Half-Life CalculatorAmount remaining, elapsed time and half-life for isotopes and medicines
Solve any half-life problem, see the decay curve, and get the decay constant and mean lifetime. Presets cover common radioactive isotopes and first-order drug elimination.
By Manzoor Ahmad, pharmacist · Updated How do you calculate half-life decay?
Use N = N₀ × (½)^(t ÷ t½). The amount left equals the starting amount times one-half raised to the number of half-lives that have passed. Example: 200 mg of caffeine with a 5-hour half-life leaves 200 × 0.5^(24 ÷ 5) = 7.2 mg after 24 hours. To find the half-life itself, use t½ = t × ln 2 ÷ ln(N₀ ÷ N).
Half-life timeline
| Half-lives | Time | Amount left | % left |
|---|
Half-life formulas
Radioactive decay and most drug elimination are first-order processes: a constant fraction disappears in each equal time interval. That is why half-life does not depend on how much you start with.
The same law can be written N = N₀e^(−λt). Both forms give identical answers; the calculator uses them interchangeably.
How to use the half-life calculator
- Pick a preset (an isotope or medicine) or keep Custom to type your own half-life.
- Choose what to solve for: amount left, elapsed time, the half-life itself, or the original amount.
- Enter the other values. Time and half-life can use different units. The amount label (mg, g, %, Bq, mCi) is free text.
- Read the result, the decay curve, λ, τ and the timeline of each half-life.
Worked examples
1. Caffeine after 24 hours
200 mg of caffeine with a typical adult half-life of 5 hours. Half-lives elapsed = 24 ÷ 5 = 4.8. Remaining = 200 × 0.5^4.8 = 7.18 mg (3.6%). This is the calculator’s default.
2. Iodine-131 in nuclear medicine
I-131 has a half-life of 8.02 days. Time for activity to fall to 12.5% = 8.02 × ln(100/12.5) ÷ ln2 = 8.02 × 3 = 24.06 days.
3. Finding an unknown half-life
A drug level falls from 100 mg/L to 25 mg/L in 10 hours. t½ = 10 × 0.6931 ÷ ln(4) = 5.0 hours. Two halvings in 10 hours, so each takes 5.
How much is left after each half-life
| Half-lives elapsed | Fraction remaining | % remaining | % gone |
|---|---|---|---|
| 1 | 1/2 | 50% | 50% |
| 2 | 1/4 | 25% | 75% |
| 3 | 1/8 | 12.5% | 87.5% |
| 4 | 1/16 | 6.25% | 93.75% |
| 5 | 1/32 | 3.13% | 96.88% |
| 7 | 1/128 | 0.78% | 99.22% |
| 10 | 1/1,024 | 0.098% | 99.90% |
Half-lives of common radioactive isotopes
| Isotope | Half-life | Where you meet it |
|---|---|---|
| Fluorine-18 | 109.77 minutes | PET scans (FDG) |
| Technetium-99m | 6.01 hours | Most common diagnostic radiotracer |
| Radon-222 | 3.82 days | Indoor radon gas |
| Iodine-131 | 8.02 days | Thyroid therapy |
| Cobalt-60 | 5.27 years | Radiotherapy, sterilization |
| Tritium (H-3) | 12.32 years | Self-lit exit signs and watches |
| Caesium-137 | 30.17 years | Fallout tracer, industrial gauges |
| Radium-226 | 1,600 years | Historic luminous paint |
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Uranium-238 | 4.468 billion years | Dating rocks and the Earth |
Drug half-life: what it means in practice
In pharmacy, half-life answers three everyday questions. How often should a dose be given? How long until a steady level is reached? How long until a medicine has washed out before starting another?
- Steady state is reached after about 4–5 half-lives of regular dosing, at about 94–97% of the final level.
- Practical elimination is also about 5 half-lives after the last dose, when about 97% has been cleared.
- Long half-life drugs such as fluoxetine (several days, with an active metabolite lasting longer) need longer washout periods before switching.
Medicine presets use typical adult values from published references. Real half-lives vary with age, kidney and liver function, genetics, pregnancy, smoking and interacting drugs. Never use this calculator to change a dose; ask your pharmacist or prescriber.
Half-life calculator FAQs
Half-life (t½) is the time it takes for half of a quantity to decay or be eliminated. After one half-life 50% remains, after two 25% remains, and after five about 3% remains.
The amount remaining is N = N₀ × (1/2)^(t / t½), where N₀ is the starting amount, t is the elapsed time and t½ is the half-life. It can be rearranged to solve for any of the four values.
Use t½ = t × ln(2) ÷ ln(N₀ / N). If 100 mg drops to 25 mg in 10 hours, t½ = 10 × 0.693 ÷ ln(4) = 5 hours.
Use t = t½ × ln(N₀ / N) ÷ ln(2). For iodine-131 (t½ = 8.02 days) to fall from 100% to 12.5% takes three half-lives, or 24.06 days.
The decay constant λ is the fraction that decays per unit time, related to half-life by λ = ln(2) ÷ t½. Carbon-14's decay constant is about 1.21 × 10⁻⁴ per year.
Mean lifetime τ is the average time a particle survives before decaying, τ = t½ ÷ ln(2) ≈ 1.443 × t½. After one mean lifetime, about 36.8% (1/e) remains.
A drug is usually considered practically eliminated after about 5 half-lives, when roughly 97% has been cleared. This assumes first-order kinetics, which most drugs follow at normal doses.
Caffeine's half-life in healthy adults is typically about 3 to 7 hours, often quoted as 5 hours. With a 5-hour half-life, 200 mg at 8 a.m. leaves about 7 mg after 24 hours. Pregnancy, smoking, liver function and some medicines change this considerably.
No. For first-order processes like radioactive decay, half-life is constant regardless of how much you start with. That is what makes it useful for dating and dosing.
Yes. Choose the unit for each field separately, for example a half-life in days and an elapsed time in hours. The calculator converts both to seconds before solving.
No. Alcohol and some drugs at high doses follow zero-order kinetics, where a fixed amount is removed per hour rather than a fixed fraction. A half-life model does not apply to them.
No. It shows the math of first-order elimination for education. Actual dosing depends on age, kidney and liver function, interactions and the specific product, so follow your prescriber and pharmacist.
Sources
This half-life calculator is for education. It is not medical advice and must not be used to set or change medication doses, or for radiation safety decisions.