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Decay Constant Calculator

Work out decay constant instantly with clear inputs, formula shown and shareable results.

About Decay Constant Calculator

The decay constant is the probability per second that a given nucleus decays, and it relates to half-life as lambda = ln2/t(half). Carbon-14's 5730 year half-life gives lambda = 3.83e-12 per second and a mean lifetime of 8267 years - always 1/ln2 times the half-life, about 44% longer.

Formulas

Decay constant

lambda = ln2 / t(half)

Mean lifetime

tau = 1 / lambda = t(half) / ln2

Worked example

With the default values below, Decay Constant Calculator returns Decay Constant of 3.83325 × 10⁻¹². Change any input above and every figure here is recalculated in your browser.

Inputs used

Half-lifeminimum 0
5,730
Half-life unitone of Seconds, Minutes, Hours, Days, Years
Years

Results

Decay Constant
3.83325 × 10⁻¹² 1/s
Mean Lifetime
2.6088 × 10¹¹ s
Half-Life In Seconds
1.8083 × 10¹¹
Fraction Decaying Per Year
0.01210%

Step by step

  1. 1Values used
  2. 2Decay constant
  3. 3Mean lifetime
  4. 4Decay Constant= 0.00000 1/s
  5. 5Mean Lifetime= 260,875,000,000.0000 s
  6. 6Half-Life In Seconds= 180,825,000,000.0000
  7. 7Fraction Decaying Per Year= 0.01210

Assumptions and limits

  • The result is derived only from the 2 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 5 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

Why is the mean lifetime longer than the half-life?

Because the distribution has a long tail. Half the nuclei are gone by the half-life, but the survivors keep the average up to t(half)/ln2.

Does the decay constant ever change?

No, it is intrinsic to the nuclide and unaffected by temperature, pressure or chemistry - which is what makes radiometric dating reliable.

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