Half-Life Calculator Formula

Understand the math behind the half-life calculator. Each variable explained with a worked example.

Use the Half-Life Calculator

Formulas Used

Remaining

remaining = initial * pow(0.5, time / half_life)

Decayed

decayed = initial - initial * pow(0.5, time / half_life)

Num Halves

num_halves = time / half_life

Pct Remaining

pct_remaining = pow(0.5, time / half_life) * 100

Variables

VariableDescriptionDefault
initialInitial Quantity100
half_lifeHalf-Life5
timeElapsed Time15

How It Works

Half-Life Formula

Formula

N(t) = N₀ × (1/2)^(t/t½)

Where:

  • N₀ = initial quantity
  • t = elapsed time
  • t½ = half-life

    • Properties

  • After 1 half-life: 50% remains
  • After 2 half-lives: 25% remains
  • After 3 half-lives: 12.5% remains
  • After 10 half-lives: ~0.1% remains

    • Worked Example

    100 units with a half-life of 5 after 15 time units.

    initial = 100half_life = 5time = 15
    1. 01Number of half-lives = 15/5 = 3
    2. 02Remaining = 100 × (0.5)³
    3. 03= 100 × 0.125
    4. 04= 12.5

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