Half-life formula and unit consistency
Half-life is the time it takes for half of a quantity to remain in a process described by exponential decay. It is used in physics, chemistry, and other contexts where a quantity decreases by a consistent fraction over equal time intervals. It is not the same as losing a fixed number of units every period.
Formula
remaining = initial amount × (1/2)elapsed time ÷ half-life. For example, if a sample starts at 80 units and three half-lives pass, 40 remain after the first, 20 after the second, and 10 after the third.
Use compatible time units for elapsed time and half-life; the calculator converts between the options you select. The equation models ideal exponential decay and does not determine whether a real substance is hazardous or how it should be handled. Follow qualified lab or safety guidance for real materials.
Tips for accurate results
The remaining amount is N = N₀ × (1/2)^(t/T), where T is the half-life and t is the elapsed time. Use the same time unit for both. Carbon-14 has a half-life of about 5,730 years, so after 11,460 years, two half-lives, a quarter of the original remains.
Common mistakes and limits
After five half-lives about 3 percent remains, which is why a substance is often treated as nearly gone after that time. The model assumes exponential decay with a constant half-life, and it does not apply to processes that behave differently. In medicine, biological half-life depends on the person and the drug, so follow clinical guidance.