Half-Life Calculator
Calculate radioactive decay and remaining amount over time
Calculator
N(t) = N₀ × (½)^(t/t½) = 100 × (0.5)^(11460/5730) = 25.0000
Half-Lives Passed
2.00
% Remaining
25.00%
Decay Constant (λ)
1.2097e-4
Half-Life Formulas
- N(t) = N₀ × (½)^(t/t½)
- N(t) = N₀ × e^(-λt)
- λ = ln(2) / t½ (decay constant)
- t = t½ × log₂(N₀/N)
- After n half-lives: N = N₀ / 2ⁿ
How to Use
Calculate radioactive decay and remaining material
Enter half-life
Input half-life or select from common isotopes
Enter initial amount
Input the starting quantity
Enter time
Input elapsed time in matching units
View decay
See remaining amount and decay percentage
Radioactive Decay
N(t) = N0 x (1/2)^(t/half-life)
Remaining amount equals initial amount times one-half raised to the power of time divided by half-life.
Frequently Asked Questions
Half-life is the time required for half of a radioactive sample to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. Each isotope has a characteristic half-life ranging from fractions of seconds to billions of years.
Use N(t) = N0 x (1/2)^(t/half-life), where N0 is initial amount, t is elapsed time, and half-life is the decay period. Alternatively: N(t) = N0 x e^(-lambda x t), where lambda = ln(2)/half-life is the decay constant. Both give the same result.
The decay constant (lambda) measures probability of decay per unit time. lambda = ln(2)/half-life, approximately 0.693/half-life. Larger lambda means faster decay (shorter half-life). Carbon-14 has lambda approximately 1.21x10^-4 per year (half-life = 5730 years).
Carbon-14: 5,730 years (archaeology). Uranium-238: 4.5 billion years (geology). Iodine-131: 8 days (medical). Cobalt-60: 5.27 years (radiation therapy). Radium-226: 1,600 years. Plutonium-239: 24,100 years (nuclear waste).