What is neutron flux?

Neutron flux (phi) is the total path length traveled by all neutrons per unit volume per unit time. It equals neutron density (n) multiplied by the average neutron speed (v), and is expressed in units of n/cm²·s.

What are typical neutron flux values in a reactor?

Thermal reactors typically operate at a flux of 10¹² to 10¹⁴ n/cm²·s. Research reactors can reach 10¹⁵ n/cm²·s, while high-flux test reactors approach 10¹⁵–10¹⁶ n/cm²·s.

What neutron density and velocity correspond to thermal neutrons?

Thermal neutrons at room temperature (20 °C) have a most-probable speed of about 2,200 m/s (220,000 cm/s). A typical thermal reactor core has a neutron density on the order of 10⁸ n/cm³.

Why is neutron flux important in reactor design?

Reaction rates for fission, capture, and activation are directly proportional to neutron flux. Engineers must know the flux distribution to predict power output, fuel depletion, and radiation damage to materials.

Can I use this for fast neutrons?

Yes. Simply enter the appropriate neutron density and speed for your neutron energy group. Fast neutrons have speeds on the order of 10⁷–10⁹ cm/s, much higher than thermal neutrons.

Neutron Flux Calculator

Calculate neutron flux density (phi) from neutron density (n) and average neutron velocity (v) using phi = n * v.

Inputs

Quick Presets

Neutron Density (n)

n/cm³

Average Neutron Velocity (v)

cm/s

Thermal neutrons at 20 °C: ~2.2 × 10⁵ cm/s

Result

Enter values and click Calculate

Formula Reference

φ = n × v

Neutron flux definition

n [n/cm³]

Neutron number density

v [cm/s]

Average neutron speed

Copied!

Summary

Neutron flux (phi) is a fundamental quantity in nuclear reactor physics, defined as the product of neutron density (n) and average neutron speed (v): phi = n × v. This calculator uses conventional reactor-engineering units: n/cm³, cm/s, and n/(cm²·s).

How it works

Enter the neutron density (n) in neutrons per cubic centimeter (n/cm³).
Enter the average neutron velocity (v) in centimeters per second (cm/s).
The calculator applies the formula phi = n * v.
Neutron flux (phi) is displayed in neutrons per cm² per second (n/cm²·s).
Switch between thermal, epithermal, and fast neutron presets to auto-fill typical values.
Copy the result to the clipboard with one click.

Use cases

Estimate reactor core neutron flux for design calculations.
Cross-check hand calculations in nuclear engineering coursework.
Verify neutron flux inputs for shielding analysis.
Quickly compare thermal vs. fast neutron flux magnitudes.
Convert between different neutron density and speed representations.
Support research in neutron activation analysis.
Educational demonstration of the flux-density-velocity relationship.
Preliminary reactor physics feasibility checks.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu