Half-Life Calculator
Calculate Half-Life values for science, physics, chemistry, and engineering problems.
This half-life calculator finds how much of a substance remains after a given amount of time, based on its half-life - the time it takes for exactly half of a quantity to decay or be eliminated, used for radioactive decay, drug elimination, and other exponential decay processes.
Enter the initial quantity, half-life, and elapsed time, and the calculator returns the remaining quantity.
Worked Calculation Examples
| Scenario | Result | Calculation Step |
|---|---|---|
| 100g sample, 5-day half-life, 15 days elapsed | 12.5g remaining | 15 days ÷ 5 days = 3 half-lives. Remaining = 100 × (1/2)³ = 100 × 0.125 = 12.5g. |
| 80mg dose, 6-hour half-life, 18 hours elapsed | 10mg remaining | 18 hours ÷ 6 hours = 3 half-lives. Remaining = 80 × (1/2)³ = 80 × 0.125 = 10mg. |
The Half-Life Formula
Remaining quantity = initial quantity x (1/2)^(t / half-life), where t is the elapsed time. After one half-life, 50% remains; after two half-lives, 25% remains; after three, 12.5% - the quantity halves repeatedly but never mathematically reaches exactly zero.
Half-Life Applies Beyond Radioactivity
While half-life is best known from radioactive decay, the same exponential decay math applies to how the body eliminates many medications, how caffeine clears from the bloodstream, and other processes where a quantity decreases by a constant proportion over equal time intervals.
How to Use the Half-Life Calculator
- Open the Half-Life Calculator and enter the values requested in the input fields.
- Check the units, percentages, dates, or time periods before reading the answer.
- Review the instant result and adjust any value to compare another scenario.
- Use the formula, example, and FAQs below to understand how the half life calculator works.
Frequently Asked Questions
How do you calculate remaining quantity using half-life?
Use: remaining = initial x (1/2)^(elapsed time / half-life). Each full half-life period cuts the remaining quantity in half.
Does a substance ever completely disappear according to half-life math?
Mathematically, no - the exponential decay formula approaches zero but never reaches it exactly, though after enough half-lives the remaining amount becomes negligible in practice.
Is half-life the same for every substance?
No - each radioactive isotope or substance has its own characteristic half-life, ranging from fractions of a second to billions of years, determined by its specific decay rate.
How do I use this half life calculator?
Enter the known values, review the units or settings, and the calculator updates the result instantly. The formula and example on this page show how the answer is produced.
What does the Half-Life Calculator calculate?
Calculate Half-Life values for science, physics, chemistry, and engineering problems. It is designed for fast browser-based calculations without sign-up, downloads, or manual spreadsheet setup.
What formula does this half-life use?
The formula is: N(t) = N₀ × (1/2)^(t / half-life). Radioactive half-life was discovered by Ernest Rutherford and Frederick Soddy in 1902 while studying thorium decay, a finding that soon enabled radiometric dating - most famously carbon-14 dating, developed by chemist Willard Libby in 1949 (earning him the 1960 Nobel Prize), which uses carbon-14's roughly 5,730-year half-life to estimate the age of organic archaeological and geological samples.
Related Calculators
pH Calculator
Calculate pH values for science, physics, chemistry, and engineering problems.
Ideal Gas Law Calculator
Calculate Ideal Gas Law values for science, physics, chemistry, and engineering problems.
Wavelength Frequency Calculator
Calculate Wavelength Frequency values for science, physics, chemistry, and engineering problems.
Density Calculator
Calculate Density values for science, physics, chemistry, and engineering problems.
Molarity Calculator
Calculate Molarity values for science, physics, chemistry, and engineering problems.
Dilution Calculator
Calculate Dilution values for science, physics, chemistry, and engineering problems.
Last updated: September 27, 2026.