Fission Product Inventory Calculator
Estimates the radioactive inventory of a specific fission product in a reactor core after a given operating period. Used by nuclear engineers to assess source terms, plan refueling, or evaluate accident scenarios.
Last updated: September 2026
Formula below · 2 sources (nrc.gov, Wikipedia) · Updated Sep 2026
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About this calculator
Each fission produces a given fission product with a characteristic cumulative yield (for thermal U-235: I-131 about 2.9%, Xe-135 6.6%, Cs-137 6.2%, Sr-90 5.8%, Tc-99 6.1%). While the reactor runs, the inventory N grows from production and shrinks by decay: dN/dt = P − λN, giving N(t) = P × (1 − e^(−λt)) / λ, where P = fission rate × yield is the production rate. The calculator converts your fission rate (per second) to per day (× 86,400) so that it matches the decay constant in day⁻¹ and the operating time in days; choosing an isotope sets λ = ln 2 / half-life, and 'Custom' uses the decay constant you enter (0 gives the no-decay limit N = P·t). At long times the inventory saturates at P/λ (reached within a few half-lives for I-131 and Xe-135); long-lived nuclides like Cs-137 accumulate almost linearly. Xe-135 also burns out by neutron capture in a running reactor, so this decay-only estimate overstates its at-power inventory.
How to use
Example: a 3,000 MWth core fissions about 9.4×10¹⁹ times per second. For I-131 (yield 2.9%, half-life 8.02 days) after 365 days: P = 9.4×10¹⁹ × 86,400 × 0.029 = 2.36×10²³ atoms/day; λ = 0.693 / 8.02 = 0.0864 day⁻¹; N = 2.36×10²³ × (1 − e^(−31.5)) / 0.0864 = 2.73×10²⁴ atoms (the saturation value), an activity of N × λ / 86,400 = 2.7×10¹⁸ Bq (about 74 MCi). With the defaults (10¹⁸ fissions/s, 6.2% yield, I-131, 365 days) the result is 6.2×10²² atoms.
Frequently asked questions
What does fission yield mean in the fission product inventory calculator?
Fission yield is the percentage of all fission events that produce a specific mass-chain fragment. For uranium-235 thermal fission, values range from near zero for some masses to about 6–7% for the most probable products near mass 90 and 140. Entering the correct chain yield ensures the production rate is scaled accurately. Some calculators also accept the independent yield of a specific nuclide rather than the cumulative chain yield, so confirm which convention your data source uses.
Why does fission product inventory reach a saturation limit over time?
Saturation occurs because the isotope is simultaneously produced by fission and destroyed by radioactive decay. As the inventory grows, the decay rate (λN) also grows until it exactly equals the production rate, at which point dN/dt = 0. This equilibrium is reached after roughly five half-lives of continuous irradiation. Short-lived fission products like iodine-131 (t½ ≈ 8 days) saturate within weeks, while long-lived products like cesium-137 (t½ ≈ 30 years) accumulate for years before approaching equilibrium.
How does decay constant affect the calculated fission product inventory?
The decay constant λ = ln(2) / t½ appears in both the denominator and the exponent of N = P(1 − e^(−λt))/λ. A larger λ (shorter half-life) lowers the saturation inventory P/λ but lets the inventory reach it sooner: I-131 saturates in about a month, while Cs-137 would need centuries, so for any realistic operating time its inventory is close to P × t. λ must be in the same time unit as the operating time (days here).