Select a solve mode
Choose remaining quantity, elapsed time, decay constant, half-life, or initial quantity.
Nuclear decay calculator
Radioactive Decay Calculator
Solve radioactive decay problems using the exponential decay equation. Calculate remaining quantity, elapsed time, initial quantity, decay constant, or half-life with a clear scientific breakdown.
Five solve modes
Decay timeline
Half-life conversion
Calculation setup
Choose the unknown value
Select what you want to calculate, enter the known values, and keep the decay constant consistent with the selected time unit.
The decay constant is interpreted as per selected time unit.
Core equation
N = N₀ × e−λt
N is the remaining quantity, N₀ is the initial quantity, λ is the decay constant, and t is elapsed time.
Calculated result
Decay analysis
Your result will appear here
Enter the known values to calculate the missing decay variable and view a detailed half-life timeline.
Simple calculation process
How the radioactive decay calculator works
The calculator rearranges the exponential decay equation for the unknown value and provides related decay measurements.
Enter known values
Add the available quantity, time, and decay information using consistent units.
Apply exponential decay
The tool applies exponential functions or logarithms according to the selected unknown.
Review the analysis
See the main answer, percentage remaining, half-life, decay constant, and timeline.
What is a radioactive decay calculator?
A radioactive decay calculator models the reduction of unstable nuclei over time. Because every nucleus has a probability of decaying, a large collection of nuclei follows an exponential pattern rather than decreasing by a fixed amount during each time interval.
This calculator can determine any major variable in the radioactive decay equation. It also converts the decay constant into half-life and shows how much of the original quantity remains after each half-life.
Radioactive decay equation
N = N₀ × e−λt
In this equation, N is the remaining number of nuclei or amount, N₀ is the initial quantity, λ is the decay constant, and t is elapsed time.
Decay constant and half-life
The decay constant describes the probability of decay per unit time. Half-life is the period required for the quantity to decrease to one-half of its initial value.
T½ = ln(2) ÷ λ
Common uses
- Estimating how much radioactive material remains
- Calculating the age of a sample from radioactive decay
- Converting between decay constant and half-life
- Solving nuclear physics and chemistry problems
- Modeling activity when activity is proportional to the number of undecayed nuclei
Helpful answers
Frequently asked questions
Learn more about radioactive decay, half-life, decay constants, formulas, and units.
What is radioactive decay?
Radioactive decay is the spontaneous transformation of an unstable atomic nucleus. The number of undecayed nuclei decreases exponentially over time.
Which radioactive decay formula does this calculator use?
The calculator uses N = N0 × e^(-λt), where N is the remaining quantity, N0 is the initial quantity, λ is the decay constant, and t is elapsed time.
How are decay constant and half-life related?
The relationship is T½ = ln(2) ÷ λ. A larger decay constant produces a shorter half-life, while a smaller decay constant produces a longer half-life.
Can I calculate elapsed time from two quantities?
Yes. Select Elapsed Time, then enter the initial quantity, remaining quantity, and known decay constant.
Which time units can I use?
You can use seconds, minutes, hours, days, weeks, months, or years. The decay constant is interpreted as per selected time unit.
Can I calculate half-life without entering a decay constant?
Yes. Select Half-Life and enter the initial quantity, remaining quantity, and elapsed time. The calculator first determines the decay constant and then calculates half-life.
Why does the calculated quantity not become exactly zero?
The ideal exponential model approaches zero continuously but does not reach exactly zero during a finite period of time.