Universal Decay Calculator - HELP

(last updated 22 Feb 2026)

Contents:

• Introduction · Nuclide Input · Output Parameters · Bibliography

Introduction

Initial activities of up to 16 nuclide series can be defined in the Nuclide Input table. For a time given in the Output Parameters table, the resulting activities of the nuclides given, plus those of any decay products growing in are calculated.
The calculator moreover determines the decay heat and assesses the radiation hazard from the nuclides by calculating the air kerma (kinetic energy released per unit mass: the kinetic energy of charged particles liberated by photon and neutron interactions per unit mass), whereby the nuclides are treated as a point source without any effective shielding.
The database contains a total of 1252 nuclides.

The calculator performs a complete decay analysis (i.e. including all branches) for the nuclides entered and all their decay products, according to [Bateman 1910]; minor nuclides are listed at the end.
Note: For the air kerma calculations, the air kerma coefficient K_air,δ for a hypothetical point source from [ICRP 2008] is used. It includes gamma rays, characteristic x rays, and inner bremsstrahlung, but does not necessarily cover all radiations from a real source.

The results for the List Time chosen are presented in numerical form in the Results table.

Half lives of radionuclides are shown in a color scheme changing from blue for long half lives to red for short ones, with the value specified for "Max. half life for short-lived progeny (+)" in the center (magenta).

The hazard from the point source air kerma rate is illustrated by the following icons:

• ☢   ≥ 100 nGy/h   (10 µrad/h)   - higher than typical background radiation
• ⚠   ≥ 10 µGy/h   (1 mrad/h)   - higher than average dose rate allowed for workers (20 mSv/a @ 2000 h/a)
• ⛨   ≥ 1 mGy/h   (100 mrad/h)   - annual allowed dose for workers (20 mSv) attained within 20 hours (and less)
• ☠   ≥ 1 Gy/h   (100 rad/h)   - radiation sickness after 1-2 hours, lethal after 3-4 hours (and less)

In addition, the results are optionally presented in an Output Chart showing the total series values for each series specified, or values for each individual nuclide, vs. time. The output chart type can be chosen as a line chart, a stacked area chart, or an animated bar chart.
Note: If the mouse pointer is hovering over the graph, the name of the nuclide under the pointer is shown above the graph (for stacked areas), or - along with data details - next to the pointer (for line charts).
Note: Please be aware that, in line charts, a nuclide curve may be hidden by others. Clicking on a nuclide name in the legend toggles the corresponding curve on/off.

The contents of the database for any nuclide can be checked with the "Query nuclide database" button (shows half-life, specific activity, possible parent nuclides, and decay products with branching ratios and decay type).
Note: Only alpha and beta decays are listed: in addition, each decay emits gamma radiation.

See special instructions for offline use of this calculator.

Other calculators of interest:

• For dose calculations from shielded radiation sources, see the External Radiation Dose Calculator (Virtual Geiger Counter)
• For decay calculations of uranium, the Uranium Decay Calculator offers more options, such as a variety of uranium compounds found in the uranium mining and nuclear fuel industry, and the inclusion of decay energy results.
• For comparison of the activities of the various radioactive wastes produced during nuclear fuel production and use, see the Nuclear Fuel Chain Waste Activity Calculator .

Nuclide Input

• Enter initial activities for each nuclide in up to 16 nuclide series, or
• enter a mass number, select a mass unit and enter the name of a nuclide under Series Name, or
• select one of the pre-defined nuclide mixes from the sample data pick list:

  g U(nat) pure

  gram of pure natural uranium, no decay products present

  g U(nat) equil.

  gram of natural uranium in secular equilibrium with its decay products

  g Th(nat) pure

  gram of pure natural thorium *), no decay products present

  g Th(nat) equil.

  gram of natural thorium *) in secular equilibrium with its decay products

  t uranium ore (grade 0.1% U)

  metric tonne(s) of uranium ore with an ore grade of 0.1% U

  t uranium mill tailings (from ore grade 0.1% U at 90% extraction)

  metric tonne(s) of uranium mill tailings left behind from processing of an ore with an ore grade of 0.1% U with an extraction efficiency of 90%

  g U(nat-enr) (3.5 wt-% U-235)

  gram of enriched natural uranium, enriched to 3.5 weight-% U-235

  g U(nat-dep) (0.2 wt-% U-235)

  gram of depleted uranium with 0.2 weight-% U-235, generated from enrichment of natural uranium to 3.5 weight-% U-235

  Heels in [...] 48Y cylinder(s) formerly holding 12,500 kg UF6(nat)

  heels (non-volatile residue) left from unloading of [...] Type 48Y cylinder(s) by heating, initially holding 12,500 kg natural UF₆ **)

  Heels in [...] 30B cylinder(s) formerly holding 2,277 kg UF6(nat-enr) (3.5wt-% U-235)

  heels (non-volatile residue) left from unloading of [...] Type 30B cylinder(s) by heating, initally holding 2,277 kg of enriched (3.5wt-% U-235) UF₆ **)

  g U(rep) (init. enr. 3.5%, 39 GWd/t, 5 y delay)

  gram of reprocessed uranium, initial enrichment 3.5 weight-% U-235, after burnup of 39 GWd/t in light water reactor separated from spent fuel 5 years after unload

  g U(rep-enr) (init. enr. 3.5%, 39 GWd/t, 5 y delay)

  gram of re-enriched reprocessed uranium, re-enriched to equivalent of initial enrichment 3.5 weight-% U-235, after burnup of 39 GWd/t in light water reactor separated from spent fuel 5 years after unload

  g U(rep-dep) (0.2 wt-% U-235, init. enr. 3.5%, 39 GWd/t, 5 y delay)

  gram of depleted uranium with 0.2 weight-% U-235, generated from re-enrichment of reprocessed uranium to equivalent of initial enrichment of 3.5 weight-% U-235, after burnup of 39 GWd/t in light water reactor separated from spent fuel 5 years after unload

  tHM spent fuel (33 GWd/t, at unload)

  metric tonne(s) of heavy metal contained in spent fuel from a light water reactor after burnup of 33 GWd/t, at time of unload (short-lived nuclides omitted)

  tHM spent fuel (33 GWd/t, 5 y after unload)

  metric tonne(s) of heavy metal contained in spent fuel from a light water reactor after burnup of 33 GWd/t, 5 years after unload

  HLW from reproc. of [...] tHM spent fuel (33 GWd/t, reproc. 5 y after unload)

  High-Level Waste from reprocessing of [...] tonne(s) of heavy metal contained in spent fuel from a light water reactor after burnup of 33 GWd/t, reprocessed 5 years after unload

  g Th-232 pure: Thorium series (4n)

  g Pu-241 pure: Neptunium series (4n+1)

  g U-238 pure: Uranium series (4n+2)

  g U-235 pure: Actinium series (4n+3)

  Bq Ra-226 pure: Secular equilibrium with short-lived progeny

  Bq Pb-212 pure: Transient equilibrium with slightly shorter-lived progeny

  Bq Bi-211 pure: No equilibrium with longer-lived progeny

  *) Strictly speaking, there is no such thing as "natural thorium": here it is used for Th-232 in secular equilibrium with Th-228.
  **) Please note that the air kerma is calculated without shielding from the cylinder wall!

Series Name

Enter nuclide name using the notation  Th-232 , for example.
Enter here the first member (for which an activity is to be specified) of a decay series, or a nuclide which is not a member of a series.
The name is checked with the database immediately on entry. If the nuclide is not found, the available nuclides resp. elements are listed.
Upon entry of a valid nuclide name, all decay products are listed in the "Nuclide Name" pick list; minor nuclides are listed at the end.

Nuclide Name

Select nuclide within the series, for which an activity value is to be entered or viewed.

Initial Activity

Enter number for initial activity of the nuclide selected in the "Nuclide Name" pick list, and select activity unit.

Initial Progeny: none

Check, in case only the pure nuclide shown in "Series Name" is present initially. The activities of all decay products are set to zero.

Initial Progeny: + (short-lived)

Check, in case only the short-lived decay products of the nuclide shown in "Series Name" initially are present in secular equilibrium. Once a nuclide with a half life greater than the one specified under "Max. half life for short-lived progeny (+)" is encountered in the decay chain, the activities of this and all further nuclides are set to 0.

Initial Progeny: ++ (secular equlibrium)

Check, in case all decay products of the nuclide shown in "Series Name" initially are present in secular equilibrium.

Initial Progeny: ind.

Check, in case individual entries are to be made for the initial activities of each nuclide in the series.
Note: If only a few nuclides of the series differ from the "none", "+", or "++" state, select the appropriate button first, and then select "ind." and modify the activity of the nuclide(s) in question.

Max. half life for short-lived progeny (+)

Enter number and select unit for the maximum half life, beyond which the decay chain will be truncated for short-lived progeny (+).
(time units: s=seconds, m=minutes, h=hours, d=days, a=years)
Note: The half life definitions for "short-lived" vary widely:
- ~15 h - Medical imaging
- ~10 d - Medical treatment
- 10 d - IAEA transport regulations
- 100 d - European Nuclear Society (ENS)
- 5 a - French Centre National de la Recherche Scientifique (CNRS)
- 31 a - French National Radioactive Waste Management Agency (Andra)
- 40 a - Australian Radioactive Waste Agency (ARWA)
- 100e6 a - Cosmology

Under "Initial Series Overview", color-filled circles indicate nuclides, for which an activity was entered, while transparent circles indicate nuclides without an activity entry. Nuclides from minor branches are shown as smaller circles at the end.
Note: The color scheme of the filled circles follows the half-life color scheme mentioned earlier; in addition, the intensity of the fill color indicates the relative strength of the activity within the series.
Note: If the mouse is hovering over a circle, the data entered for this nuclide is shown above.

Output Parameters

Time

Enter numbers for Start, End, and List time and select appropriate time unit.
(time units: s=seconds, m=minutes, h=hours, d=days, a=years)
The numerical results displayed in the Results field are for the specified List Time, while the charts cover the whole time period between Start and End time.
Note: In case of a linear time axis, the Start time 0 is used, independent of the entry made.
Note: The List time can also be set by clicking in the output chart.

Chart Type

Select option.
Note: Nuclide colors other than "normal" only work for Chart Detail options involving individual nuclides.
Note: Nuclide colors for "decay type" are green for alpha decays and red for beta decays. If a nuclide has alpha and beta decays (e.g. Bi-212), the color is proportional to the branching ratio in between red and green. Other decays (e.g. IT) are shown as black. Please be aware that these colors are just for the decay mode: therefore, for the actual radiation emission from these decays, check the decay energy rates under Chart Data!
Note: Nuclide colors for "half life" follow the color scheme mentioned above.

Chart Data

Select option.
If "air kerma" is chosen, select air kerma unit and enter air kerma point source distance [m]
Note: total energy rates are shown by radiation type gamma, alpha , and electron/beta, if Chart Detail "grand total" is selected.

Chart Detail

Select options.
If "skip minor nuclides" is selected, then the chart legend shows only those nuclides that are actually visible in the chart.
Note: The number of minor nuclides can further be reduced by reducing the "Max. decades on log. Y axis" value, if "log. Y axis" is chosen for line charts.
Note: For Chart Detail "grand total", total energy rates are shown by radiation type: gamma, alpha , and electron/beta

Chart Axes

Select option.
Note: The number of decades on the log. Y axis is automatically reduced, if there are no curves in the lower decades.

Bibliography

[Bateman 1910] Harry Bateman: Solution of a system of differential equations occurring in the theory of radioactive transformations , in: Proceedings of the Cambridge Philosophical Society, Mathematical and physical sciences. Cambridge [etc.] Cambridge Philosophical Society. v. 15 (1908-10): Pages 423-427

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