Select a solve mode
Choose remaining amount, elapsed time, half-life, or initial amount.
Exponential decay calculator
Half-Life Calculator
Calculate remaining amount, elapsed time, initial amount, or half-life using a clear exponential decay model and detailed result breakdown.
Four solve modes
Any consistent units
Decay timeline
Calculation setup
Choose what to calculate
Select a solve mode, enter the known values, and keep all time values in the same unit.
Core formula
N = N₀ × (1/2)t/T½
N is the remaining amount, N₀ is the initial amount, t is elapsed time, and T½ is the half-life.
Calculated result
Decay breakdown
Your result will appear here
Enter the known values to calculate the missing half-life variable and view the decay timeline.
Simple calculation process
How the half-life calculator works
The calculator rearranges the exponential decay equation according to the value you need to find.
Enter known values
Add the values you already know and select clear amount and time units.
Apply decay math
The tool applies exponential decay and logarithms where required.
Review the timeline
See the answer, percentage remaining, decay constant, and half-life stages.
What is a half-life calculator?
A half-life calculator determines how an amount changes during exponential decay. It can calculate the remaining quantity after a known time or rearrange the same relationship to solve for elapsed time, the original quantity, or the half-life itself.
The calculation is useful when a process decreases by the same proportion over equal time intervals. Although radioactive decay is the most familiar example, the same mathematical model can also describe medication elimination, chemical breakdown, and other decay processes.
The half-life formula
N = N₀ × (1/2)t/T½
After one half-life, 50% remains. After two half-lives, 25% remains. After three half-lives, 12.5% remains.
Important unit rule
Elapsed time and half-life must use the same unit. For example, if the half-life is entered in days, the elapsed time must also be entered in days.
Common uses
- Estimating radioactive isotope decay
- Understanding medication elimination
- Modeling chemical or biological clearance
- Solving classroom exponential decay problems
Helpful answers
Frequently asked questions
Learn more about exponential decay, formulas, units, and half-life calculations.
What is half-life?
Half-life is the time required for half of an initial quantity to decay, transform, or be removed through an exponential process.
What formula does this calculator use?
The calculator uses N = N0 × (1/2)^(t/T), where N is the remaining amount, N0 is the initial amount, t is elapsed time, and T is half-life.
Can this calculator solve for elapsed time?
Yes. Select Elapsed Time and enter the initial amount, remaining amount, and known half-life.
Can I calculate the half-life from two amounts?
Yes. Enter the initial amount, remaining amount, and elapsed time. The calculator will solve for the half-life.
Which units can I use?
You may use any consistent amount unit and any consistent time unit. The same time unit must be used for elapsed time and half-life.
Does half-life always mean radioactive decay?
No. Half-life can describe radioactive decay, medication elimination, chemical processes, biological clearance, and other exponential decay systems.
Why does the amount never reach exactly zero?
The ideal exponential decay model repeatedly halves the remaining amount, so it approaches zero without becoming exactly zero in finite time.