Half-Life Calculator
Enter an initial amount, a half-life and a time to see how much remains.
What this tool does
After each half-life, half of the substance remains: N = N₀ × (1/2)^(t ÷ half-life). Start with 100, with a half-life of 10, and after 30 you have 12.5. To fall to 25% takes two half-lives, 20 units of time.
Applies the half-life formula to your initial amount and elapsed time.
Also finds the time to reach a target percentage and the decay constant.
How to use it
- Enter the initial amount.
- Enter the half-life and the time elapsed in the same unit.
- Optionally enter a target percentage remaining.
- Read the amount left and the other results.
Why use this calculator
Calculates the amount remaining after a time, the fraction left, the number of half-lives, the decay constant and the time to reach any target percentage. Exponential decay is hard to estimate by feel. The half-life formula applies to radioactive isotopes, drug concentration, cooling and many other processes, and the calculator shows both directions of the question.
Why we built it
We built the half-life calculator to answer both directions - how much is left, and how long until a level - and to give the decay constant. The logarithm calculator and exponent calculator help with the maths behind it.
Who this tool is for
- Chemistry and physics students
- Teachers needing worked examples
- Anyone modelling exponential decay
When to use it
- Physics and chemistry coursework.
- Understanding isotope decay.
- Estimating how long until something falls to a level.
- Any exponential decay with a known half-life.
How it works
N = N₀ × (1/2)^(t ÷ T½). The time to reach a fraction f is T½ × log₂(1 ÷ f). The decay constant is λ = ln 2 ÷ T½, so N = N₀ × e^(−λt).
Example: N₀ = 100, T½ = 10, t = 30. Three half-lives give 100 × 1/8 = 12.5. The time to fall to 25% is 10 × log₂(4) = 20.
This is a mathematical model. It is not guidance on safety, dosing or medication.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Initial amount | 100 |
| Half-life | 10 |
| Time elapsed | 30 |
| Time to fall to this percentage left | 25 |
With those inputs, the calculator returns:
- Amount remaining: 12.5
- Fraction remaining: 12.5000%
- Number of half-lives elapsed: 3
- Amount decayed: 87.5
- Time to reach 25% remaining: 20
- Decay constant (λ): 0.069315
What you give it, and what you get back
| Item | Details |
|---|---|
| Initial amount | Any quantity. |
| Half-life and time | In the same unit. |
| Target percent | The percentage remaining to find the time for. |
| Output | Amount remaining, fraction, half-lives elapsed, decayed amount, time to target, decay constant. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Units differ | Time and half-life must use the same unit. | Convert one to match. |
| Result is tiny | Many half-lives have passed. | This is expected; the amount never reaches exactly zero. |
| Growth instead of decay | This model is decay only. | Use the compound interest or exponent tools. |
Assumptions and limitations
- A single exponential decay process.
- No chains of decay or biological variation.
Frequently asked questions
What is half-life?
The time it takes for half of a quantity to decay or be removed.
How do I calculate how much is left?
Multiply the initial amount by (1/2) raised to the number of half-lives elapsed.
How many half-lives until it is gone?
It never reaches zero, but after 10 half-lives less than 0.1% remains.
What is the decay constant?
λ = ln 2 divided by the half-life; it is the rate in N = N₀e^(−λt).
Can I use it for medicine?
It illustrates the maths only. It is not medical guidance.
Is my data sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.
Sources and accuracy
Remaining quantity follows the exponential decay law N = N0 times one half to the power of elapsed time divided by the half-life. Half-life values for radionuclides are physical constants reported in nuclear reference data.
Figures last checked against the source on . Standards and rates can change — if you are relying on this for something that matters, confirm against the source above. Think a figure is wrong or out of date? Send a correction.