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Half Life Calculator

Select any parameter and the calculator will calculate its value by using the half life formula, with necessary parameters being provided.

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Converter

Find:

Quantity Remains (N_t):

Initial Quantity (N₀):

Half Life (t):

Related

An online half-life calculator allows you to compute the remaining amount of a substance after a given time. Calculating half-life, mean lifetime, and decay constant manually can be time-consuming, but these calculators provide accurate results in seconds. This guide explains half-life, its formulas, and how to calculate it.

What is Half-Life?

Half-life is the time required for half of the atoms in a radioactive substance to decay or transform into another element. This concept was first discovered by Rutherford in 1907 and is commonly represented as t_1/2.

Example: If a substance has a half-life of 1 hour, after 1 hour, half of it will have decayed. After 2 hours, only one-fourth of the original substance remains.

Reaction Half-Life

In chemical reactions, the half-life is the time it takes for a reactant’s concentration to reduce to 50% of its initial value. It is expressed in seconds, minutes, or hours depending on the reaction.

Half-Life Formulas

The commonly used formulas to calculate half-life or decay are:

N(t) = N₀ (½)^(t / t₁/₂)
N(t) = N₀ e^(–t / τ)
N(t) = N₀ e^(–λt)

Where:

N₀ = initial quantity of the substance
N(t) = quantity remaining at time t
t₁/₂ = half-life of the substance
τ = mean lifetime of the substance
λ = decay constant

Calculating Elapsed Time

To find the elapsed time for a decaying substance:

\(T = t_{1/2} \frac{\ln(N_t / N_0)}{-\ln 2}\)

Where:

T = elapsed time
t₁/₂ = half-life
N₀ = initial quantity
N_t = remaining quantity at time T

Half-Life, Decay Constant, and Mean Lifetime

The relationship between half-life, decay constant, and mean lifetime is:

\(t_{1/2} = \frac{\ln(2)}{\lambda} = \tau \ln(2)\)

Where:

t₁/₂ = half-life
τ = mean lifetime
λ = decay constant
ln = natural logarithm

How to Calculate Half-Life?

Determine the initial amount of the substance (e.g., N₀ = 2.5 kg).
Measure the remaining quantity (e.g., N(t) = 2.1 kg).
Note the elapsed time (e.g., 5 minutes).
Input the values into an online half-life calculator to get the result. For example, t₁/₂ ≈ 19.88 minutes.
Optionally, verify using the manual half-life formula for accuracy.

How Does the Half-Life Calculator Work?

Input

You can calculate half-life, elapsed time, or remaining quantity:

Select the type of calculation from the drop-down (half-life, elapsed time, initial or final quantity).
Enter the known values in the corresponding fields.

Mean Lifetime and Decay Constant Conversion

Choose half-life, decay constant, or mean lifetime and enter the known value.

Output

The calculator provides step-by-step results for half-life, elapsed time, and remaining quantity.
It can convert between half-life, mean lifetime, and decay constant.

FAQ

What is radioactive decay?

Radioactive decay is the process in which unstable nuclei lose energy by emitting radiation, such as alpha particles, beta particles, gamma rays, or through electron capture.

How many types of radioactive decay are there?

Alpha decay
Beta decay
Gamma decay

What is the half-life of carbon-14?

Carbon-14 has a half-life of 5730 ± 40 years.

How Does Radioactivity Work?

Atoms of heavier elements often have an unstable proton-to-neutron ratio. To reach stability, they undergo radioactive decay, emitting energy and particles.

Conclusion

Online half-life calculators make it easy to compute the decay of substances. They help determine half-life, elapsed time, remaining quantities, and decay constants efficiently, saving time and minimizing errors compared to manual calculations.