THE NUMORIX GUIDE
How to use the Radioactive Decay Calculator
Last reviewed September 14, 2026
What this calculator does
The engine first obtains the decay constant from lambda = ln(2)/t1/2, then applies N(t) = N0*exp(-lambda*t).
Formula and method
The engine first obtains the decay constant from lambda = ln(2)/t1/2, then applies N(t) = N0*exp(-lambda*t). It reports remaining amount, percent decayed = ((N0 - N)/N0)*100, and the decay constant; the entered half-life and time must use the same time unit.
Variables and inputs
Enter an initial amount, half-life, and elapsed time. The amount can be a count, mass, or activity-like quantity as long as the model uses one consistent quantity; no unit labels are collected. The live UI has no positive-value validation, and the engine's step text labels lambda as s^-1 even when the entered time is not seconds.
Worked example
For N0 = 100, half-life = 5730 time units, and t = 10000 time units, lambda = ln(2)/5730 = about 1.2097e-4 per time unit. The engine gives N(t) = 29.8292 and percent decayed = 70.17%.
How to interpret the result
The result is the expected remaining amount for a large population of identical unstable nuclei. Half-life is the time for the expected amount to halve; it does not mean each individual atom waits exactly that long before decaying.
Common mistakes to avoid
Use the same unit for half-life and elapsed time, and do not enter the decay constant where the half-life field is expected. Distinguish remaining percentage from percent decayed, especially after more than one half-life.
Assumptions and limitations
This is a single-isotope exponential model with no daughter-product chain, replenishment, background, detector efficiency, or sample uncertainty. Negative or zero inputs are not rejected by the live component, and the hardcoded s^-1 label can be misleading when the input unit is years or another time unit.