What is half-life?
Half-life is the time required for a quantity undergoing exponential decay to decrease to half its initial value. In radioactive decay, it is the time for half the nuclei in a sample to transform. In pharmacokinetics, it is the time for the concentration of a drug in the bloodstream to fall by 50%. In reliability and signal processing, half-life can describe how quickly a process attenuates. The concept assumes exponential decay, meaning the rate of decrease is proportional to the current amount.
How the Half-Life Calculator works
The fundamental decay relationship is N(t) = N0 × 2^(?t/T1/2), where N0 is the initial amount, T1/2 is the half-life, and t is elapsed time. Our calculator rearranges this core equation to solve for any one of the three variables when the other two are known:
- Remaining amount N(t) when you know N0, T1/2, and t
- Half-life T1/2 when you know N0, N(t), and t
- Time elapsed t when you know N0, N(t), and T1/2
Behind the scenes, the calculator converts time units to a common base, applies natural logarithms where appropriate, and returns nicely rounded results in your chosen units.
How to use the calculator
- Choose “Solve for” to select remaining amount, half-life, or time elapsed.
- Enter the initial amount N0. This must be greater than 0.
- Provide the other known values: remaining amount, half-life, or time as needed.
- Select the corresponding time units for half-life and elapsed time.
- Optionally, add an isotope or substance name to label your results.
- Set the number of decimal places and press Calculate.
For example, if you start with 100 grams of a substance with a half-life of 5 days, and 10 days pass, the remaining amount is 100 × 2^(?10/5) = 25 grams. If instead you observe that 25 grams remain after 10 days from an initial 100 grams, the half-life is 10 × ln(2) / ln(100/25) = 5 days.
Supported units and conversions
You can enter half-life and time in seconds, minutes, hours, days, or years. The tool handles conversions automatically so you don’t have to. This is particularly helpful when data sheets list half-life in hours while your observation period is in minutes, or when radiometric dating uses years but lab timing is in days.
Use cases
- Radioactive decay calculations for isotopes like Carbon-14, Iodine-131, or Cobalt-60
- Drug elimination and dosing intervals in pharmacokinetics
- Environmental decay of pollutants or tracers
- Signal attenuation and filter responses in engineering
- Battery discharge and component degradation modeling
Accuracy tips
- Ensure the process follows exponential decay; many real-world systems do.
- Use consistent and accurate units; select the correct unit from the dropdowns.
- When solving for half-life or time, the remaining amount should be between 0 and the initial amount.
- Choose suitable decimal places for your discipline (e.g., 2–4 for lab work, more for scientific analysis).
Why use this Half-Life Calculator?
It’s fast, unit-aware, and flexible. Whether you’re cross-checking lab results, planning a dose schedule, or teaching exponential decay, this calculator gives clear, reliable results in a couple of clicks. Add an optional label for the isotope or substance and export the numbers in your preferred precision.
