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Half Life Calculator

Calculate half-life, initial quantity, remaining quantity, or elapsed time in exponential decay with interactive decay curve visualization, step-by-step formulas, and preset isotope values.

Half Life Calculator

Exponential Decay Calculator

Calculate half-life, remaining quantity, initial amount, or elapsed time with interactive visualization

Quick Examples - Click to Try
Isotope Presets - Set Half-Life Only

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About Half Life Calculator

Welcome to the Half Life Calculator, a comprehensive tool for calculating exponential decay in radioactive materials, pharmacokinetics, and any process following first-order decay kinetics. This calculator features an interactive decay curve visualization, step-by-step formula breakdowns, preset values for common radioactive isotopes, and high-precision calculations.

What is Half-Life?

Half-life (t½) is the time required for a quantity to reduce to half of its initial value. This concept is fundamental in nuclear physics, chemistry, pharmacology, and many other fields where substances decay or diminish exponentially over time.

The defining characteristic of half-life is its constancy: regardless of how much material you start with, it always takes the same amount of time for half of it to decay. This property makes half-life an intrinsic characteristic of radioactive isotopes.

The Exponential Decay Formula

Half-Life Decay Equation
$$N(t) = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}$$

Where:

Alternative Forms

The half-life equation can be expressed using the decay constant (λ):

Decay Constant Form
$$N(t) = N_0 \times e^{-\lambda t}$$

where λ = ln(2)/t½ ≈ 0.693/t½

How to Use This Calculator

  1. Select what to calculate: Choose which variable you want to solve for - remaining quantity, initial quantity, elapsed time, or half-life.
  2. Use isotope presets (optional): Click on any common isotope button to auto-fill its half-life value. Presets include Carbon-14, Uranium-238, Iodine-131, and more.
  3. Enter known values: Fill in the three known values. The fourth field (being solved for) will be calculated.
  4. Set precision: Choose decimal places (2-15) for your results.
  5. Calculate: Click the button to see results, decay curve visualization, and step-by-step calculations.

Common Radioactive Isotopes

IsotopeHalf-LifePrimary Use
Carbon-145,730 yearsArchaeological dating (radiocarbon dating)
Uranium-2384.468 billion yearsGeological dating, nuclear fuel
Iodine-1318.02 daysThyroid cancer treatment
Cobalt-605.27 yearsRadiation therapy, industrial radiography
Technetium-99m6.01 hoursMedical imaging (SPECT scans)
Radon-2223.82 daysEnvironmental monitoring
Strontium-9028.8 yearsNuclear fallout tracking
Plutonium-23924,110 yearsNuclear weapons, reactors

Applications of Half-Life

Radiocarbon Dating

Carbon-14 dating is used to determine the age of organic materials up to about 50,000 years old. Living organisms maintain a constant C-14/C-12 ratio through metabolism. After death, C-14 decays without replacement. By measuring remaining C-14, scientists calculate time since death.

Nuclear Medicine

Medical isotopes like Technetium-99m (t½ = 6 hours) are chosen for their short half-lives, providing enough time for imaging while minimizing patient radiation exposure. Iodine-131 treats thyroid conditions by delivering targeted radiation.

Pharmacokinetics

Drug half-life determines dosing schedules. For example, caffeine has a half-life of about 5 hours in adults. After 4-5 half-lives (20-25 hours), over 95% of a drug is typically eliminated from the body.

Geological Dating

Long-lived isotopes like Uranium-238 (t½ = 4.5 billion years) and Potassium-40 (t½ = 1.25 billion years) date rocks and determine Earth's age at approximately 4.5 billion years.

Environmental Science

Understanding half-lives of pollutants and radioactive contamination helps predict environmental recovery. Cesium-137 from nuclear accidents (t½ = 30 years) remains a concern for decades.

Understanding the Decay Constant

The decay constant (λ) represents the probability of decay per unit time. It relates to half-life through:

Decay Constant Relationship
$$\lambda = \frac{\ln(2)}{t_{1/2}} \approx \frac{0.693}{t_{1/2}}$$

A larger decay constant means faster decay and shorter half-life. The decay constant is useful in differential equations and when combining multiple decay processes.

Multiple Half-Lives

After n half-lives, the remaining fraction is (1/2)ⁿ:

Beyond Radioactivity: Other Applications

The half-life concept applies to any exponential decay process:

Frequently Asked Questions

What is half-life in radioactive decay?

Half-life is the time required for half of the radioactive atoms in a sample to decay. It is a constant property of each radioactive isotope. For example, Carbon-14 has a half-life of 5,730 years, meaning after this period, half of the original C-14 atoms will have decayed into Nitrogen-14.

What is the exponential decay formula?

The exponential decay formula is N(t) = N₀ × (1/2)^(t/t½), where N(t) is the remaining quantity at time t, N₀ is the initial quantity, t is the elapsed time, and t½ is the half-life. This formula can be rearranged to solve for any of these four variables.

How is half-life used in carbon dating?

Carbon dating uses the known half-life of Carbon-14 (5,730 years) to determine the age of organic materials. Living organisms maintain a constant ratio of C-14 to C-12 through respiration and food intake. After death, C-14 decays without replenishment. By measuring the remaining C-14, scientists can calculate how long ago the organism died.

What is the decay constant and how does it relate to half-life?

The decay constant (λ) represents the probability of decay per unit time. It is related to half-life by the formula λ = ln(2)/t½ ≈ 0.693/t½. A larger decay constant means faster decay and shorter half-life.

Can half-life be applied to non-radioactive processes?

Yes, the half-life concept applies to any exponential decay process. This includes drug elimination from the body (pharmacokinetics), chemical reaction rates, electrical capacitor discharge, population decay, depreciation of assets, and even the decay of internet memes or news relevance.

Why does half-life remain constant regardless of the amount of material?

Half-life is constant because radioactive decay is a random process at the atomic level. Each atom has the same probability of decaying in any given time period, independent of other atoms. This statistical behavior results in a fixed fraction decaying per unit time.

Additional Resources

Reference this content, page, or tool as:

"Half Life Calculator" at https://MiniWebtool.com/half-life-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 25, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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