Half-Life Calculator

Calculate radioactive decay, remaining quantity, and time elapsed using half-life formula

Calculate What?

Choose what to calculate

Input Values

Enter known values

Starting quantity of substance

Time for half to decay

years

Time since start

Result

Remaining Amount
70.7107
units
% Remaining
70.71%
% Decayed
29.29%
Decay Constant (λ)
1.2097e-4 years⁻¹
λ = ln(2) / t½

Formula

N(t) = N₀ × (½)^(t/t½)
Exponential decay formula
N(t):Remaining Amount
N₀:Initial Amount
t:Time Elapsed
t½:Half-Life
λ:Decay Constant

Common Radioactive Isotopes

Reference table of commonly used isotopes

Carbon-14
t½: 5,730 years
Archaeological dating
Uranium-238
t½: 4.5 billion years
Geological dating
Iodine-131
t½: 8 days
Medical treatment
Cobalt-60
t½: 5.27 years
Cancer therapy
Plutonium-239
t½: 24,100 years
Nuclear fuel
Radon-222
t½: 3.8 days
Environmental monitoring
Tritium (H-3)
t½: 12.3 years
Nuclear fusion
Technetium-99m
t½: 6 hours
Medical imaging

About Half-Life

Half-life is the time required for half of a radioactive substance to decay. This calculator uses the exponential decay formula to determine remaining quantity, time elapsed, half-life period, or initial amount.

Key Concepts

  • Half-Life Period: Time for 50% of atoms to decay
  • Exponential Decay: Decay rate proportional to amount present
  • Decay Constant: λ = ln(2) / t½, probability of decay per unit time
  • Independent Process: Each atom decays independently of others

Applications

  • Carbon-14 dating for archaeology
  • Medical imaging and cancer treatment
  • Nuclear power plant safety calculations
  • Geological and cosmological age determination
  • Radioactive waste management

Example Calculation

If you start with 100g of Carbon-14 (half-life 5,730 years) and 2,865 years pass, you'll have 50g remaining. After another 2,865 years (total 5,730 years), only 25g remains.

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