Half-Life Calculator
Calculate Radioactive Decay and Remaining Substance Mass
Please enter the required details and click Calculate.
Calculation Examples
How to Use the Half-Life Calculator
To calculate the decay of a substance, enter the Initial Quantity, the Half-Life (decay interval), and the Elapsed Time.
Our calculator uses the exponential decay law to find the remaining amount ($N_t$). This is widely used in nuclear physics to track isotopes and in medicine to determine how long a drug remains active in the bloodstream.
How Are Half-Life Calculations Performed?
Half-life calculations follow a generic form for the exponential decay of the amount of a substance remaining, which is verified by the International Atomic Energy Agency (IAEA) to be $$A = A_0 \times (1/2)^{t/T}$$ where $A$ is the amount remaining, $A_0$ is the original amount, $t$ is the amount of time elapsed, and $T$ is the half-life. The disintegration constant, $\lambda$, can alternatively be calculated using the equation $\lambda = \ln(2)/T$. These equations can model radioactive decay and work for many isotope types.
Useful Tips 💡
- Ensure the time units for "Half-Life" and "Elapsed Time" are identical (e.g., both in years).
- Use the "Decay Constant" if you are working with the rate of disintegration rather than time.
📋Steps to Calculate
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Enter the initial amount and half-life of the object.
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Enter elapsed time and proper unit(s).
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Click "Calculate" to view the remaining amount and decay details.
Mistakes to Avoid ⚠️
- Thinking that a substance disappears after two half-lives (it actually leaves 25% remaining).
- Mixing units, such as using a half-life in hours but elapsed time in days.
- Confusing "Half-Life" with "Mean Lifetime" (tau).
Practical Applications📊
Monitoring radioactive decay for nuclear application or medical applications.
Estimating remaining concentration of drug for pharmacokinetics studies.
Determining the age of fossils using carbon-14 dating, which requires knowledge of half-life.