Half-life is the time it takes for exactly half of a radioactive substance to decay. After one half-life 50% remains, after two half-lives 25% remains, and so on. The formula is N(t) = N₀ × (1/2)^(t/t½).

How do you calculate the remaining amount after radioactive decay?

Use N(t) = N₀ × (1/2)^(t/t½), where N₀ is the initial quantity, t is elapsed time, and t½ is the half-life. For example, starting with 100g of a substance with a 5-year half-life, after 10 years: N = 100 × (1/2)^(10/5) = 100 × 0.25 = 25g.

What are some common radioactive half-lives?

Carbon-14: 5,730 years (used in radiocarbon dating). Uranium-238: 4.47 billion years. Iodine-131: 8.02 days (medical imaging). Polonium-210: 138 days. Potassium-40: 1.25 billion years.

☢️ Nuclear Physics

Half-Life Calculator

Calculate radioactive decay — find remaining quantity, determine the half-life from measurements, or work out elapsed time. Full step-by-step working included.

Presets:

Initial quantity N₀

Remaining quantity N(t)

Elapsed time (t)

Half-life (t½)

☢️ Result

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—% Remaining

—% Decayed

—Decay const. λ

—Half-lives elapsed

📝 Step-by-step solution

Radioactive decay curve

Decay progression

Half-lives elapsedTime elapsed% Remaining

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Key insight

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Half-life formulas

Half-life describes exponential radioactive decay. The three main forms of the equation let you solve for any unknown:

Remaining quantity: N(t) = N₀ × (½)^(t / t½)
Half-life from data: t½ = t × ln(2) / ln(N₀/N(t))
Elapsed time: t = t½ × ln(N₀/N(t)) / ln(2)
Decay constant: λ = ln(2) / t½ ≈ 0.693 / t½

Isotope	Half-life	Use / notes
Carbon-14	5,730 years	Radiocarbon dating
Iodine-131	8.02 days	Medical imaging & thyroid treatment
Radium-226	1,600 years	Historical medical use
Polonium-210	138 days	Short-lived alpha emitter
Uranium-238	4.47 × 10⁹ years	Geological dating
Technetium-99m	6.01 hours	Most common medical imaging isotope
Cesium-137	30.17 years	Nuclear fallout marker

Frequently asked questions

What is half-life?

Half-life (t½) is the time it takes for exactly half of a radioactive substance to undergo decay. After one half-life, 50% remains. After two half-lives, 25% remains. After ten half-lives, less than 0.1% remains. The process follows exponential decay.

Does the half-life change over time?

No. A radioactive substance always decays at the same proportional rate — the half-life is constant regardless of temperature, pressure, chemical state, or how much of the substance remains. This is what makes it useful for dating materials.

What is the decay constant?

The decay constant (λ) represents the probability per unit time that a nucleus will decay. It relates to half-life by λ = ln(2)/t½ ≈ 0.693/t½. A larger decay constant means faster decay (shorter half-life).

Will a substance ever fully decay?

Mathematically never — each half-life reduces the amount by half, so in theory there is always a tiny fraction remaining. Practically, a substance is considered "effectively decayed" after about 10 half-lives (remaining ≈ 0.1% of original).