Reactor safety · residual heat

Decay Heat Calculator

How much thermal power a reactor still produces after shutdown — in megawatts and as a percentage of full power, via the full ANSI/ANS-5.1-2005 standard (four nuclides + actinide term) or the Wigner–Way correlation.

operating time effectively infinite (equilibrium)
Custom fuel mix — % of fission power (4 nuclides, ANS-5.1-2005)
Recoverable energy per fission Q (MeV)
The G(t) formula is rigorous for cooling times ≤ 10⁴ s (operating time ≤ 4 yr, ψ < 3). Beyond 10⁴ s the tool applies the standard's tabulated upper-bound Gmax(t) (Table 13). The ²³⁹U/²³⁹Np term (§4) is reactor-specific — R must be supplied and justified by the user; leave it off unless you have a value.
Decay Heat
ANSI/ANS-5.1-2005 prediction

Decay heat (% of full power) vs time after shutdown — hover or drag across the curve

Time after shutdown% full powerHeat (MWt)
● CASE A
● CASE B

Absolute decay heat (MWt) vs time — compare two reactors or two methods

Operational perspective

What is decay heat?

Decay heat is the thermal power a reactor keeps producing after the fission chain reaction has stopped. When a reactor scrams, the neutron chain reaction ends within seconds — but the fuel is full of radioactive fission products that keep decaying, releasing energy as they do. Immediately after shutdown this residual power is roughly 6–7% of the reactor's full thermal rating, falling off slowly over hours, days and weeks.

Why did Fukushima need cooling after shutdown?

All three operating units at Fukushima Daiichi scrammed successfully in the 2011 earthquake — the chain reaction stopped as designed. What followed was a loss of cooling: the tsunami disabled the power needed to run the decay-heat removal systems. With no way to carry the residual heat away, fuel temperatures climbed until the cores melted. Stopping the chain reaction was not enough; the fuel still had to be actively cooled, precisely because of decay heat.

How the calculation works

ANSI/ANS-5.1-2005 represents fission-product decay heat as a sum of 23 exponential terms, fitted to experimental measurements, for each of four fissioning nuclides — U-235, Pu-239, U-238 and Pu-241. The tool integrates these over the reactor's operating history, weights them by the fuel's fission-power mix, applies the standard's neutron-capture correction G(t), and can optionally add the ²³⁹U/²³⁹Np heavy-element (actinide) contribution the 2005 standard prescribes separately. The Wigner–Way correlation is a faster single-equation estimate that runs slightly high. For the reader who wants the underlying relations:

ANS-5.1-2005:  P_d/P₀ = G(t) · Σⱼ xⱼ (1/Qⱼ) Σᵢ (αᵢ/λᵢ)(1 − e^(−λᵢT)) e^(−λᵢt)  +  PdHE/P₀
²³⁹U/²³⁹Np:  P_dHE/P₀ = (1/Q_eff) · [ F_U(t,T) + F_Np(t,T) ]  (§4, Eqs 12–14)
Wigner–Way:  P/P₀ = 0.0622 · [ t⁻⁰·² − (t + T)⁻⁰·² ]  (t, T in seconds)

The 23-term coefficients used here are those of the current-generation ANSI/ANS-5.1-2005 standard (Tables 9–12). Reconstructing the standard's own tabulated F(t,∞) values from these coefficients reproduces them to within 0.3% across all four nuclides — the small residual is the rounding of the published input data, not the method.

Frequently asked questions

How much decay heat right after shutdown?

About 6–7% of the reactor's full thermal power in the first seconds after shutdown — for a 3,000 MWt reactor, on the order of 180–200 MW of heat, which is why immediate, reliable cooling is essential.

Why is decay heat highest immediately after shutdown?

Right after shutdown the fuel holds its largest inventory of short-lived fission products, which release their energy fastest. As these short-lived isotopes decay away over seconds to hours, the heat drops sharply; the longer-lived isotopes that remain release energy more slowly, so the curve flattens.

Why can't control rods remove decay heat?

Control rods stop the fission chain reaction by absorbing neutrons — but decay heat comes from the radioactive decay of fission products already created. That decay is a property of the nuclei and cannot be switched off. Inserting every rod stops fission within seconds, yet ~6–7% of full power remains as decay heat that only active cooling can remove.

How long does decay heat last?

It never fully disappears but falls quickly at first: roughly ~1% of full power around an hour after shutdown, ~0.5% after a day, and a few tenths of a percent after a week. Even months later, spent fuel still generates measurable heat, which is why it is stored in cooled pools.

How accurate is ANSI/ANS-5.1?

For light-water reactors it is highly accurate — in the 2005 standard the U-235 decay-heat function is known to about ±2%, with somewhat larger uncertainty for Pu-239, U-238 and Pu-241. This calculator uses the 2005 coefficients (Tables 9–12) and reproduces the standard's own tabulated F(t,∞) values to within 0.3% across all four nuclides. Real-world accuracy depends on using the correct fuel mix, operating history and recoverable-energy values.

Which revision of the standard does this use — and is it current?

This tool implements ANSI/ANS-5.1-2005, which added Pu-241 as a fourth fissioning nuclide and a separate ²³⁹U/²³⁹Np actinide term relative to the older 1979 revision. The most recent revision is ANSI/ANS-5.1-2014 (reaffirmed 2019 and 2023); for the light-water-reactor regime most users care about — the first seconds to roughly a day after shutdown for U-235/Pu-239 — the 2005 and 2014 curves are very close, and the 2005 revision is a major step beyond the older data most online estimators rely on.

What is the ²³⁹U / ²³⁹Np contribution?

Neutron capture in U-238 breeds ²³⁹U, which decays to ²³⁹Np and then to Pu-239. The 2005 standard treats the heat from these two short-lived actinides as a separate additive term (§4), most significant in roughly the first 10⁴ seconds after shutdown. It depends on R — the number of ²³⁹U atoms produced per fission — which is reactor-specific and must be supplied and justified by the user, so it is left off by default in this tool.

What is the difference between Wigner–Way and ANS-5.1?

Wigner–Way is a single-equation correlation that gives a fast estimate and tends to run slightly high. ANSI/ANS-5.1 is the industry standard: a 23-term isotopic model that is more accurate and accounts for the fuel mix and neutron capture. This tool offers both so you can compare them directly in the Compare tab.

Does this work for BWRs?

Yes. Decay heat is a property of the fission products, so ANSI/ANS-5.1 applies to any light-water reactor — PWR or BWR. Only the inputs (thermal power, fuel mix, operating history) differ between plants; the physics and the standard are the same.

Does this work for CANDU / PHWR?

The underlying physics is the same, but ANSI/ANS-5.1 was fitted for light-water reactors. For heavy-water reactors, use this tool as a first-order estimate with a plutonium-heavier fuel mix — natural-uranium fuel and online refuelling make the exact fission-product mix reactor-specific.

References

Methods: "ANS-5.1" uses the finite-irradiation summation with the 23-term U-235 / Pu-239 / U-238 / Pu-241 coefficients of the ANSI/ANS-5.1-2005 standard (Tables 9–12), the neutron-capture correction G(t) (§3.5, with the Table 13 Gmax upper bound beyond 10⁴ s), and the optional ²³⁹U/²³⁹Np actinide term (§4). Coefficient sets reproduce the standard's own tabulated F(t,∞) to within 0.3%. "Wigner–Way" uses P/P₀ = 0.0622[t⁻⁰·²−(t+T)⁻⁰·²]. Educational estimate — verify against your governing standard for any safety use.
Built & reviewed by a practicing PWR reactor engineer · NeutronRise.com
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