Free Half-Life Calculator
Calculate the remaining quantity of a radioactive substance after any elapsed time, determine the number of half-lives that have passed, or find the half-life from decay measurements. Free, private — all calculations run in your browser.
N(t) = 1000 × (½)^(2.000) = 250.0
λ = ln(2) / t½ = 3.833e-12 s⁻¹ | τ = 1/λ = 2.609e+11 s
Scenario: Same Quantity, Different Half-Lives
About This Half-Life Calculator
The Half-Life Calculator models exponential radioactive decay — one of nature's most precise and reliable processes. Given the initial quantity, elapsed time, and half-life of a substance, it calculates how much remains. It can also solve backwards: given initial and final quantities, it determines the number of half-lives elapsed and the total time.
The Formula
Half-life is a constant property of each radioactive isotope — it does not change with temperature, pressure, or chemical state. This constancy makes radioactive decay the basis of highly reliable dating methods in archaeology (radiocarbon dating) and geology (uranium-lead, potassium-argon dating).
Notable Half-Lives
- •Carbon-14 (C-14): 5,730 years — used for archaeological dating
- •Uranium-235 (U-235): 703,800,000 years — nuclear reactor fuel
- •Iodine-131 (I-131): 8.02 days — medical imaging and thyroid treatment
- •Radium-226 (Ra-226): 1,600 years — historical radiotherapy source
- •Polonium-210 (Po-210): 138 days — high toxicity; historically in poisoning cases
- •Tritium (H-3): 12.32 years — used in luminescent watch dials and fusion research
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When to Use This Calculator
Calculate remaining quantity after decay, number of half-lives, or determine the half-life from two data points for nuclear physics problems.
Calculate radiotracer activity at time of administration vs. imaging, and determine when radioactive waste from medical procedures reaches safe levels.
Understand the mathematics behind radiocarbon dating and radiometric age dating using isotopes like U-238 and K-40.
Apply the half-life concept to drug concentration: how long until a dose drops below therapeutic levels or clears the system entirely.
Calculate how long radioactive waste remains above safe background levels and model reactor fuel consumption over time.
💡 Pro Tips
After every half-life, exactly half remains — but this compounds. After n half-lives, the fraction remaining is (1/2)ⁿ. This is why radioactive materials take so long to become safe: carbon-14 has a half-life of 5,730 years, meaning after 57,300 years (10 half-lives) only 0.1% remains. Nuclear waste with half-lives of thousands of years requires geological-timescale storage.
The decay constant λ = ln(2)/t½ ≈ 0.693/t½ connects half-life to the continuous exponential decay formula N = N₀e^(−λt). The two formulas are mathematically identical — choose whichever is more convenient for your problem. The (1/2)^(t/t½) form is often more intuitive; the e^(−λt) form is easier to differentiate.
In pharmacology, a drug reaches approximately 97% of its steady-state concentration after 5 half-lives of dosing, and decreases to approximately 3% of peak after 5 half-lives post-dose. This is why drug dosing intervals and washout periods are typically expressed as multiples of the drug's half-life.
The number of half-lives n = log₂(N₀/N) — or equivalently n = ln(N₀/N) / ln(2). This formula is used to work backwards: given an initial and final quantity, how many half-lives elapsed? Divide by the half-life period to get the total elapsed time. This is the basis of radiocarbon age dating.
Frequently Asked Questions
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