Half-Life/Decay Calculator
Calculate remaining activity and decay constant for a radioactive isotope.
About Half-Life/Decay Calculator
Decay is exponential, so each half-life removes half of what remains rather than a fixed amount. Ten half-lives leave under a thousandth of the original activity, which is the usual rule for practical disposal. Isotope selection in imaging balances half-life against dose: too short and it decays before imaging, too long and the patient carries activity unnecessarily.
Formula
Half-Life/Decay
A = A₀ × (1/2)^(t ÷ t½); decay constant λ = ln2 ÷ t½
- half-life
- Time for activity to fall by half
- mean lifetime
- The reciprocal of the decay constant, about 1.44 half-lives
Worked example
With the default values below, Half-Life/Decay Calculator returns Remaining Activity of 6.2789. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Initial activityminimum 0 MBq
- 100 MBq
- Half-lifeminimum 0
- 6.01
- Half-life unitone of Seconds, Hours, Days, Years
- Hours
- Elapsed timeminimum 0
- 24
- Elapsed time unitone of Seconds, Hours, Days, Years
- Hours
Results
- Remaining Activity
- 6.2789 MBq
- Half-Lives Elapsed
- 3.9933
- Decay Constant
- 0.0000320368 1/s
- Fraction Remaining
- 6.2789%
- Mean Lifetime
- 31,214.15 s
Step by step
- 1Values used
- 2Half-Life/Decay
- 3Remaining Activity= 6.2789 MBq
- 4Half-Lives Elapsed= 3.9933
- 5Decay Constant= 0.0000320368 1/s
- 6Fraction Remaining= 6.2789
- 7Mean Lifetime= 31,214.15 s
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Half-Life/Decay calculated?
A = A₀ × (1/2)^(t ÷ t½); decay constant λ = ln2 ÷ t½ Decay is exponential, so each half-life removes half of what remains rather than a fixed amount. Ten half-lives leave under a thousandth of the original activity, which is the usual rule for practical disposal.
Why does Half-Life/Decay matter?
Isotope selection in imaging balances half-life against dose: too short and it decays before imaging, too long and the patient carries activity unnecessarily.
What values do I need to enter?
This calculator takes 5 inputs: Initial activity, Half-life, Half-life unit, Elapsed time, Elapsed time unit. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.