Half-Life Calculator

Calculate half-life, elapsed time, initial, or remaining quantity using this easy calculator. Read below to learn the half-life formula and how to solve it.

What is Half-Life?

Half-life is the time needed to reduce the quantity of a substance to half its initial amount. It’s is commonly used to define the decay of radioactive material, where half-life is the amount of time needed for half the atoms of a particular isotope to decay.^[1]

In the medical world, half-life is also used to describe the time it takes for the concentration of a substance to be reduced to half of the initial dose in your body.^[2] This is known as elimination half-life.

How to Calculate Half-Life

You can calculate the amount of substance that will remain after an elapsed time period, given the half-life of the substance and the equation for half-life.

Half-Life Formula

The half-life formula states:

N(t) = N₀ × (12)^t/t_½

Thus, the remaining quantity N(t) is equal to the initial quantity N₀ times 1/2 to the power of the elapsed time t divided by the half-life t_½

How to Calculate Time using Radioactive Decay

Using a technique known as carbon dating, it’s possible to estimate the age of an organic compound. This is done by measuring the amount of carbon-14 present in a sample of organic (or previously organic) material and comparing it to the amount that should be present.

Because the half-life of carbon-14 is known to be 5,730 years, we can use the half-life formula to calculate the elapsed time, or age of the material.

Half-Life Formula for Time

By rearranging the half-life formula, we can solve for the amount of time elapsed for an initial quantity to reduce to the remaining quantity.

t = t_½ × ln(N(t) ÷ N₀)-ln(2)

The time elapsed t for a substance to be reduced is equal to the half-life t_½ times the natural log of the remaining quantity N(t) divided by the initial quantity N₀, divided by the negative natural log of 2.

Half-Life Decay Table