Half-Life Calculator
Track radioactive decay. Find how much material remains after a certain time, or calculate how long decay takes, using the half-life.
N(t) = N₀ × (1/2)^(t/T)
How the Half-Life Calculator Works
Select what you want to calculate: remaining amount, elapsed time, half-life, or initial amount. Enter the known values including the initial quantity, half-life of the substance, and time elapsed (or remaining amount).
The calculator applies the radioactive decay formula: N(t) = N₀ × (1/2)^(t/t₁/₂), where N₀ is initial amount, N(t) is remaining amount, t is elapsed time, and t₁/₂ is the half-life. Alternative forms using decay constant λ are also available.
Results show the calculated value with proper units. A decay curve graph shows how the amount decreases over multiple half-lives. The calculator also shows how many half-lives have elapsed and the percentage remaining.
When You'd Actually Use This
Radiometric dating
Calculate ages of archaeological samples. Carbon-14 dating uses 5,730 year half-life. Measure remaining C-14 to determine how long ago an organism died.
Medical isotope dosing
Plan nuclear medicine procedures. Radioactive tracers decay during procedures. Calculate remaining activity to ensure proper imaging doses.
Nuclear waste management
Estimate how long waste remains hazardous. Plutonium-239 has 24,000 year half-life. Calculate storage time needed for safe disposal.
Radiation therapy planning
Calculate radiation dose from implanted seeds. Radioactive seeds decay during treatment. Account for decreasing activity in dose calculations.
Geological age determination
Date rocks using uranium-lead or potassium-argon methods. Long half-lives (millions to billions of years) date Earth's oldest materials.
Physics and chemistry education
Solve nuclear decay problems. Calculate remaining amounts, elapsed times, or half-lives for various radioactive isotopes.
What to Know Before Using
Half-life is constant for each isotope.Temperature, pressure, and chemical state don't affect nuclear decay. Each radioactive isotope has a fixed, unchangeable half-life.
Decay is exponential, not linear.After one half-life, 50% remains. After two, 25% (not 0%). After ten, about 0.1%. The amount approaches zero but never reaches it.
Half-life relates to decay constant.λ = ln(2)/t₁/₂ ≈ 0.693/t₁/₂. The decay constant appears in the differential equation: dN/dt = -λN.
Decay is random but predictable statistically.You can't predict when a specific atom decays. But for large numbers, the half-life precisely predicts the fraction that decays.
Pro tip: After 10 half-lives, only 0.1% remains. After 20 half-lives, only 0.0001% remains. For practical purposes, a sample is "gone" after about 10-20 half-lives.
Common Questions
What is half-life?
Time for half the radioactive atoms in a sample to decay. It's a statistical measure - after one half-life, half the atoms remain on average.
Can half-life be changed?
No. Nuclear decay rates are fundamental constants. Unlike chemical reactions, they're unaffected by temperature, pressure, or chemical bonds.
What's the shortest/longest half-life?
Shortest: fractions of a second for highly unstable isotopes. Longest: tellurium-128 at 2.2 × 10²⁴ years (trillions of times the age of the universe).
How does carbon dating work?
Living things maintain constant C-14/C-12 ratio. After death, C-14 decays (5,730 year half-life). Measuring the ratio reveals time since death.
What's the decay constant?
λ = probability of decay per unit time. Related to half-life by λ = ln(2)/t₁/₂. Appears in the exponential: N(t) = N₀e^(-λt).
Why use half-life instead of decay constant?
Half-life is more intuitive. "5,730 years" is easier to grasp than "λ = 1.21 × 10⁻⁴ per year." Both contain the same information.
What's mean lifetime?
Average time an atom survives before decaying. τ = 1/λ = t₁/₂/ln(2) ≈ 1.44 × t₁/₂. Used in some physics calculations.
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