Half Life Reaction Calculator
Calculate half-life and remaining quantity for first-order decay or reaction.
About Half Life Reaction Calculator
Each half-life removes half of whatever remains, so decay is exponential rather than linear. Reaching one per cent takes about 6.6 half-lives, which is the practical definition of complete decay. Half-life is independent of starting quantity for first-order processes, which is what makes radiometric dating possible.
Formula
Half Life Reaction
N = N₀ × (½)^(t/t½); k = ln2 ÷ t½
- t½
- Time for half the material to be consumed
- k
- First-order rate constant, related to half-life by ln 2
Worked example
With the default values below, Half Life Reaction Calculator returns Amount Remaining of 25.000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Half-lifeminimum 0 s
- 5,730 s
- Time elapsedminimum 0 s
- 11,460 s
- Initial amountminimum 0
- 100
Results
- Amount Remaining
- 25.000000
- Fraction Remaining
- 25.00000%
- Half-Lives Elapsed
- 2.0000
- Rate Constant
- 0.0001209681 1/s
- Time to Fall to 1% Remaining
- 38,069.30 s
Step by step
- 1Values used
- 2Half Life Reaction
- 3Amount Remaining= 25.000000
- 4Fraction Remaining= 25.00000
- 5Half-Lives Elapsed= 2.0000
- 6Rate Constant= 0.0001209681 1/s
- 7Time to Fall to 1% Remaining= 38,069.30 s
Assumptions and limits
- The result is derived only from the 3 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 Reaction calculated?
N = N₀ × (½)^(t/t½); k = ln2 ÷ t½ Each half-life removes half of whatever remains, so decay is exponential rather than linear. Reaching one per cent takes about 6.6 half-lives, which is the practical definition of complete decay.
Why does Half Life Reaction matter?
Half-life is independent of starting quantity for first-order processes, which is what makes radiometric dating possible.
What values do I need to enter?
This calculator takes 3 inputs: Half-life, Time elapsed, Initial amount. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.