Half Life Formula Calculator
If you’re working with radioactive substances, drug metabolism, or any decaying quantity over time, understanding half-life is crucial. Our Free Online Half-Life Calculator makes it effortless to compute how much of a substance remains after a given time or how much has decayed. Whether you’re a student, scientist, or simply curious, this tool provides quick, accurate results with just a few inputs.
What Is a Half-Life?
Half-life is the time it takes for a quantity to reduce to half its initial value. It’s commonly used in:
- Nuclear physics to measure radioactive decay
- Pharmacology to calculate how long a drug stays in your system
- Environmental science for pollution breakdown
- Archaeology to estimate age using isotopic decay (e.g., carbon dating)
The basic formula behind half-life is:
sqlCopyEditRemaining Amount = Initial Amount × (0.5)^(Elapsed Time ÷ Half-Life)
Our tool uses this formula to calculate two values:
- Remaining Amount: How much of the original substance is left
- Decayed Amount: How much has decomposed or been used
How to Use the Half-Life Calculator
Using the calculator is simple. Follow these steps:
- Enter the Initial Amount
Input how much of the substance you started with (in any unit: grams, mg, etc.). - Enter the Half-Life Time
Provide the half-life value of the substance. This can be in seconds, hours, days, or even years – just stay consistent. - Enter the Elapsed Time
Specify how much time has passed since the decay process began. - Click “Calculate”
The tool instantly displays:- The Remaining Amount
- The Decayed Amount
- Click “Reset” to start over with new values.
Practical Examples
Example 1: Radioactive Material
You begin with 100 grams of a radioactive isotope that has a half-life of 5 years. After 15 years, how much remains?
- Initial Amount: 100
- Half-Life: 5
- Elapsed Time: 15
- Result:
- Remaining Amount: 12.5 grams
- Decayed Amount: 87.5 grams
This is because the substance halves every 5 years:
- After 5 years → 50g
- After 10 years → 25g
- After 15 years → 12.5g
Example 2: Drug Elimination
Let’s say a medication has a half-life of 6 hours and you took 500mg. How much is left after 18 hours?
- Initial: 500mg
- Half-Life: 6 hours
- Elapsed Time: 18 hours
- Remaining: 62.5mg
- Decayed: 437.5mg
Why Use This Tool?
- ✅ Instant results — no manual math required
- ✅ Simple interface — just enter numbers and click
- ✅ Flexible — works for any time unit or measurement
- ✅ Accurate — uses the standard exponential decay formula
- ✅ No sign-up — 100% free and browser-based
Real-World Use Cases
This tool is applicable in numerous fields:
- Healthcare: Monitor drug dosage and safe intervals
- Radiology: Calculate safe handling times for isotopes
- Environmental Science: Study breakdown rates of pollutants
- Archaeology: Understand how much of a dating isotope remains
- Nuclear Engineering: Plan waste management and containment
Helpful Tips
- Keep units consistent. If you input half-life in hours, elapsed time should also be in hours.
- Use decimals for precise inputs — the tool accepts values like 0.0001.
- You can input any scale of numbers, from micrograms to tons, as long as they match.
Frequently Asked Questions (FAQs)
1. What is the formula used in this calculator?
The tool uses:Remaining = Initial × (0.5)^(Elapsed ÷ Half-Life)
2. Can I use different time units (e.g., hours and days)?
Yes, but you must use the same unit for both half-life and elapsed time.
3. Is this calculator suitable for drug half-life estimation?
Absolutely. It’s ideal for understanding how long a medication stays active in your body.
4. Can this be used for carbon dating?
Yes. Just input the half-life of carbon-14 and the estimated time that has passed.
5. What does “decayed amount” mean?
It’s the portion of the initial substance that has broken down or been eliminated.
6. How accurate is this tool?
It uses the precise exponential decay equation, ensuring accurate calculations.
7. Do I need to enter units?
No. As long as you’re consistent with time and quantity units, the results are valid.
8. What happens if I enter a zero or negative number?
The tool requires positive values and will show an alert if invalid input is entered.
9. Is there a limit to how large or small the numbers can be?
There’s no fixed limit — decimals and large numbers are both supported.
10. Can I use this for chemical reaction rates?
Only if the reaction follows a first-order decay process like radioactive decay.
11. Does this tool store my data?
No, it’s a privacy-friendly, one-time-use calculator. Nothing is saved.
12. Can I use this calculator offline?
Once the page is loaded, it works without internet since it runs entirely in your browser.
13. Can I use this on mobile?
Yes, it’s fully responsive and works on all screen sizes.
14. Is there a way to reset values?
Yes. Use the “Reset” button to clear the inputs instantly.
15. What’s the difference between decay and degradation?
In this context, they’re interchangeable — both refer to reduction over time.
16. Is exponential decay always accurate?
It is for processes governed by half-life, such as radioactive decay or certain drugs.
17. How do I know the half-life of a substance?
Scientific literature, labels, or data sheets typically provide half-life information.
18. Can I embed this calculator on my website?
Yes, if you have access to the code and permissions, it can be reused or adapted.
19. Does the calculator support batch calculations?
Currently, it handles one calculation at a time for clarity and accuracy.
20. Who is this tool for?
Anyone needing to model decay: students, researchers, pharmacists, engineers, or hobbyists.
Final Thoughts
Understanding half-life doesn’t have to be complex. With this intuitive online tool, you can instantly calculate decay and remaining quantities with minimal effort. Whether you’re calculating how long a drug stays in your system or estimating the radioactive decay of an element, this calculator provides reliable, easy-to-interpret results every time.