Half-life (T₁/₂) is the time required for exactly half of the radioactive atoms in a sample to decay. After one half-life, 50% remains; after two half-lives, 25% remains; after three half-lives, 12.5% remains, and so on. Half-life is a constant property of each radioisotope and is unaffected by temperature, pressure, or chemical environment.

Carbon-14 dating relies on the radioactive decay of ¹⁴C (half-life ~5,730 years). Living organisms constantly exchange carbon with the atmosphere, maintaining a ¹⁴C/¹²C ratio similar to atmospheric levels. When an organism dies, ¹⁴C intake stops, and the existing ¹⁴C decays exponentially. By measuring the remaining ¹⁴C ratio, scientists can estimate the time since death—effective for dating organic materials up to ~50,000 years old.

The fundamental decay equation is N(t) = N₀ × e^−λt, where N(t) is the amount at time t, N₀ is the initial amount, and λ is the decay constant (λ = ln(2)/T₁/₂). This can also be written as N(t) = N₀ × (½)^t/T₁/₂. This exponential model accurately describes radioactive decay across all time scales.

Yes—half-life is an intrinsic nuclear property of each radioisotope. It does not change with physical conditions like temperature, pressure, or chemical bonding. This constancy makes radioactive decay an exceptionally reliable "clock" for geological and archaeological dating. Some isotopes have half-lives of microseconds, while others exceed billions of years.

Half-lives span an enormous range. Short-lived isotopes like Polonium-214 have a half-life of just 164 microseconds. Medical isotopes like Iodine-131 have a half-life of ~8 days. Carbon-14 is 5,730 years. Uranium-238 has a half-life of ~4.47 billion years. Our calculator supports seconds, minutes, hours, days, years, and geological time units (thousands, millions, billions of years) to accommodate this vast range.

Radiometric dating is remarkably accurate when properly applied. For Carbon-14 dating, the typical uncertainty is ±30–80 years for samples up to ~10,000 years old. For Uranium-Lead dating of zircon crystals, precision can reach ±0.1–1% of the age. Accuracy depends on proper sample collection, contamination avoidance, and using appropriate isotope systems for the expected age range.

Exponential decay asymptotically approaches zero but mathematically never reaches it—there's always a non-zero probability that some atoms remain. In practice, after about 10 half-lives, less than 0.1% of the original material remains (~1/1024), and after 20 half-lives, less than 1 part per million remains. At some point, the remaining quantity becomes statistically undetectable.