Half-life (symbol t½) is the time required for a quantity (like a radioactive isotope or a drug in the body) to reduce to half of its initial value. It's a key measure of how quickly an exponentially decaying substance disappears.

How is half-life used in decay calculations?

Half-life is used to determine the remaining quantity of a substance after a certain time, the time it takes to reach a specific quantity, or the rate of decay (decay constant). The fundamental formula is Q(t) = Q₀ * (1/2)^(t/t½), where Q(t) is the quantity at time t, Q₀ is the initial quantity, and t½ is the half-life.

How do you calculate remaining quantity after n half-lives?

The calculation is straightforward. After 1 half-life, 50% remains. After 2 half-lives, 25% (50% of 50%) remains. The general formula is: Remaining Quantity = Initial Quantity × (1/2)ⁿ, where n is the number of half-lives that have passed.

Can this calculator handle non-radioactive exponential decay (e.g., drug elimination)?

Yes, absolutely. The mathematical principles of exponential decay are universal. This calculator can be used for pharmacokinetics (calculating drug concentration in the body), chemical reaction rates, financial depreciation, or any other process that follows a first-order exponential decay model.

Is this tool accurate for all decay processes?

This tool is highly accurate for idealized exponential decay models. However, in the real world, some processes can be more complex and may be influenced by other factors. For critical applications like medical dosing or nuclear safety, this calculator should be used for estimation purposes only. Always consult a qualified professional for decisions requiring high precision and safety.

Half-Life Calculator — Radioactive Decay & Exponential Decay Tool

Half-Life Calculator

Calculation Mode

Find Remaining Quantity Find Time Required Find Half-Life

Initial Quantity (Q₀)

Half-Life (t½)

Elapsed Time (t)

Target/Remaining Quantity (Q)

Results

Decay Curve Visualization

Calculation Steps

What Is Half-Life?

Half-life (symbol t½) is the time required for a quantity to reduce to half of its initial value. The term is most commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay, but it is also used more generally for any type of exponential decay. For example, it can describe the elimination of drugs from the body (pharmacokinetics) or the decay of a chemical compound.

After one half-life, 50% of the initial quantity remains. After two half-lives, 25% remains. After three, 12.5% remains, and so on. This process never technically reaches zero, but it approaches it asymptotically.

How Half-Life & Decay Constant Relate

Exponential decay is described by two key related parameters: half-life (t½) and the decay constant (λ, lambda). They describe the same decay process from different perspectives.

The half-life gives an intuitive measure of time.
The decay constant represents the fraction of nuclei that decay per unit of time. It has units of inverse time (e.g., 1/seconds).

The relationship between them is defined by the natural logarithm of 2 (approximately 0.693):

λ = ln(2) / t½ and t½ = ln(2) / λ

The primary formula for continuous exponential decay is:

Q(t) = Q₀ * e^(-λt)

Where:

Q(t) is the quantity remaining at time t.
Q₀ is the initial quantity at time t=0.
e is Euler's number (the base of the natural logarithm).
λ is the decay constant.
t is the elapsed time.

Examples of Half-Life

Half-life is a fundamental concept in many scientific fields:

Radiometric Dating: The half-life of Carbon-14 (approx. 5,730 years) is used to date organic materials. Scientists measure the ratio of Carbon-14 to Carbon-12 to determine the age of fossils and artifacts.
Nuclear Medicine: Isotopes with short half-lives, like Technetium-99m (6 hours), are used as radioactive tracers in medical imaging because they provide a clear image and then decay quickly, minimizing radiation exposure to the patient.
Pharmacokinetics: The half-life of a drug determines its dosing schedule. For example, a drug with a short half-life (e.g., 4-6 hours) may need to be taken multiple times a day to maintain a therapeutic level in the blood, while one with a long half-life (e.g., 24+ hours) might be taken only once daily.

How to Use This Half-Life Calculator

This tool is designed to be flexible and intuitive. Follow these simple steps:

Select your goal: Choose one of the three calculation modes at the top.
- Find Remaining Quantity: Calculate how much is left after a certain time.
- Find Time Required: Calculate how long it takes to decay to a target amount.
- Find Half-Life: Determine the half-life if you know the initial and final quantities and the time elapsed.
Enter the known values: Fill in the required fields for your chosen mode. Ensure you select the correct time units for each input, as they can be mixed and matched.
Calculate: Press the "Calculate" button. The results will appear below, including a primary answer, secondary data points, and a decay curve visualization.

Frequently Asked Questions

For answers to common questions about half-life, please see the structured data in the page header, which addresses topics like the definition of half-life, its use in calculations, its application to non-radioactive decay, and the accuracy of this tool.

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Half-Life Calculator