radioactive atom before it decays.
Formula:
Mean Lifetime = Half-Life ÷ ln(2)
This value is commonly used in physics and nuclear engineering.
Common Radioactive Isotopes
| Isotope | Common Use | Half-Life |
|---|---|---|
| Oxygen-15 | PET scans | 122 seconds |
| Iodine-131 | Thyroid treatment | 8.02 days |
| Cobalt-60 | Medical therapy | 5.27 years |
| Carbon-14 | Archaeological dating | 5,730 years |
| Plutonium-239 | Nuclear fuel | 24,100 years |
| Uranium-235 | Nuclear reactors | 704 million years |
Frequently Asked Questions
What units can I use?
You can use any unit, such as:
- Grams
- Milligrams
- Kilograms
- Liters
- Percentages
Just make sure both the initial amount and remaining amount use the same unit.
Can the remaining amount be larger than the initial amount?
No.
Half-life measures decay, so the remaining amount must always be less than or equal to the initial amount.
Is this Half-Life Calculator free?
Yes!
Our Half-Life Calculator is completely free and works instantly in your browser without registration or downloads.
Calculate Half-Life with Confidence
Whether you’re studying radioactive decay, analyzing laboratory results, or learning nuclear physics, our Half-Life Calculator helps you calculate decay rates quickly and accurately.
Try our Free Half-Life Calculator today and simplify your scientific calculations in just a few clicks.