Solve radioactive decay, remaining quantity, or elapsed time from a half-life, instantly in your browser.
Half-Life Calculator Online
Solve radioactive decay, remaining quantity, or elapsed time from a half-life, instantly in your browser.
The Half-Life Calculator runs entirely in your browser. The quantities, times, and half-life values you enter are computed locally and never leave your device.
Half-Life Calculator solves exponential decay problems for radioactive isotopes, drug elimination, carbon dating, and any other quantity that halves at a constant rate. Choose what you want to solve for — the remaining amount, the elapsed time, or the half-life itself — then fill in the other three values: initial quantity, remaining quantity, elapsed time, and half-life. The tool applies the decay formula N = N₀ × (1/2)^(t/T) and its logarithmic inverses, so you get an exact answer instead of working through change-of-base algebra by hand. It flags impossible inputs, such as a remaining amount larger than the starting quantity. Useful for chemistry and physics homework, pharmacokinetics, and nuclear-decay estimates. Everything runs locally in your browser, so the figures you enter never leave your device.
Features
Solve for remaining quantity, elapsed time, or half-life from the other three values
Uses the standard decay formula N = N0 x (1/2)^(t/T) and its logarithmic inverses
Segmented control switches instantly between the three solve modes
Clear error messages for impossible inputs, like a remaining amount above the initial amount
Works with any consistent time unit — seconds, days, years, or anything else
Copy the computed result with one click for use in a lab report or spreadsheet
Handles fractional and very small half-lives without losing precision
Runs entirely in your browser with no decay figures sent anywhere
How to use the Half-Life Calculator
Pick what to solve for: remaining amount, elapsed time, or half-life
Enter the other three known values in matching time units
Read the solved result, shown with a copy button
Switch solve modes to check the answer against a different unknown
Example
Input
N0=100, t=2, T=1
Output
Remaining: 25
After two half-lives (t/T = 2), the quantity is 100 x (1/2)^2 = 25.
Common errors & troubleshooting
Result shows an error about the remaining quantity exceeding the initial quantity. — Decay only reduces a quantity over time, so the remaining amount must be less than (or equal to) the initial amount. Swap the two fields if they were entered backwards.
Solving for half-life gives an error even though the numbers look reasonable. — If the remaining quantity equals the initial quantity, no decay has occurred and a half-life cannot be computed — enter an elapsed time where some decay has actually happened.
The elapsed time and half-life were entered in different units (e.g. days vs. years). — Convert both time fields to the same unit before solving; the Half-Life Calculator does not perform unit conversion for you.
Expected a whole number of half-lives but got a fractional result. — That is normal — t/T does not need to be an integer. A fractional exponent just means the elapsed time falls partway between two half-lives.
Frequently asked questions
What formula does the Half-Life Calculator use?
It uses N = N0 x (1/2)^(t/T), where N0 is the initial quantity, N is the remaining quantity, t is elapsed time, and T is the half-life. To solve for t or T, it rearranges the formula using logarithms.
Can the Half-Life Calculator solve for the half-life itself?
Yes. Choose the 'Half-life' solve mode and enter the initial quantity, the remaining quantity, and the elapsed time; the calculator returns the half-life that fits those three values.
Does the Half-Life Calculator work for anything other than radioactive decay?
Yes. The same exponential decay math applies to drug elimination half-lives, capacitor discharge, cooling curves, and any other quantity that decreases by a fixed fraction over a fixed interval.
What time units does the Half-Life Calculator accept?
Any consistent unit — seconds, hours, days, years, or anything else — as long as the elapsed time and the half-life are entered in the same unit.
Is the Half-Life Calculator accurate for real radioactive isotopes?
It applies the exact exponential decay formula, so results are mathematically accurate for the half-life you enter. It is a math estimate, though, so confirm isotope-specific half-life values against a reference table for real applications.
Does the Half-Life Calculator upload the numbers I enter?
No. The Half-Life Calculator runs entirely in your browser. The quantities and times you type are computed locally and never leave your device.
Related tools
Log Calculator — Compute logarithms in any base, plus natural log and log base 10.
Exponent Calculator — Raise a base to any power, including negative and fractional exponents.