☢️ Physics Calculator

Half-Life Calculator

Calculate radioactive decay, remaining quantity, elapsed time, or the half-life itself — using the exponential decay formula for nuclear physics, pharmacokinetics, and carbon dating.

Radioactive Decay

Enter 3 values — solve for the 4th

Solve for

Initial quantity (N₀)

Remaining quantity (N)

Half-life (T½)

Elapsed time (t)

Enter 3 values to solve for the 4th

Formula: N = N₀ × (½)^(t/T½) · λ = ln(2)/T½

Common Half-Lives

Isotope / Substance	Half-Life
Carbon-14	5,730 years
Uranium-238	4.47 billion years
Iodine-131	8.02 days
Radon-222	3.82 days
Caffeine (in body)	~5–6 hours

Frequently Asked Questions

What is half-life?

Half-life (T½) is the time it takes for half of a substance to decay or be eliminated. After 1 half-life, 50% remains. After 2: 25%. After 10: ~0.1%. Formula: N = N₀ × (½)^(t/T½).

What is the decay constant (λ)?

The decay constant λ = ln(2)/T½ ≈ 0.693/T½ describes the rate of decay per unit time. N = N₀ × e^(−λt) is the equivalent continuous form of the decay formula.