Half-Life Remaining Amount Calculator Formula

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

Use the Half-Life Remaining Amount Calculator

Formulas Used

Amount Remaining

remaining = initial_amount * pow(0.5, num_half_lives)

Percent Remaining

pct_remaining = pow(0.5, num_half_lives) * 100

Amount Decayed

amount_decayed = initial_amount * (1 - pow(0.5, num_half_lives))

Variables

VariableDescriptionDefault
initial_amountInitial Amount100
num_half_livesNumber of Half-Lives Elapsed5

How It Works

Remaining After n Half-Lives

Each half-life reduces the remaining amount by half. After n half-lives, the fraction remaining is (1/2)^n.

Formula

N = N0 × (1/2)^n

This applies to radioactive decay, drug elimination, chemical degradation, and any first-order process.

Worked Example

Starting with 100 grams, after 5 half-lives.

initial_amount = 100num_half_lives = 5
  1. 01Remaining = 100 × (0.5)^5
  2. 02Remaining = 100 × 0.03125 = 3.125 grams
  3. 03Only 3.125% remains after 5 half-lives

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