Calculator
Example Data Table
These sample values help you validate your inputs and compare common neutron regimes.
| Case | Input Basis | Representative Value | Approx. Energy | Approx. Velocity |
|---|---|---|---|---|
| Very Cold | Wavelength | 1.0 nm | 0.818 meV | 396 m/s |
| Thermal | Wavelength | 1.798 Å | 25.3 meV | 2198 m/s |
| Room Temperature | Temperature, kT | 300 K | 25.9 meV | 2222 m/s |
| Epithermal | Energy reference | 1 eV | 1 eV | 13,830 m/s |
| Fast | Energy reference | 1 MeV | 1 MeV | 13.8 Mm/s |
Formula Used
Classical kinetic energy: KE = 1/2 m v²
Use this when neutron speed is much smaller than light speed.
Relativistic kinetic energy: KE = (γ − 1)mc²
Lorentz factor: γ = 1 / √(1 − v²/c²)
This model is safer for very fast neutrons.
From wavelength: p = h/λ
Classical momentum form: KE = p²/(2m)
Relativistic momentum form: KE = √((pc)² + (mc²)²) − mc²
From temperature: KE = αkBT
Choose α = 1 for the common kT convention.
Choose α = 3/2 for average translational kinetic energy.
How to Use This Calculator
- Select an input mode: velocity, wavelength, momentum, or temperature.
- Enter the value and choose matching units.
- Pick classical, relativistic, or auto selection mode.
- Optionally set a flight path to estimate time of flight.
- Press the calculate button to display results above the form.
- Review energy conversions, wavelength, momentum, speed, and the graph.
- Export the result table as CSV or PDF whenever needed.
FAQs
1) What is neutron kinetic energy?
Neutron kinetic energy is the energy a neutron has because it is moving. It is often expressed in electronvolts, and it strongly affects scattering, absorption, moderation, and time-of-flight behavior in experiments.
2) Which equation should I trust most?
For slow neutrons, classical formulas work very well. For high-energy neutrons, relativistic formulas are more reliable. Auto mode compares speed with light speed and selects the more appropriate model automatically.
3) Can I calculate energy from wavelength?
Yes. The calculator first converts de Broglie wavelength into momentum using Planck’s constant. It then finds neutron kinetic energy with classical or relativistic momentum formulas, depending on the physics model you choose.
4) Why does the tool show both classical and relativistic values?
Showing both values helps you see whether relativistic corrections matter. For thermal and cold neutrons, the difference is tiny. For very energetic neutrons, the gap becomes important and can affect interpretation.
5) How does temperature input work?
Temperature mode converts thermal energy into kinetic energy using either the common kT convention or the average translational relation 3/2 kT. This is useful for reactor, beamline, and neutron moderation estimates.
6) What does the de Broglie wavelength output mean?
The de Broglie wavelength describes the neutron’s wave nature. It is especially useful for diffraction, crystallography, and scattering calculations, where wavelength determines how neutrons interact with atomic spacings and structures.
7) What units are supported?
You can enter velocity in m/s, km/s, cm/s, or fractions of light speed. Wavelength, momentum, temperature, flight-path units, and multiple energy output scales are also included for practical physics work.
8) Why is time of flight included?
Time of flight is widely used in neutron instruments. Once speed is known, travel time over a chosen path length is easy to estimate, helping with detector timing, beamline design, and experiment planning.