Your result will appear here
Fill in the fields and press Calculate.
A half-life is the time it takes for half of a quantity to decay away — used for radioactive isotopes, medications leaving the body, and any process with exponential decay. Enter the starting amount, the half-life and the elapsed time, and this tool works out how much remains.
Half-Life Calculator: step-by-step worked example
- Initial amount
- 100 g
- Half-life
- 5,730 years
- Elapsed time
- 10,000 years
- 1
Number of half-lives elapsed
n = t ÷ T½
10,000 ÷ 5,730 = 1.7452
- 2
Fraction remaining
Fraction = 0.5ⁿ
0.5^1.7452 = 29.8292%
- 3
Amount remaining
N = N₀ × 0.5^(t ÷ T½)
100 × 0.298292 = 29.8292 g
- 4
Amount decayed
Decayed = N₀ − N
100 − 29.8292 = 70.1708 g
- Remaining:100 g → 6.25 g
Good to know: Elapsed time and half-life must use the SAME unit (both years, days or hours). Example: carbon-14 has a half-life of 5,730 years, so about 30% remains after 10,000 years. The amount halves every half-life and never quite reaches zero.
Half-Life Calculator — how it works
Exponential decay
remaining = initial × 0.5^(elapsed ÷ half-life)
Each half-life halves what’s left, so decay is exponential, not linear:
| Half-lives passed | Fraction remaining |
|---|---|
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 4 | 6.25% |
Same units for time
The elapsed time and the half-life must be in the same unit — seconds, hours, years, whatever fits — because only their ratio matters. That ratio is the number of half-lives, and the tool reports it alongside the amount.
Where it applies
Radioactive dating and safety, the clearance of drugs and caffeine from the body, the decay of a signal, and charge or heat loss with a characteristic decay time.
Worked example
Caffeine has a half-life of about 5 hours. Start with 200 mg from a strong coffee: after 5 hours (one half-life) 100 mg remains, after 10 hours 50 mg, after 15 hours 25 mg. That’s 0.5^(15 ÷ 5) = 0.5³ = 12.5% of the original — which is why an afternoon coffee can still affect sleep.
Frequently asked questions
What is a half-life?+
The time it takes for half of a quantity to decay or be eliminated. After one half-life, 50% remains; after two, 25%; after three, 12.5%. It applies to radioactive isotopes, drugs in the body and any exponential-decay process.
How do I calculate how much remains?+
Multiply the starting amount by one-half raised to the number of half-lives elapsed: remaining = initial × 0.5^(elapsed ÷ half-life). The calculator does this from the three values you enter.
Why is decay exponential and not steady?+
Because each period removes a fixed fraction of what’s currently left, not a fixed amount. Halving 100 gives 50, halving 50 gives 25 — the absolute loss shrinks each time, producing a curve that approaches zero without ever quite reaching it.
Do the time units matter?+
Only that they match. The elapsed time and the half-life must use the same unit, since the calculation depends on their ratio. Mixing hours and days would give a wrong number of half-lives.
Can I use it for medications?+
Yes — drug elimination often follows first-order (exponential) kinetics with a characteristic half-life, so the same formula estimates how much of a dose remains over time. For medical decisions, always rely on a clinician rather than an estimate.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
Spotted a wrong result? Use the "Report a bug" button at the top of the page; every report is reviewed.
How we calculate and our accuracy policy →
Results are for information only. For official matters the relevant authority's calculation prevails.
Last updated: