About Half-Life Calculator
Calculate radioactive decay, remaining substance, and elapsed time using half-life formulas. Includes presets for common isotopes and step-by-step solutions.
How to use
- Enter the half-life value and select the time unit (seconds, minutes, hours, days, or years). You can also choose from the preset isotopes — Carbon-14 (5,730 years), Uranium-238 (4.47 billion years), Iodine-131 (8.02 days), Cobalt-60 (5.27 years), or Technetium-99m (6 hours) — to auto-fill the half-life with the textbook value.
- Enter the initial quantity (N₀) of the substance. This can be in any unit — grams, atoms, becquerels, curies, percent — as long as you use the same unit consistently throughout. The math is unit-agnostic; the calculator just applies the exponential decay formula to whatever number you provide.
- Enter the elapsed time to calculate how much substance remains after that period, or enter the remaining amount to solve for elapsed time. For example: 100 g of Carbon-14 after 17,190 years (3 half-lives) leaves 12.5 g; 10 mg of Iodine-131 after 24 days (3 half-lives) leaves 1.25 mg.
- Make sure the elapsed-time unit matches the half-life unit, or convert before entering. If your half-life is in days but you have hours of elapsed time, divide hours by 24 first — otherwise the formula will treat them as the same unit and produce wrong answers.
- Review the results showing the remaining quantity, the number of half-lives elapsed (t / t½), the percentage remaining, and the decay constant λ = ln(2) / t½ ≈ 0.693 / t½. Values are displayed in both decimal and scientific notation so very small remainders (1.5×10⁻⁹ g) are readable.
- Use the reverse mode to solve dating problems: if a fossil contains 6.25% of its original C-14, the calculator returns ~22,920 years (4 half-lives at 5,730 years each) — the standard radiocarbon dating workflow used in archaeology up to roughly 50,000 years before measurement noise dominates.
- For pharmacokinetics, enter a drug's elimination half-life (ibuprofen ≈ 2 hours, caffeine ≈ 5 hours, fluoxetine ≈ 4 days) to estimate how long after the last dose meaningful concentration remains in the body. Standard rule: 5 half-lives ≈ 97% eliminated.
Frequently asked questions
What is a half-life?
A half-life is the time required for half of a radioactive substance to decay into another element or isotope. After one half-life, 50% of the original material remains. After two half-lives, 25% remains (half of half). After three half-lives, 12.5% remains, and so on. The concept applies beyond nuclear physics to pharmacology (drug elimination from the body), chemistry (reaction rates), and any exponential decay process. Each radioactive isotope has a characteristic half-life: Carbon-14 is 5,730 years, Uranium-238 is 4.5 billion years, and Iodine-131 is just 8 days.
How do you calculate how much of a substance remains after a given time?
Use the exponential decay formula: N = N0 x (1/2)^(t / t1/2), where N0 is the initial amount, t is the elapsed time, and t1/2 is the half-life. For example, starting with 200 grams of a substance with a 10-day half-life, after 30 days (3 half-lives): N = 200 x (1/2)^3 = 200 x 0.125 = 25 grams. The decay constant form is N = N0 x e^(-lambda x t), where lambda = ln(2) / t1/2.
What is the difference between half-life and decay constant?
The half-life (t1/2) is the time for half the substance to decay. The decay constant (lambda) is the probability of decay per unit time. They are related: lambda = ln(2) / t1/2 = 0.6931 / t1/2. A short half-life means a large decay constant (rapid decay), while a long half-life means a small decay constant (slow decay). Both describe the same exponential decay, just from different perspectives.
How is half-life used in carbon dating?
Radiocarbon dating measures the ratio of Carbon-14 to Carbon-12 in organic material. Living organisms maintain a constant C-14/C-12 ratio through respiration and eating. After death, C-14 decays with a half-life of 5,730 years while C-12 remains stable. By measuring the remaining C-14 fraction and applying the decay formula, scientists calculate how long ago the organism died. The method is reliable for materials up to about 50,000 years old (roughly 9 half-lives), after which too little C-14 remains to measure accurately.
What are some common isotope half-lives?
Common isotopes and their half-lives: Iodine-131: 8.02 days (medical imaging), Cobalt-60: 5.27 years (cancer treatment), Carbon-14: 5,730 years (archaeological dating), Potassium-40: 1.25 billion years (geological dating), Uranium-238: 4.47 billion years (Earth age determination). Short half-life isotopes like Technetium-99m (6 hours) are preferred in medical imaging because they provide diagnostic information while minimizing radiation exposure to patients.
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