Math Tools
Half-Life Calculator
Calculate remaining amount, elapsed time, or half-life for exponential decay.
Half-Life Calculator
Calculate remaining amount, elapsed time, or half-life for exponential decay problems.
Calculate how much remains after a given time using the half-life formula.
Formula
A = A₀ × (1/2)t / h
Remaining amount
25
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What this calculator does
This calculator solves common half-life problems. You can calculate remaining amount, elapsed time, or half-life itself.
What is a half-life calculator?
A half-life calculator is a tool used to solve exponential decay problems. It helps determine how much of a substance remains after a given time, how much time has passed, or what the half-life must be based on the values you already know.
This is useful in radioactive decay, chemistry, medicine, pharmacokinetics, biology, carbon dating, and any other situation where an amount decreases by half over regular time intervals.
Half-life formula and exponential decay
The standard half-life formula is A = A₀ × (1/2)t / h, where A is the remaining amount, A₀ is the initial amount, t is elapsed time, and h is the half-life.
This equation describes exponential decay, which means the amount decreases by the same proportion over equal intervals of time. In a half-life process, the amount becomes half of what it was at the start of each half-life period.
Examples for remaining amount calculations
These worked examples show common half-life calculations for the selected mode.
| Example values | Result |
|---|---|
| 100 initial, half-life 10, time 10 | 50 |
| 100 initial, half-life 10, time 20 | 25 |
| 80 initial, half-life 5, time 15 | 10 |
Half-life decay table
This quick reference table shows how much remains after each number of half-lives.
| Number of half-lives | Remaining fraction | Remaining percent |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
How to calculate half-life step by step
First, identify what you are solving for: remaining amount, elapsed time, or the half-life itself. Then enter the known values into the calculator. The tool will apply the half-life formula automatically.
If you are solving manually, start with the exponential decay equation, substitute the known values, and isolate the unknown variable. This can involve exponents and logarithms, which is why an online half-life calculator can save time and reduce mistakes.
Half-life examples in science and medicine
In radioactive decay, half-life helps estimate how much of a radioactive isotope remains after a period of time. In medicine, it can describe how quickly a drug concentration decreases in the body.
The same idea can also appear in chemistry, biology, environmental science, and other exponential decay situations where a quantity reduces by a consistent fraction over time.
Where a half-life calculator is useful
A half-life calculator is useful in radioactive decay problems, carbon dating, nuclear science, medicine dosage decay, and drug elimination studies. It is also useful in chemistry and biology when tracking substances that decay over time.
Students often use a half-life calculator to check homework and understand exponential decay formulas, while professionals may use it for lab work, analysis, or applied science calculations.
Half-life calculator FAQ and common half-life formula questions
What is half-life?
Half-life is the time it takes for a quantity to decay to half of its original amount.
What is the formula for half-life decay?
The standard formula is A = A₀ × (1/2)t / h, where A is remaining amount, A₀ is initial amount, t is elapsed time, and h is half-life.
How do you calculate remaining amount after half-life?
Multiply the initial amount by one-half raised to the power of elapsed time divided by half-life.
How do you calculate elapsed time in a half-life problem?
Use the initial amount, remaining amount, and half-life in the exponential decay formula, then solve for time.
Where is a half-life calculator used?
It is used in radioactive decay, chemistry, medicine, biology, carbon dating, and general exponential decay modeling.
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