This half life calculator estimates how much of a quantity remains after exponential decay. Enter initial amount, half-life length, and elapsed time to get remaining = initial × (1/2)^(time ÷ half). Defaults of 100, 5, and 15 leave 12.5.
Chemistry and physics students use it for decay drills. For molecular mass of a formula string, see the molecular weight calculator.
How the formula works
Each full half-life multiplies the amount by 1/2. Fractional half-lives use the same exponential, so the decay curve is smooth rather than only stepping at whole intervals.
Worked example
Initial 100, half-life 5, time 15. Exponent = 15 ÷ 5 = 3. Remaining = 100 × (1/2)^3 = 12.5.
| Input | Value |
|---|---|
| Initial amount | 100 |
| Half-life | 5 |
| Time elapsed | 15 |
| Remaining | 12.5 |
How to use the fields
- Initial is the starting quantity in any consistent unit.
- Half is the half-life duration in the same time unit as time.
- Time is how long decay has run.
Keeping time units consistent
If half-life is in days, elapsed time must be in days. Mixing hours and days without converting breaks the exponent.
Common mistakes
- Subtracting half the amount once regardless of how many half-lives passed
- Using a zero or negative half-life
- Confusing remaining amount with amount decayed
- Applying one half-life model to multi-phase processes
Classroom checklist
- Write initial, half-life, and time with units.
- Compute time ÷ half-life.
- Evaluate (1/2) to that power.
- Multiply by initial and state remaining units.
Amount decayed
If you need how much disappeared, subtract remaining from initial after you compute remaining. The calculator itself returns the leftover quantity.
Table of successive halves
Starting at 100 with half-life 5: after 5 time units remaining is 50, after 10 it is 25, after 15 it is 12.5, after 20 it is 6.25. The default stops at three half-lives, but extending the table shows the pattern clearly for students who distrust exponents at first.
Graphing remaining amount versus time produces a decaying curve, not a straight line. Linear subtraction would be the wrong model for classic half-life stories.
Fractional half-lives
If time is 7.5 and half-life is 5, the exponent is 1.5. Remaining = 100 × (1/2)^1.5, which is between 50 and 25. You do not have to wait for whole half-lives for the formula to apply.
Keep a calculator handy for fractional exponents instead of inventing a linear interpolation between whole steps.
Lab and medicine caveats
Radioactive decay lab problems often match this model well. Biological half-life for drugs can involve multiple compartments. If your course or clinician uses a single half-life approximation, this page matches that simplification. If they use a multi phase model, follow their worksheet instead.
Always align the time unit of the cited half-life with the elapsed time you enter.
Amount decayed versus remaining
Teachers sometimes ask how much decayed. Subtract remaining from initial after you compute remaining. For the default, 100 – 12.5 = 87.5 decayed. Saying “87.5 remaining” would be the common mix up to avoid.
Percent remaining language
After three half-lives, 12.5 percent of the original 100 remains, which is the same statement as remaining 12.5 when initial was 100. Mixing “12.5 remaining” with “12.5 percent decayed” confuses readers. Prefer explicit units: amount remaining versus percent of initial.
For other initials, percent remaining is remaining ÷ initial × 100. The exponential factor (1/2)^(time/half) is already that fraction.
Choosing inputs from a word problem
Underline the initial amount, the half-life constant, and the elapsed time. Convert all times to one unit before entry. If a problem gives decay in years and elapsed time in months, convert months to years or years to months first. The exponent only makes sense with matched units.
Graph reading skills
On a remaining amount versus time graph, each half-life step drops the height by half relative to the previous labeled point. If a graph scale is logarithmic, the decay can look straighter. Know which scale you are reading before you estimate values by eye.
Compare a hand estimate from the graph with the calculator result for the same time to confirm you read the axes correctly.
Reporting clarity
State initial amount, half-life, elapsed time, and remaining amount in one sentence when you share results. Bare numbers without those anchors force readers to guess which scenario you ran.
Limitations
The model assumes a constant half-life and pure exponential decay. Branching decay chains and dose schedules need richer models.