Half-Life Calculator
Calculate radioactive decay, remaining quantity, elapsed time, mean lifetime, and decay constants.
Half-Life Calculator
Provide any 3 values to calculate the 4th value using $N(t) = N_0 \cdot (1/2)^{t / t_{1/2}}$.
Half-Life Formulas & Definitions
Half-life ($t_{1/2}$) is the time required for a quantity to reduce to half of its initial value. It is widely used in nuclear physics, radiometric dating, and chemical kinetics.
$$N(t) = N_0 \cdot \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} = N_0 \cdot e^{-\lambda t} = N_0 \cdot e^{-\frac{t}{\tau}}$$
Key Relationships:
- Decay Constant ($\lambda$): $\lambda = \frac{\ln(2)}{t_{1/2}} \approx \frac{0.693147}{t_{1/2}}$
- Mean Lifetime ($\tau$): $\tau = \frac{1}{\lambda} = \frac{t_{1/2}}{\ln(2)} \approx 1.4427 \times t_{1/2}$
Frequently Asked Questions (FAQs)
Half-life is the duration required for a decaying substance to decrease to half of its initial amount.
Carbon-14 decays exponentially after an organism dies. By measuring the remaining ratio relative to living tissue, age can be calculated using its 5,730-year half-life.