Nuclear Fission Yield Calculator
Calculate the total thermal energy released by a nuclear fission process over a given time interval, given the fission rate and energy per fission event. Used in reactor physics and nuclear engineering to estimate power output and fuel burnup.
About this calculator
The total energy released by fission over a time interval is: E (joules) = fission rate × energy per fission × time interval × 1.602 × 10⁻¹³, where the fission rate is in fissions per second, energy per fission is in MeV, time interval is in seconds, and the conversion factor 1.602 × 10⁻¹³ converts MeV to joules. A single fission of U-235 releases roughly 200 MeV, split among kinetic energy of fragments (~167 MeV), prompt neutrons (~5 MeV), prompt gamma rays (~7 MeV), and delayed beta and gamma radiation (~21 MeV). The fission rate itself depends on the neutron flux, fuel cross-section, and number of fissile nuclei. This formula gives the instantaneous thermal power output when divided by the time interval, expressed in watts.
How to use
Consider a U-235 fuel sample undergoing fission at a rate of 3 × 10¹⁵ fissions/s, releasing 200 MeV per fission, over a 10-second interval. Enter fission rate = 3 × 10¹⁵, energy per fission = 200 MeV, time interval = 10 s. Calculation: E = 3×10¹⁵ × 200 × 10 × 1.602×10⁻¹³ = 3×10¹⁵ × 200 = 6×10¹⁷; × 10 = 6×10¹⁸; × 1.602×10⁻¹³ ≈ 9.61 × 10⁵ J (about 961 kJ). The average thermal power during this interval is 961 kJ / 10 s = 96.1 kW.
Frequently asked questions
How much energy is released per fission of uranium-235 versus plutonium-239?
A single fission of U-235 releases approximately 202 MeV of recoverable energy in a reactor, while Pu-239 fission releases about 210 MeV per event. The difference arises from the slightly higher mass excess of Pu-239 and differences in the prompt gamma and neutron spectra. In practice both values are close enough that U-235's 200 MeV is often used as a standard approximation. Over a large number of fissions these differences accumulate and affect fuel cycle economics and burnup calculations.
What is the relationship between fission rate and reactor thermal power?
Reactor thermal power (in watts) equals the fission rate (fissions/s) multiplied by the recoverable energy per fission in joules. Using 200 MeV per fission and the conversion 1 MeV = 1.602 × 10⁻¹³ J, each fission releases 3.204 × 10⁻¹¹ J. Therefore, 1 watt of thermal power corresponds to about 3.12 × 10¹⁰ fissions per second. A 1,000 MW thermal reactor sustains roughly 3.12 × 10¹⁹ fissions every second, consuming on the order of 1 kg of U-235 per day.
Why does the fission energy formula include the conversion factor 1.602 × 10⁻¹³?
Nuclear physicists conventionally express energy at the atomic scale in megaelectronvolts (MeV) because the values are conveniently sized (200 MeV rather than 3.2 × 10⁻¹¹ J). However, engineering quantities like power and heat are measured in SI units (joules and watts). The conversion factor 1 MeV = 1.602 × 10⁻¹³ J comes from the definition of the electron volt: 1 eV is the energy gained by one electron charge (1.602 × 10⁻¹⁹ C) accelerated through 1 volt, so 1 MeV = 10⁶ × 1.602 × 10⁻¹⁹ J = 1.602 × 10⁻¹³ J. Multiplying MeV values by this factor converts them to joules for use in power calculations.