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Half-Life Radioactive Decay & Elimination Calculator

Compute radioactive exponential decay, remaining quantities, and half-life durations.

Quick Answer:Input initial quantity (N0), half-life (t1/2), and elapsed time (t). Remaining amount = N0 × (0.5)^(t / t1/2).

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How to Use the Half-Life Calculator: Radioactive Decay & Elimination

1Enter the starting initial quantity of substance (N₀).
2Enter the half-life duration of the isotope or compound (t½).
3Enter the total elapsed time interval (t).
4View the remaining quantity, percentage remaining, and radioactive decay constant (λ).

N(t) = N₀ × (½)^(t / t½) = N₀ × e^(-λt); λ = ln(2) / t½

Models first-order radioactive kinetics using exponential decay equations.

Input: Initial: 100g, Half-Life: 5,730 yrs, Elapsed: 11,460 yrs

Explanation: 11,460 years is exactly two half-lives: 100g → 50g (1 half-life) → 25g (2 half-lives).

Result: Remaining: 25.000g (25.00% remaining)

What is a half-life?▼

A half-life is the time required for exactly half of the radioactive atoms or drug molecules in a sample to decay or be eliminated.

Does a substance ever decay completely to zero?▼

In mathematical theory, exponential decay approaches zero asymptotically; physically, the last atom eventually decays.

How many half-lives are required for 99% elimination?▼

Approximately 7 half-lives reduce a substance to less than 1% of its original quantity ((0.5)⁷ ≈ 0.78%).

What is the decay constant lambda (λ)?▼

Lambda is the fractional decay rate per unit time, defined mathematically as ln(2) / t½ ≈ 0.69315 / t½.

Isotope / Drug	Half-Life (t½)	Decay Mode	Application
Carbon-14 (C-14)	5,730 Years	Beta decay	Archaeological dating
Iodine-131 (I-131)	8.02 Days	Beta / Gamma	Thyroid radiotherapy
Caffeine	5.0 Hours	Metabolic elimination	Pharmacokinetics
Uranium-238 (U-238)	4.468 Billion Yrs	Alpha decay	Geological age dating

•Using mismatched time units for half-life duration and elapsed time (e.g. days vs hours).
•Assuming linear decay instead of exponential decay over time.

•Archaeological radiocarbon dating (Carbon-14) of fossils and ancient artifacts.
•Pharmacokinetic tracking of medical drug elimination half-lives in patient bloodstreams.

Last reviewed & updated: 2026-11-11

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