Half-Life & Radioactive Decay Calculator
Decay amounts · Half-life finder · Decay series · Isotope reference
What is Half-Life & Radioactive Decay Calculator?
The Half-Life and Radioactive Decay Calculator is a science tool that helps you compute quantities related to radioactive decay — the process by which unstable atomic nuclei lose energy by emitting radiation over time. It solves for remaining quantity after a given time, elapsed time from a remaining quantity, or the half-life of a substance from decay measurements.
The half-life of a radioactive isotope is the time required for half of the atoms in a sample to decay. This value varies enormously between isotopes: Carbon-14 has a half-life of about 5,730 years (used in radiocarbon dating), Iodine-131 is 8 days (used in medical treatments), and Polonium-214 decays in just fractions of a millisecond. The calculator includes a reference table of common isotopes so you can select one directly without needing to look up values.
The underlying formula used is N(t) = N0 x (1/2)^(t/t1/2), where N0 is the initial quantity, t is elapsed time, and t1/2 is the half-life. This tool is useful for students studying nuclear chemistry or physics, medical professionals working with radiopharmaceuticals, and anyone exploring concepts in radiometric dating or nuclear engineering.
How to Use Half-Life & Radioactive Decay Calculator
- Choose what to solve for
Select whether you want to find remaining quantity, elapsed time, or the half-life of the substance.
- Enter the known values
Input initial quantity, elapsed time, remaining quantity, or half-life as needed for your chosen calculation.
- Select an isotope (optional)
Pick a common isotope from the reference table to auto-fill its half-life, or enter a custom value.
- View result and decay curve
See the calculated answer along with a decay curve showing how the quantity changes over time.
Key Benefits
Calculate remaining quantity, elapsed time, or half-life depending on which values you know.
Select from common isotopes like Carbon-14, Uranium-238, and Iodine-131 to auto-fill half-life values.
A graphical decay curve shows how the quantity decreases over time for intuitive understanding.
The exact formula and substituted values are shown so students can follow the working step by step.
Frequently Asked Questions
The calculator uses N(t) = N0 x (1/2)^(t/t1/2), where N0 is the initial amount, t is elapsed time, and t1/2 is the half-life. This is equivalent to N(t) = N0 x e^(-λt) where λ = ln(2)/t1/2.
Yes. Select Carbon-14 from the isotope list (half-life 5,730 years), enter the remaining percentage of C-14, and the calculator estimates the age of the sample.
The calculator accepts seconds, minutes, hours, days, years, and thousands or millions of years. Use whichever unit is appropriate for the isotope and timeframe you are working with.
No, this calculator models simple single-step decay. Decay chains, where one isotope decays into another radioactive isotope, require more complex differential equations not covered here.