Half-Life, Decay Constant and Mean Life Calculator

λ = ln2/t½ and the mean life that is 1.4427 times the half-life rather than 0.6931 — with NPL’s published uncertainties, the time to one per cent, a tenth of one and a millionth, and the ten nuclides whose published half-lives disagree.

The decay arithmetic here is exact; what you put into it is not. A half-life, an activity quoted for a stated date and the assay time itself all carry uncertainty, and an activity projected far from the calibration date compounds it. Nothing here tells you whether a source is safe to handle or to move, and nothing here replaces the certificate the source came with.

Three constants, one logarithm, and the 1.4427 that is not a physical quantity

Half-life, uncertainty, decay constant and mean life for all twenty-two

How long until one per cent, a tenth of one, and a millionth

Where the published half-lives disagree, and by how much

One line of arithmetic, four reciprocal units, and the uncertainties every other table drops

λ = ln2/t½ is one line of arithmetic, so this page has to earn its place on the other three things. The first is the mean life. τ = 1/λ = t½/ln2 = 1.4427 t½, which makes it 44 per cent LONGER than the half-life, and that pair is swapped often enough to be worth a row of its own. The reason the mean life exists at all is that it is what appears naturally in the exponent: the activity falls to 1/e, about 36.8 per cent, in exactly one mean life, and e^−t/τ is the decay law with no logarithm in it. The ratio 1.4427 is 1/ln2 and contains no physics whatever, so it is the same for every nuclide that exists — which is why this page prints λ·τ as a check row that must read exactly 1.

The second is NPL’s uncertainties, which nearly every table drops. They are not uniform and the range is wide: manganese-54’s half-life is known to 0.0096 per cent and technetium-99m’s to 0.016, while radium-223’s is known to 0.44 and caesium-137’s to 0.27 — a factor of forty-five between the ends. Whether that matters depends entirely on how many half-lives you are projecting over, because a relative error in the half-life is multiplied by the number of half-lives before it reaches the answer. Over a six-hour technetium correction it contributes nothing measurable and the error is all in the clock and the dose calibrator. Over the six hundred years it takes caesium-137 to reach a millionth, the same 0.27 per cent is worth 7.8 per cent on the surviving fraction. The page computes that second number for whatever projection you ask for, so it can be read instead of guessed at.

The third is how long a source has to be kept, which is the question behind most searches for a half-life. The answer is always a multiple of the half-life and the multiples are pure numbers: 6.6439 half-lives to one per cent, 9.9658 to a tenth of one per cent, 19.9316 to a millionth. For technetium-99m that is forty, sixty and a hundred and twenty hours; for caesium-137 it is 200, 299 and 599 years. Ten half-lives — 0.098 per cent, one part in 1,024 — is the figure everybody quotes, and it is worth knowing that it is no longer a regulatory requirement in the United States. 10 CFR 35.92 contains no holding period at all; it asks instead that the material be surveyed at the surface and found indistinguishable from background. NRC Regulatory Issue Summary 2004-17 Revision 1 states that the rulemaking eliminated the ten-half-lives requirement and deleted the licence condition carrying it. Ten half-lives remains an excellent estimate of how long the wait will be; the test at the end of it is an instrument.

And the sources do not agree, which is why the disagreement table is on this page rather than hidden in a footnote. Ten of the twenty-two nuclides here have a second published half-life that differs from NPL’s. Caesium-137 is 10,976 ± 30 days to NPL, 11,000 ± 90 on a published decay sheet, 30.08 years in the most commonly quoted figure and 30.04 in a third place. Iodine-125 is 59.407 days to NPL and 60.1 on a university safety data sheet — a difference of 77 times NPL’s stated uncertainty, which is a real disagreement between compilations and not a rounding. One lutetium-177 data sheet prints 6.73 days and 6.65 days in the same line. None of this changes an answer over a day or a month. All of it changes the fifth significant figure, and this site quotes five, so the table says which column every page uses: the NPL one.

What the half-life is not. It is not a property of the material, only of the nucleus, so it does not depend on temperature, pressure, chemical form or how much you have — which is exactly what makes the arithmetic here exact rather than approximate. It is not the mean life, as above. It is not the biological half-life, which is how fast the body clears the substance and is a completely separate quantity; the two combine into an effective half-life that is shorter than either. And for a nuclide with a daughter it is not the whole story: a molybdenum-99 generator’s output is governed by two half-lives at once, and caesium-137’s 662 keV photon is emitted by barium-137m, whose own half-life is two and a half minutes.

Frequently asked questions

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References

1. A. Pearce, NPL Report IR 6: Recommended Nuclear Decay Data, National Physical Laboratory. Cited, not reproduced — Crown copyright. It is the source of every half-life on this page and, more usefully, of every half-life’s UNCERTAINTY, which most published tables drop. Those uncertainties are the reason the nuclide table here prints a ± column: manganese-54 is known to 0.03 days in 312.13, which is 0.0096 per cent, and technetium-99m to 0.000 04 days in 0.250 28, which is 0.016; caesium-137 is known to 30 days in 10 976, which is 0.27 per cent, and radium-223 to 0.05 days in 11.43, which is 0.44 and is the widest in the set — a factor of forty-five across the list, and a projection over many half-lives inherits whichever end it lands on.
2. 10 CFR 35.92, Decay-in-storage (US Nuclear Regulatory Commission; a US Government work, quoted). It permits a licensee to hold byproduct material “with a physical half-life of less than or equal to 120 days” for decay in storage “without regard to its radioactivity” provided the licensee “monitors byproduct material at the surface before disposal and determines that its radioactivity cannot be distinguished from the background radiation level with an appropriate radiation detection survey meter set on its most sensitive scale and with no interposed shielding”, and removes or obliterates the radiation labels. Read in full for this batch because of what is NOT in it: there is no ten-half-lives holding period anywhere in the section.
3. NRC Regulatory Issue Summary 2004-17, Revision 1, Revised Decay-in-Storage Provisions for the Storage of Radioactive Waste Containing Byproduct Material, Office of Nuclear Material Safety and Safeguards, 27 September 2005 (a US Government work, quoted). This is the document that settles the ten-half-lives question. It describes the rulemaking as “eliminating the requirement to hold radioactive waste for a period of 10 half lives before disposal”, replaced by the rule that “the waste must be held in storage until the radiation exposure rate cannot be distinguished from background radiation levels”, and states that the “License Condition 140 stipulation that decay-in-storage waste be held for 10 half-lives will be deleted”. Ten half-lives was therefore real, and is now history: the test is a survey meter, not a calendar.
4. Radioactive Material Safety Data Sheet: Cs-137, Stuart Hunt & Associates Ltd. (read 7 October 2026 through the University of Florida radiation safety document library). It gives 3 220 GBq/g against a half-life of 30.22 years. This is the second, self-consistent caesium-137 figure that the derivation reproduces to 0.15 per cent, and it is why the Wikipedia row of 83 Ci/g is treated here as the outlier rather than as the answer.
5. Radioisotope Safety Data Sheets, University of Michigan Environment, Health & Safety, Radiation Safety Service (read 7 October 2026). Four published specific activities come from this series, each with the half-life the sheet itself used, which is what makes the comparison fair: iodine-125 17 353 Ci/g at 60.1 days and explicitly labelled “theoretical/carrier free”; iodine-131 124 068 Ci/g at 8.05 days; technetium-99m 5 243 820 Ci/g at 6.02 hours carrier-free, with 3.4×10⁶ Ci/g given separately for the pertechnetate form; thallium-201 2.159×10⁵ Ci/g at 3.04 days; and sodium-22 6 244 Ci/g at 2.602 years. Where the derivation here differs by more than a per cent — iodine-125 by 1.4, thallium-201 by 1.1 — the difference is the half-life each side used, not the arithmetic.
6. Nuclide Safety Data Sheets, published by the North Carolina chapter of the Health Physics Society (nchps.org) and mirrored by the University of Virginia Environmental Health & Safety radiation safety service (read 7 October 2026). Two maximum specific activities are taken from them: fluorine-18 at 9.51×10⁷ Ci/g [3.52×10¹⁸ Bq/g], and lutetium-177 at 1.1×10⁵ Ci/g [4.1×10¹⁵ Bq/g] max. Both reproduce to better than a quarter of a per cent. The lutetium sheet is also a small lesson in half-life disagreement: it prints two values, 6.73 days and 6.65 days, side by side in one line.
7. Cobalt-60, Wikipedia (read 7 October 2026). Quoted for “the radioactive activity of a gram of ⁶⁰Co is close to 42 TBq (1,100 Ci)”, which the derivation reproduces at 41.87 TBq/g. Also the source for the half-life cross-check at 5.2714 years.
8. Iridium-192, Wikipedia (read 7 October 2026). Quoted for one number: “a specific activity of 341 TBq·g⁻¹ (9.22 kCi·g⁻¹)” against a half-life of 73.82 days. The derivation from NPL’s 73.827 days and the isotopic mass gives 340.9 TBq/g, which is 0.03 per cent away — the closest agreement of any row in the check.
9. Technetium-99m, Wikipedia (read 7 October 2026). Read for the generator description and for the branching figure a single-nuclide decay calculation silently assumes away: “over 87% of the decays lead to the desired ^99mTc”. It also gives the half-life as 6.0066 hours, against NPL’s 6.0067, and notes that a generator “must be replaced weekly, since the half-life of ⁹⁹Mo is still only 66 hours”.
10. The 2019 revision of the SI, as published by the BIPM and tabulated in NIST’s Fundamental Physical Constants. Two exact values are used here and both are exact by definition rather than by measurement: the Avogadro constant N_A = 6.022 140 76×10²³ mol⁻¹, and the elementary charge, through which 1 eV = 1.602 176 634×10⁻¹⁹ J. One curie is likewise 3.7×10¹⁰ Bq by definition, so every curie figure on these pages is a rename of a becquerel figure and adds no uncertainty of its own.