Conversion formulas — Neutron Calculator

Calculation of: from:	$λ$ in m	$E$ in J	$v$ in m/s	$T$ in K
$λ$ in m		$\frac{h^{2}}{2 m_{n} λ^{2}}$	$\frac{h}{m_{n} λ}$	$\frac{h^{2}}{2 m_{n} k λ^{2}}$
$E$ in J	$\frac{h}{\sqrt{2 m_{n} E}}$		$\sqrt{\frac{2 E}{m_{n}}}$	$\frac{E}{k}$
$v$ in m/s	$\frac{h}{m_{n} v}$	$\frac{1}{2} m_{n} v^{2}$		$\frac{m_{n} v^{2}}{2 k}$
$T$ in K	$\frac{h}{\sqrt{2 m_{n} k T}}$	$k T$	$\sqrt{\frac{2 k T}{m_{n}}}$

$λ = \frac{h}{m_{n} v}$ (de Broglie's law) ; $E = \frac{1}{2} m_{n} v^{2}$ (kinetic energy)

Legend

$E$ : neutron kinetic energy

$v$ : neutron speed

$T$ : neutron temperature (K)

$h$ : Planck's constant

$m_{n}$ : neutron mass

$k$ : Boltzmann's constant

Constants

$h$ =	6.626 070 15 × 10⁻³⁴ J·s (exact)
$m_{n}$ =	1.674 927 500 56(85) × 10⁻²⁷ kg
$k$ =	1.380 649 × 10⁻²³ J K⁻¹ (exact)
$c$ =	299 792 458 m s⁻¹ (exact)
$N_{A}$ =	6.022 140 76 × 10²³ mol⁻¹ (exact)

Unit conversions

1 Å =	1 × 10⁻¹⁰ m (exact)
1 eV =	1.602 176 634 × 10⁻¹⁹ J (exact)
1 cal =	4.184 J (exact, thermochemical)

Reference

Values marked (exact) are fixed numerical definitions of the SI base units (2019 redefinition). The neutron mass $m_{n}$ is taken from CODATA 2022, NIST, USA.

Note

These formulas do not take into account relativistic effects and assume $v ≪ c$ .