Neutron Flux Calculator
Calculate the neutron flux inside a nuclear reactor from neutron density and velocity. Used by nuclear engineers and physicists to assess reactor power levels and neutron-induced reaction rates.
About this calculator
Neutron flux (φ) quantifies the total path length travelled by all neutrons in a unit volume per second, and is the key quantity governing fission reaction rates in a reactor. The formula is φ = n × v / 100, where n is the neutron density in n/cm³ and v is the neutron velocity in m/s. The division by 100 converts velocity from m/s to cm/s so units are consistent, yielding flux in units of n/(cm²·s). Flux directly determines the reaction rate R = φ × Σ, where Σ is the macroscopic cross-section of the material. Thermal reactors typically operate at fluxes around 10¹³ to 10¹⁴ n/(cm²·s). Higher flux means more fissions per second and therefore greater reactor power output.
How to use
Suppose a reactor core has a neutron density of 5 × 10⁸ n/cm³ and a thermal neutron velocity of 2,200 m/s. Apply the formula: φ = (5 × 10⁸ × 2,200) / 100 = (1.1 × 10¹²) / 100 = 1.1 × 10¹⁰ n/(cm²·s). Enter 500,000,000 for neutron density and 2200 for neutron velocity. The calculator returns a flux of 1.1 × 10¹⁰ n/(cm²·s), which can then be used alongside a macroscopic cross-section to find the fission reaction rate.
Frequently asked questions
What is neutron flux and why is it important in nuclear reactor design?
Neutron flux is the number of neutrons passing through a unit area per second, measured in n/(cm²·s). It is the central parameter controlling how frequently neutrons collide with fuel nuclei and cause fissions. Higher flux yields more power from the same fuel volume but also increases radiation damage to reactor materials. Engineers balance flux levels to maximize power output while keeping structural materials within safe radiation exposure limits.
How does neutron velocity affect the neutron flux calculation?
Neutron flux is directly proportional to neutron velocity because faster neutrons sweep through a larger volume per second, increasing the probability of encountering a target nucleus. Thermal neutrons (v ≈ 2,200 m/s at room temperature) are used in most commercial reactors because they have much higher fission cross-sections in uranium-235 than fast neutrons. Fast reactors use unmoderated neutrons at higher velocities and require significantly enriched fuel or different fissile materials to sustain a chain reaction.
What units does neutron flux use and how do I convert between them?
Neutron flux is expressed in neutrons per square centimetre per second, written as n/(cm²·s) or n·cm⁻²·s⁻¹. This calculator requires density in n/cm³ and velocity in m/s, then converts velocity to cm/s internally by dividing by 100 before multiplying. If your velocity is already in cm/s, skip the division or adjust your input accordingly. Integrated flux over time, called fluence, is measured in n/cm² and is used to track cumulative radiation damage in reactor components.