Half-Life Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding and Jack Bowater
Last updated: Dec 08, 2021

The half-life calculator is a tool that helps you understand the principles of radioactive decay. You can use it to not only learn how to calculate half-life, but also as a way of finding the initial and final quantity of a substance or its decay constant. This article will also present you with the half-life definition and the most common half-life formula.

Half-life definition

Each radioactive material contains a stable and an unstable nuclei. Stable nuclei don't change, but unstable nuclei undergo radioactive decay, emitting alpha particles, beta particles or gamma rays and eventually decaying into a stable nuclei. Half-life is defined as the time required for half of the unstable nuclei to undergo their decay process.

Each substance has a different half-life. For example, carbon-10 has a half-life of only 19 seconds, making it impossible for this isotope to be encountered in nature. Uranium-233, on the other hand, has the half-life of about 160 000 years.

This term can also be used more generally to describe any kind of exponential decay - for example, the biological half-life of metabolites.

Half-life is a probabilistic measure - it doesn't mean that exactly half of the substance will have decayed after the time of the half-life has elapsed. Nevertheless, it is an approximation that gets very accurate when a sufficient number of nuclei are present.

Half-life formula

The number of unstable nuclei remaining after time t can be determined according to this equation:

N(t) = N(0) * 0.5(t/T)


  • N(t) is the remaining quantity of a substance after time t has elapsed.
  • N(0) is the initial quantity of this substance.
  • T is the half-life.

It is also possible to determine the remaining quantity of a substance using a few other parameters:

N(t) = N(0) * e(-t/τ)

N(t) = N(0) * e(-λt)

  • τ is the mean lifetime - the average amount of time a nucleus remains intact.
  • λ is the decay constant (rate of decay).

All three of the parameters characterizing a substance's radioactivity are related in the following way:

T = ln(2)/λ = ln(2)*τ

How to calculate the half-life

  1. Determine the initial amount of a substance. For example, N(0) = 2.5 kg.
  2. Determine the final amount of a substance - for instance, N(t) = 2.1 kg.
  3. Measure how long it took for that amount of material to decay. In our experiment, we observed that it took 5 minutes.
  4. Input these values into our half-life calculator. It will compute a result for you instantaneously - in this case, the half-life is equal to 19.88 minutes.
  5. If you are not certain that our calculator returned the correct result, you can always check it using the half-life formula.

Confused by exponential formulas? Try our exponent calculator.

Half life is a similar concept to the doubling time in biology. Check our generation time calculator to learn how exponential growth is both useful and a problem in laboratories!


What is half life?

Half-life is defined as the time taken by a substance to lose half of its quantity.

How to calculate half life?

To find half-life:

  1. Find the substance's decay constant.
  2. Divide ln 2 by the decay constant of the substance.

What is the half life of radium?

Half-life of radium-218 is 25.2 x 10-6 seconds.

What is the half life of carbon?

Half-life of carbon-20 is 16 x 10-3 seconds.

What is the half life of uranium?

Half-life of uranium-235 is 22.21 x 1015 seconds.

Bogna Szyk
Formula for half-life, given the decay constant and the mean lifetime
Initial quantity (N(0))
Half-life time (T)
Total time
Remaining quantity (N(t))
Decay constant (λ)
per s
Mean lifetime (τ)
Check out 35 similar physical chemistry calculators ⚗️
Air-fuel ratio (AFR)Arrhenius equationAtomic mass… 32 more
People also viewed…

Air-fuel ratio (AFR)

The AFR calculator gives you the rate between the mass of air and the mass of fuel of a complete combustion process.

Humans vs vampires

Vampire apocalypse calculator shows what would happen if vampires were among us using the predator - prey model.

Meat footprint

Check out the meat impact - on the environment and your health.

ppm to molarity

If you need to convert ppm (parts per million) to molarity for solutions, this calculator is for you!
Copyright by Omni Calculator sp. z o.o.
Privacy policy & cookies
main background