Half-Life Calculator

Choose the mode based on what you want to find:

• Find Remaining Amount: Enter the initial amount, the half-life, and the elapsed time. The calculator finds how much remains.
• Find Half-Life: Enter the initial amount, remaining amount, and elapsed time. The calculator determines the half-life of the substance.
• Find Time: Enter the initial amount, remaining amount, and half-life. The calculator finds how much time has passed.

Time units must be consistent: if the half-life is in years, elapsed time must also be in years. The reference table shows half-lives for common isotopes.

Core formula: N(t) = N₀ × (1/2)^(t/t½)

Where:
  N(t)  = remaining amount at time t
  N₀    = initial amount
  t     = elapsed time
  t½    = half-life

Solving for half-life:
  t½ = t × ln(2) / ln(N₀/N)

Solving for time:
  t = t½ × log₂(N₀/N)
    = t½ × ln(N₀/N) / ln(2)

Decay constant: λ = ln(2) / t½
Alternative form: N(t) = N₀ × e^(-λt)

Example: Carbon-14 (t½ = 5,730 years), N₀ = 1000, t = 11,460 years
  Number of half-lives = 11460 / 5730 = 2
  N = 1000 × (1/2)^2 = 1000 × 0.25 = 250
  25% of original remains after 2 half-lives