How to use the Half-Life Calculator
Enter the starting quantity, its half-life, and the elapsed time. The calculator converts both time entries to seconds, applies N(t) = N0 x (1/2)^(t / t_half), and shows the intermediate values behind the result.
- Enter a positive value in Initial amount (N0).
- Type a label in Amount unit (label only), such as
g, if you want one shown beside the result. - Enter Half-life (t_half) and choose Half-life unit.
- Enter Elapsed time (t) and choose Elapsed time unit. The two units may differ.
- Click Calculate, then review or copy the result.
Half-life formula and remaining amount
The formula uses N0 for the initial amount, t for elapsed time, and t_half for the half-life. The result also includes lambda = ln(2) / t_half, the decay constant per second, and the number of half-lives elapsed.
For example, enter 100 with g as the label, a 5.27-year half-life, and 10 years of elapsed time. The displayed values include:
Remaining amount: 26.8402 g
Amount decayed: 73.1598 g
Percent remaining: 26.8402%
Half-lives elapsed: 1.89753Radioactive decay calculator inputs and units
Half-life unit and Elapsed time unit each offer Seconds, Minutes, Hours, Days, and Years. The calculator converts both selections to seconds, using 31557600 seconds for one year, so the two controls can use different units.
Amount unit (label only) is text beside the initial, remaining, and decayed amounts. The calculator does not convert it. Leave the field blank and the result uses units.
What the half-life calculator accepts
Initial amount (N0) and Half-life (t_half) must be greater than zero. Elapsed time (t) can be zero. Decimal notation such as 12 or 0.5 is accepted, while scientific notation such as 1e3 is rejected. Each numeric value must be no greater than 1e15. Blank, invalid, or out-of-range entries show an error. Changing an input clears the current result until you click Calculate again.
Using the result at different times
Set Elapsed time (t) to zero to see the starting amount as the remaining amount. Enter a later time to see the remaining amount, amount decayed, percent remaining, half-lives elapsed, and decay constant.
The calculation runs in the browser. After a result appears, use Copy result for plain text or Download result (.txt) to save a text file.
Choosing another science calculator
Open Science Calculators for the category list. Physics Calculator covers force, momentum, energy, pressure, wavelength, and other physics quantities. Chemistry Calculator covers pH, molarity, dilution, molar mass, stoichiometry, and specific heat. For absorbance, concentration, path length, or absorptivity, use Beer-Lambert Law Calculator.
Frequently asked questions
How do I calculate the remaining amount after a half-life?
Enter Initial amount (N0), Half-life (t_half), and Elapsed time (t), then click Calculate. The calculator applies N(t) = N0 x (1/2)^(t / t_half) and shows the remaining amount plus the intermediate values.
Can a radioactive decay calculator use different time units?
Yes. Half-life unit and Elapsed time unit work independently. Each can be Seconds, Minutes, Hours, Days, or Years, and both are converted to seconds for the calculation.
Does Amount unit convert grams, moles, or atoms?
Amount unit (label only) is text carried into the output without conversion. Leave it blank to display units as the label.
Does the half-life formula include decay chains or daughter products?
The calculator applies one constant half-life to one substance with a single exponential decay model. It does not model decay chains, branching ratios, daughter products, replenishment, or multi-species behavior.