Drawing No. EH–NR–006 // Nuclear Engineering & Radiation
Nuclear Reactor Decay Heat Calculator
Reviewed October 2026
Estimate residual thermal power after reactor shutdown, explore how operating history changes the result, and follow the decay curve from seconds to 100 days using the Way–Wigner approximation.
Worked example
An AP1000 core, one year at full power
Take a reference AP1000 at its nominal 3,400 MW thermal rating, operated continuously
for one year (Top = 8,760 h = 3.154 × 107 s) and then scrammed. The
Way–Wigner correlation gives the fission-product decay power directly:
P(t) / P₀ = 0.0622 × [ t−0.2 − (t + Top)−0.2 ]
Working one point by hand, at t = 1 hour = 3,600 s:
3600−0.2 = 0.19447 (3600 + 3.154×107)−0.2 = 0.03165
P/P₀ = 0.0622 × (0.19447 − 0.03165) = 0.01013 → 34.4 MW
Repeating across the valid range gives the post-shutdown profile:
| Time after scram | Fraction of P₀ | Decay power | What it compares to |
|---|
| 1 s | 6.02% | 205 MW | Below the validity floor — see limits |
| 10 s | 3.73% | 127 MW | Earliest defensible point |
| 1 min | 2.55% | 86.6 MW | Large industrial boiler |
| 1 hour | 1.01% | 34.4 MW | Mid-size district-heating plant |
| 8 hours | 0.60% | 20.4 MW | Typical shutdown-cooling entry window |
| 1 day | 0.44% | 15.1 MW | — |
| 7 days | 0.24% | 8.1 MW | — |
| 30 days | 0.13% | 4.4 MW | Typical pool-cooling duty scale |
| 100 days | 0.068% | 2.3 MW | Upper validity limit |
Integrating the curve over the first twenty-four hours gives roughly 490 MWh of thermal
energy — about half a gigawatt-hour that has to go somewhere whether or not the plant has offsite power.
That integral, not the instantaneous figure, is what sets the required inventory of a passive heat sink.
The widely taught rule of thumb that decay heat is "about 1% at an hour" is visible in the
table, and it is a good rule. What the table also shows is that it is only a rule for that one instant:
an hour earlier the figure is 2.5 times larger, a day later it is less than half.
The input people get wrong
Why operating history changes the answer this much
The second term in the correlation, (t + Top)−0.2, carries the irradiation history.
Short-lived fission products reach equilibrium within hours; long-lived ones are still accumulating after
years. A core that has run for a week simply has not built the inventory of a core that has run for a
year, and the difference is not small.
Holding the same reactor and the same observation time — 3,400 MWth, one day after
shutdown — and varying only how long it ran beforehand:
| Operating time before scram | Fraction of P₀ at t = 1 day | Decay power |
|---|
| 1 day | 0.083% | 2.8 MW |
| 7 days | 0.218% | 7.4 MW |
| 30 days | 0.318% | 10.8 MW |
| 90 days | 0.381% | 12.9 MW |
| 1 year | 0.444% | 15.1 MW |
| 3 years | 0.483% | 16.4 MW |
| Infinite operation | 0.639% | 21.7 MW |
A factor of 5.4 between a one-day run and infinite operation, and still a factor of two
between a week and a year. The curve flattens because the short-lived contributors saturate first, but it
never stops rising — which is why "infinite operation" is the conservative assumption used for design
basis work, and why a plant restarted after a short outage has a genuinely different decay heat profile
from one at end of cycle.
Practical consequence: if you are estimating decay heat for a
specific event, the operating time is not a formality. Using the infinite-operation limit for a reactor
that ran for a month overstates the answer by about a factor of two; using one day when the real figure
is a year understates it by more than five.
Why decay heat matters
A reactor SCRAM stops the chain reaction, but radioactive fission products continue to decay and release heat. The initial residual power is only a small fraction of full reactor power, yet for a large reactor it still represents many megawatts. Continuous heat removal remains necessary to prevent fuel, coolant, and containment temperatures from rising.
Emergency and shutdown cooling systems are therefore designed to remove heat after fission power has ended. Depending on the reactor design, these functions may be provided by residual heat removal systems, isolation condensers, passive containment cooling, steam-driven injection, natural circulation, or other engineered and passive heat sinks.
Model boundary: this page estimates heat generation only. It does not calculate coolant inventory, boiling, heat-transfer limits, fuel temperature, pressure, or whether a particular cooling system is adequate.
What the number is for
Turning decay power into a heat-removal requirement
A decay heat figure on its own decides nothing. It becomes an engineering requirement when it is
paired with a heat sink and a duration.
Shutdown cooling capacity
Residual heat removal is typically placed in service some hours after shutdown, once primary
temperature and pressure have been reduced. At eight hours the example core is still producing
20 MW; at one day, 15 MW. Those are the duties the heat exchangers and their service-water
loop must carry continuously, in summer, with one train out for maintenance. The number does not fall
below one megawatt for well over a year.
Passive systems: the inventory question
A passive heat sink is sized by energy, not power. Taking the 490 MWh integrated over the first day
and rejecting it entirely by evaporating water at atmospheric pressure
(hfg ≈ 2,257 kJ/kg) requires
490 MWh × 3600 s/h / 2257 kJ/kg ≈ 780 tonnes of water
which is why passive plant designs carry tanks of that order and why their advertised coping period
is quoted in days rather than indefinitely. Extending the period is a storage-volume problem.
Spent fuel pools
The same arithmetic governs a pool, with the difference that the heat source is older and the sink is
a much larger mass of water. For a pool holding 1,200 m³ at 35 °C and rejecting 4 MW with cooling
lost:
- Heat-up to boiling: 1.2 × 106 kg × 4.18 kJ/kgK × 65 K ÷ 4,000 kW ≈ 23 hours
- Boil-off once there: 4,000 kW ÷ 2,257 kJ/kg ≈ 1.8 kg/s, about 6.4 m³/h
- Three metres of water above the racks over a 100 m² plan area → roughly 47 hours more
before the fuel is uncovered
Three days, in round numbers, from a clean pool to an uncovered rack — and that is the honest reason
pool makeup capability and its power supply receive the attention they do. The figures above are an
illustration with assumed geometry, not a statement about any particular facility.
Method
What Way–Wigner leaves out, and what ANS-5.1 adds
Way and Wigner published this correlation in 1948. It is a single empirical fit to the aggregate
beta and gamma energy release of a fission-product mixture, and it has survived for seventy years
because it is right to within a few tens of percent across four decades of time using one line of
arithmetic. Understanding what it omits is what separates using it correctly from using it as an
answer.
Fission products only
The correlation describes the decay of fission fragments. It contains no term for actinide decay.
In a real LWR core, neutron capture in U-238 produces U-239 (half-life 23.5 min), which decays to
Np-239 (half-life 2.36 days), and both contribute heat. Their contribution peaks in the window
hours to days after shutdown — precisely the window that matters most for shutdown cooling
— and it scales with the conversion ratio, so it is fuel- and burnup-dependent in a way no single
correlation can capture.
No neutron-capture correction
Fission products themselves absorb neutrons during operation, shifting the decay chain toward
nuclides with different energy release. ANS-5.1 handles this with an explicit multiplier G(t) applied
to the fission-product term. Way–Wigner has it folded into the fitted constant, averaged over a
reactor that may not resemble yours.
One fuel, one spectrum
Decay heat per fission differs between U-235, U-239, Pu-239 and Pu-241. A fresh core and an
end-of-cycle core with a significant plutonium fission fraction do not produce the same decay heat per
unit power. ANS-5.1 carries a separate 23-term exponential fit for each fissioning nuclide and
combines them by the fission fraction. Way–Wigner carries one curve.
No uncertainty band
This is the difference that matters for licensing. ANSI/ANS-5.1 prescribes uncertainty factors to be
applied to the computed decay heat, which is what makes a result defensible in a safety analysis.
Way–Wigner returns a point value with no statement of confidence. Across its valid range and for a
conventional uranium-fuelled LWR, agreement with ANS-5.1 is typically within roughly ten to twenty
percent, with the larger deviations at the short-time end and in the first days where the unmodelled
actinide term is at its most significant.
Use this page for: order-of-magnitude estimates, teaching, scoping a heat-removal
duty, checking that someone else's number is plausible, and understanding how the curve is shaped by
power and operating history.
Do not use it for: safety analysis, licensing submissions, emergency-planning basis,
spent-fuel transport or storage cask design, or any calculation whose output will be relied on. Those
require ANSI/ANS-5.1-2014 with its uncertainty treatment, or a depletion and decay code such as
ORIGEN-type inventory calculation with plant-specific irradiation history.
Where the valid range comes from
- Below about 10 seconds the correlation diverges from reality because the reactor is
not actually at zero fission power yet. Delayed neutrons sustain a decaying fission source for tens of
seconds after the control rods are in, so the true thermal power is the sum of residual fission and
fission-product decay. Way–Wigner describes only the second term.
- Beyond about 100 days the fission-product mixture is dominated by a handful of
long-lived nuclides — Cs-137, Sr-90 and their daughters — whose behaviour is not well represented by
a single power law fitted to the aggregate early curve.
- The constant-power assumption is built into the derivation. A load-following
reactor, or one scrammed from part power, does not match it. For a stepped history the correlation can
be superposed over intervals, but that is already past the point where a real inventory code is the
better tool.