What it does
When a reactor shuts down, fission stops within seconds, but the fission products in the fuel keep decaying and giving off heat. Straight after shutdown this decay heat is several percent of full power, and it falls only slowly: this is why cores need cooling for days and spent fuel for years.
This tool uses the Way-Wigner approximation, a simple fit to the decay of the mixture of fission products:
P(t) / P₀ = 0.0622 [ t^−0.2 − (t + T)^−0.2 ]
where t is the time since shutdown and T the time the reactor ran at power P₀ (both in seconds). It gives:
- the heat at times from 1 second to 1 year, in % of P₀ and in MW, with how much water it could boil off each hour;
- the energy released over standard intervals and an interval of your own, using the exact integral of the formula;
- when the heat falls below a level you choose;
- a log-log chart of the heat (against a very long operating history) and the energy released since shutdown, with a CSV of the curve.
It is an approximation, for study. It is usually quoted as fair (within tens of percent) from about 10 seconds to a few months after shutdown. Real decay heat depends on the fuel type, enrichment, burnup and power history, and also includes actinides such as U-239 and Np-239; safety work uses detailed codes and standards.
Worked example
A made-up reactor running at 3,000 MW thermal for 365 days: 10 seconds after shutdown it still makes 111.8 MW, and 1 hour after shutdown 30.37 MW (1.012 % of P₀), enough to boil off 48.4 tonnes of water an hour. The heat falls below 1 % after 1.05 hours, and is 13.31 MW (0.4438 %) after a day. In the first day the core releases 435 MWh (1,565 GJ) of heat, and another 1,309 MWh from day 1 to day 7.
Running for only a few hours builds up fewer long-lived fission products, so the heat then dies away much faster; choose very long to see the upper limit 0.0622 t^−0.2.
FAQ
Why does the heat fall so slowly at first? It is the sum of hundreds of fission products with half-lives from seconds to years; the short-lived ones fade first.
Is anything uploaded? No. Everything runs in your browser and works offline.
Where the numbers come from
- Way-Wigner approximation P/P0 = 0.0622 [t^−0.2 − (t + T)^−0.2] for fission-product decay heat, as given in standard reactor physics and nuclear engineering textbooks (a published formula); its integral worked out by fibub.
- Checked against SciPy: the formula at 24 points, the energy integral by adaptive quadrature at 16 intervals (agreement to 1 part in a billion), and the time to fall below a level by brentq, for four operating times.
- The 3,000 MW example reactor is a made-up round number.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.