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 $N(t) = N_0 \cdot (1/2)^{t / t_{1/2}}$.

Remaining Quantity ($N_t$):

Initial Quantity ($N_0$):

Time ($t$):

Half-Life ($t_{1/2}$):

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.

Yes. Enter the initial quantity, elapsed time, and half-life to calculate the remaining amount of the substance automatically.

Half-life is the time required for a substance to reduce to half its original amount, while mean lifetime is the average lifetime of a decaying particle and is equal to 1 divided by the decay constant.

Half-life calculations are commonly used in nuclear physics, radiometric dating, medicine, chemistry, environmental science, and radioactive decay analysis.

Half-Life Calculator