Radioactive Decay Calculator Formula

Understand the math behind the radioactive decay calculator. Each variable explained with a worked example.

Use the Radioactive Decay Calculator

Formulas Used

Remaining Amount

remaining = initial_amount * pow(0.5, time_elapsed / half_life)

Amount Decayed

decayed = initial_amount - initial_amount * pow(0.5, time_elapsed / half_life)

Fraction Remaining

fraction_remaining = pow(0.5, time_elapsed / half_life)

Variables

VariableDescriptionDefault
initial_amountInitial Amount(g)100
half_lifeHalf-Life(years)5730
time_elapsedTime Elapsed(years)11460

How It Works

Radioactive Decay

Radioactive materials decay at a rate characterized by the half-life.

Formula

N = N_0 * (1/2)^(t / t_half)

where N_0 is the initial amount, t is elapsed time, and t_half is the half-life. After each half-life, exactly half the material remains.

Worked Example

100 g of Carbon-14 (half-life 5730 years) after 11,460 years (2 half-lives).

initial_amount = 100half_life = 5730time_elapsed = 11460
  1. 01N = N0 * (1/2)^(t/t_half)
  2. 02N = 100 * (1/2)^(11460/5730)
  3. 03N = 100 * (1/2)^2
  4. 04N = 100 * 0.25 = 25 g
  5. 05Decayed: 100 - 25 = 75 g

Ready to run the numbers?

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