# Half-life calculator

Our handy half life formula calculator can generate any values from the formulas for a substance in the decay to decrease by half. Just enter any other three values and enjoy seamless, precise calculations.

## Free half life calculator for easy computations

## Conversions between half-life, mean lifetime, and decay constant

## The definition a half-life formula

Halflife is the amount of time it takes for a substance to lose half of its quantity. It is often used in relation to atoms that undergo radioactive decay.

This value doesn't show exactly half of the substance but rather an approximation of it. Still, it demonstrates pretty accurate results with a sufficient number of nuclear elements.

Half-life has many applications in physics, geology, and chemistry. Half-life varies for each element. For example, half-life for carbone-10 is just 19 seconds. This means that this isotope cannot be encountered in nature. On the other hand, Uranium-233 has an approximate half-life of 160,000 years.

The half life radioactive decay formula can be visualized in this form:

N(t) = N(0) × 0.5 (t/T), where

N(t) is the quantity of a substance that remains after the time t has elapsed

N(0) is the initial quantity

T is half-time

There are also two other versions of equations describing half life exponential decay:

N(t) = N(0) × e(−t/τ)

N(t) = N(0) × e(−λt), where

τ stands for mean lifetime, or an average amount of time for which a nucleus remains unchanged
λ stands for the ratio of decay, or decay constant

Our online calculation tool helps determine the half-life of any substance in mere seconds. Solve the half-life equations in a whizz and don't pay a dime for it. For finding t1/2 (half-time), enter the values for three other elements of the forumla. Use our smart solver for your other calculations: compute a percentage, solve differential equations, determine the needed ratios, or resolve algebra problems.

## Deriving relationship between half-life constants

Using half life equations presented above, we can also derive the relationship between the half-time, decay constant, and lifetime. It can also be derived using precalculus. This relationship allows to calculate all values as long as you know at least one.