Half-life is the time required for a quantity to decrease to one-half of its initial amount under exponential decay.

What is the half-life formula?

The remaining quantity formula is N(t)=N0(1/2)^(t/T), where N0 is the initial quantity, t is elapsed time, and T is the half-life.

Can this calculator be used for medical dosing?

No. This calculator is educational and should not be used for medical dosing, radiation safety, or professional nuclear calculations.

Half-Life Calculator with Steps

What Half-Life Means

Half-life is the time required for a quantity to decrease to half of its initial value. It is commonly used for radioactive decay, chemical degradation, environmental decay, and simplified drug elimination models.

N(t) = N₀ × (1/2)^{t / T_1/2}

Here, N₀ is the initial quantity, N(t) is the remaining quantity after time t, and T_1/2 is the half-life.

Decay Constant Formula

Half-life can also be written using the exponential decay constant λ.

λ = ln(2) / T_1/2
N(t) = N₀e^−λt

What This Calculator Can Solve

Mode	What it finds	Main formula
Remaining quantity	How much remains after a known time.	N(t) = N₀(1/2)^t/T
Elapsed time	How long it takes to reach a target remaining quantity.	t = T × ln(N/N₀) / ln(1/2)
Half-life	The half-life from measured initial and remaining quantities over time.	T = t × ln(1/2) / ln(N/N₀)

Preset Isotopes

The preset isotope values are rounded educational values. For precise scientific, laboratory, environmental, or nuclear safety work, use an official nuclear data source.

Isotope	Preset half-life
Carbon-14	5730 years
Iodine-131	8.06 days
Uranium-238	4.468 billion years
Plutonium-239	24100 years
Radon-222	3.82146 days
Cesium-137	30.17 years
Tritium	12.32 years

Example Calculation

Suppose a sample starts with 100 g and has a half-life of 5730 years. After 11460 years, two half-lives have passed.

N0 = 100 g
T1/2 = 5730 years
t = 11460 years

Number of half-lives = 11460 / 5730 = 2

N(t) = 100 × (1/2)^2
N(t) = 25 g

Common Uses of Half-Life

Radioactive decay: estimating how much of a radionuclide remains.
Carbon dating: estimating age from radiocarbon decay.
Medicine: understanding simplified drug elimination trends.
Environmental science: estimating pollutant decay or degradation.
Chemistry: modeling first-order reaction decay.

This calculator is educational. Do not use it for medical dosing, radiation safety, nuclear handling, environmental compliance, or professional laboratory decisions.

Common Mistakes

Mixing units, such as using half-life in years and time elapsed in days without conversion.
Using Iodine-131 as 1600 hours instead of about 8 days.
Using Plutonium-239 as 239000 years instead of about 24100 years.
Using a target remaining quantity greater than the initial quantity for decay.
Forgetting that activity and number of atoms decay by the same exponential ratio in a simple radioactive decay model.

Frequently Asked Questions

What is half-life?

Half-life is the time needed for a quantity to decrease to half of its starting value.

What is the decay constant?

The decay constant λ describes the exponential decay rate. It is calculated as λ = ln(2) / half-life.

Can the quantity unit be grams, moles, atoms, or becquerels?

Yes. The formula works with any consistent quantity unit because it calculates a ratio of remaining amount to initial amount.

Can I calculate time from the remaining quantity?

Yes. Choose the elapsed time mode and enter the initial quantity, target remaining quantity, and half-life.

Can I calculate half-life from experimental data?

Yes. Choose the half-life mode and enter the initial quantity, remaining quantity, and elapsed time.