Time of Flight Neutron Energy Calculator

The time-of-flight method first converts the measured flight path L and time t to SI units, then computes neutron speed: v = L / t.

• Non-relativistic kinetic energy: E = ½ m_n v²
• Relativistic kinetic energy: E = (γ − 1) m_n c², where γ = 1 / √(1 − (v/c)²)

Energy is also reported in electron-volts using 1 eV = 1.602176634×10⁻¹⁹ J.

1. Enter the flight path length between the source and detector.
2. Enter the measured time of flight using your instrument timing.
3. Select the energy model and your preferred decimal precision.
4. Press Calculate to view results above the form.
5. Use CSV or PDF buttons to export the computed outputs.

1) Why time-of-flight is widely used

Time-of-flight (TOF) spectroscopy converts a measured transit time into neutron kinetic energy. Because neutron velocity depends strongly on energy, a single pulsed source and a fixed flight path can produce an energy spectrum without changing instrument settings.

2) Typical instrument ranges

Flight paths commonly range from about 1–100 m, depending on facility layout and resolution needs. Timing spans from nanoseconds (fast timing electronics) up to milliseconds (slow or thermal neutrons). These ranges correspond to energies from the meV scale through keV and into MeV for high-energy beams.

3) A thermal reference point

A useful benchmark is the “thermal” neutron near room temperature, about 25 meV (0.025 eV), with speed close to 2200 m/s. On a 5 m flight path, this corresponds to a TOF of about 2.27 ms (≈2270 µs). This calculator lets you confirm such reference checks quickly.

4) Unit discipline and data quality

TOF work is sensitive to unit mistakes. A millisecond versus microsecond mix-up shifts energy by a factor of one million because E ∝ v² and v = L/t. Always verify geometry (effective path length) and the timing reference (start/stop definition) before interpreting results.

5) Resolution insight for experiments

A practical rule is that fractional energy resolution scales roughly as ΔE/E ≈ 2(Δt/t) when length uncertainty is small. Improving timing resolution, increasing flight path, or both, tightens energy resolution. Longer paths often trade intensity for better separation of nearby energies.

6) When the relativistic option matters

Many laboratory TOF measurements involve β well below 0.01, where the classical expression is accurate. For higher-energy neutrons (multi-MeV) or exceptionally short flight times, β rises and relativistic corrections become noticeable. Use the relativistic mode when your computed β is not negligible.

7) Reporting and traceability

Professional reports typically record L, t, units, model choice, and computed velocity. Exporting results to CSV helps preserve reproducibility, while a PDF snapshot supports lab notebooks and experiment logs. Include detector distance calibration details when publishing.

8) Practical workflow recommendation

Start with a known reference (such as the thermal benchmark), then run your measured TOF values. If results look unreasonable, recheck timing offsets, cable delays, and path length definitions. Small systematic shifts in t can cause large energy bias at short times.

1) What inputs do I need for TOF neutron energy?
You need the effective flight path length between timing reference points and the measured time of flight. Select consistent units and the appropriate energy model for your speed range.

2) Why does energy change so strongly with time?
Because velocity is L/t and kinetic energy scales with v², small time differences cause large energy differences, especially for short flight times typical of faster neutrons.

3) What is a good sanity check for my setup?
Use a thermal benchmark: about 25 meV corresponds to roughly 2200 m/s. If L is 5 m, expect about 2.27 ms time of flight for thermal neutrons.

4) Should I use non-relativistic or relativistic mode?
Use non-relativistic mode for small β values. If the computed β is not negligible or your energies are in the multi-MeV range, switch to relativistic mode for improved accuracy.

5) How does timing uncertainty affect energy uncertainty?
A common approximation is ΔE/E ≈ 2(Δt/t) when length error is small. Improving timing precision or increasing flight path generally improves energy resolution.

6) Can cable delays or trigger offsets matter?
Yes. Fixed timing offsets shift t and therefore v and E. Offsets are especially impactful at short flight times, so calibrate electronics delays and define consistent start/stop references.

7) Why export to CSV or PDF?
CSV supports analysis workflows and reproducible calculations. PDF provides a stable snapshot for lab records, sharing, and documentation alongside instrument settings and calibration notes.