Half-Life Calculator
Calculate remaining quantity after radioactive or exponential decay, solve elapsed time from a known remaining amount, or solve the half-life from two measured amounts.
Enter your values
Change any assumption and calculate again to compare results.
What This Half-Life Calculator Calculates
The Half-Life Calculator works in three directions. It can estimate how much of an exponentially decaying quantity remains after a known time, calculate the elapsed time when the initial and remaining amounts are known, or solve the half-life when two amounts and the elapsed time are known.
Although half-life is strongly associated with radioactive decay, the same exponential relationship can describe other processes that halve at a constant proportional rate. The time unit is kept symbolic, so days, years, hours or another consistent unit can be used.
Formula and Calculation Method
The core relationship is N = N₀(1/2)^(t/T½), where N₀ is the initial quantity, N is the remaining quantity, t is elapsed time and T½ is the half-life. The page rearranges this same equation rather than switching to a different model when you solve for time or half-life.
For elapsed time, t = T½ × ln(N/N₀) ÷ ln(1/2). For half-life, T½ = t × ln(1/2) ÷ ln(N/N₀). The ratio N/N₀ must be between zero and one for ordinary decay.
How to Use This Calculator
- Enter the values requested in the calculator workspace and keep units consistent.
- Select Calculate. The arithmetic runs locally in your browser.
- Review the main answer together with the supporting figures and formula shown beside it.
- Change one assumption at a time when comparing scenarios so you can see which input is affecting the result.
- Use Copy Result, Save Result Image or Share Result when you need a record of the calculation.
The page is designed to show more than a single unexplained number. Supporting values make it easier to verify the arithmetic, compare results with a spreadsheet or textbook, and reproduce the calculation later. When a calculator uses a unit selector, the unit affects the calculation exactly as described in the method section rather than being treated as decoration.
Worked Example
Starting with 100 units and a half-life of 5 days, after 10 days two half-lives have passed. The remaining quantity is 25 units, so 75% has decayed.
Replace the example values with the measurements or numbers that apply to your own problem. The default values are present to make the calculator immediately testable and to show the expected input format.
How to Interpret the Result
A half-life is the time required for the quantity to fall to half its current value, not the time required for it to disappear completely. After one half-life, 50% remains; after two, 25%; after three, 12.5%.
Measured samples may include background signals, multiple isotopes or non-exponential processes. In those situations a single half-life model may not fully explain the data.
Common Search Questions About Half-Life Calculator
How do I calculate this result?
Enter the required values in the calculator above and select Calculate. The result is shown together with supporting values and the formula used, so the arithmetic can be checked instead of treated as a black box.
Can I use this calculator on a phone?
Yes. The v113 workspace is responsive, and on small screens the result opens in the current viewport after calculation.
Does OfficeCalculator.Net upload my inputs?
The arithmetic for this calculator runs locally in the browser. The page does not require an account to perform the calculation.
Important Limitations
The calculator assumes a single exponential decay process with a constant half-life. It does not model decay chains, daughter products, background correction, changing environmental conditions or measurement uncertainty.
Round only after the main calculation when practical. Rounding inputs too early can magnify small differences, especially in formulas that involve powers, roots, logarithms, repeated operations or unit conversions.
Privacy, Mobile Results and Practical Use
The calculator performs its arithmetic in the browser and does not require an account. Values entered into the form are used to generate the result shown on the page. On narrow screens the result panel opens in the current viewport after calculation, so the answer does not get lost below long explanatory content.
Use the calculator as a transparent planning and checking tool. For coursework, engineering work, financial records or any other situation where precision matters, keep the original source values and verify rounding conventions. A calculator can evaluate a formula correctly while still producing an inappropriate real-world answer if the wrong inputs, units or definitions are supplied.
Frequently Asked Questions
Does a sample reach exactly zero after several half-lives?
No. The ideal exponential model approaches zero continuously; each half-life halves whatever amount remains.
Can I use years instead of days?
Yes. Use any consistent time unit. The calculated time or half-life will be expressed in the same unit.
Can this formula be used for non-radioactive decay?
Yes, when the quantity follows the same constant proportional halving model. Whether that model is scientifically appropriate depends on the process.