Half Life Calculator
Calculate radioactive decay, half-life periods, and remaining quantities.
Half-Life & Decay
Starting amount of substance
Time for half the substance to decay
Time that has passed
☢️ Common Examples
Remaining Amount
25.00% of original
Half-Lives Elapsed
Number of half-lives
Percent Decayed
Amount lost
Step-by-Step Solution
Decay Over Time
How it works
Half-life is the time for a quantity to halve through exponential decay — common for radioactive isotopes, drug clearance, and more. After each half-life, half of what remains is gone, so the amount left follows a power of one-half.
Exponential decay
N = N₀ · (½)^(t / T)
- N₀
- starting amount
- N
- amount remaining
- t
- elapsed time
- T
- the half-life
Worked example
- Start N₀ = 100 g
- Half-life T = 8 days
- After t = 24 days
- Number of half-lives = 24 ÷ 8 = 3
- N = 100 × (½)³
≈ 12.5 g remaining (100 → 50 → 25 → 12.5).
Good to know
- After n half-lives, the fraction left is (½)ⁿ — it approaches zero but never quite reaches it.
- Decay is independent of the starting amount: the half-life is constant.
- The same math models drug levels — it's why doctors dose by a medicine's half-life.
Related Calculators
Frequently Asked Questions
What is half-life?
Half-life is the time required for half of a decaying substance to disappear. It's a fixed property of each radioactive isotope (or any first-order decay process), independent of how much material you start with.
What formula does the half-life calculator use?
N = N₀ × (1/2)^(t/T), where N₀ is the starting amount, t is elapsed time, and T is the half-life. The same relationship can be written with the decay constant λ as N = N₀e^(−λt), where λ = ln(2)/T.
How much remains after several half-lives?
Each half-life cuts the remaining amount in half: 50% after one, 25% after two, 12.5% after three, and about 0.1% after ten. The substance never reaches exactly zero mathematically — it just becomes negligible.
Is half-life only about radioactivity?
No. Any exponential decay has a half-life: drug concentrations in the bloodstream (pharmacokinetics), the discharge of a capacitor, and first-order chemical reactions all use the same math. In medicine, a drug's half-life determines dosing intervals.
How does carbon dating use half-life?
Living things constantly exchange carbon-14 with the atmosphere; when they die, the C-14 decays with a half-life of about 5,730 years. Measuring how much C-14 remains relative to stable carbon reveals the age of organic material up to roughly 50,000 years old.