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Half-life describes how long it takes for a quantity to fall to half its original amount — a concept used across radioactive decay, pharmacology, and chemistry.
This calculator finds the remaining quantity of a substance after a given elapsed time, based on its initial amount and half-life.
How it works
Enter the initial quantity, the half-life, and the elapsed time (using the same time units for both). The calculator applies the exponential decay formula \(N(t) = N_0 \times (0.5)^{t / t_{1/2}}\) to find the remaining quantity.
- Enter initial quantity.
- Enter half-life.
- Enter elapsed time (same units as half-life).
- Click Calculate to see your results.
Examples
100 units, 10-unit half-life, 30 units elapsed
A starting quantity of 100 with a half-life of 10 (any consistent time unit) has 12.5 remaining after 30 units of elapsed time — three half-lives have passed.
Who should use it
- Estimating remaining radioactive material after a given time.
- Estimating drug concentration remaining in the body based on its half-life.
Industry applications
- Chemistry and physics education
- Pharmacology and pharmacokinetics
Advantages
- Applies the standard exponential decay formula used across science and pharmacology.
- Works for any half-life and elapsed time, in any consistent unit.
Limitations
- Assumes ideal, simple exponential decay — some real-world processes follow more complex decay patterns.
Common mistakes to avoid
- Entering half-life and elapsed time in different, inconsistent units (e.g., half-life in days and elapsed time in hours).
- Assuming decay is linear rather than exponential — the amount remaining after each half-life is always half of what remained before, not a fixed absolute amount.
Best practices
- Double-check that your half-life and elapsed time inputs use the exact same time unit before reading the result.
Tips
- After 5 half-lives, less than 3.2% of the original quantity remains — a useful rule of thumb for when a decaying quantity is effectively negligible.