Planck's constant,

*h*, appears throughout quantum mechanics and is one of the fundamental constants of physics. It has a value of:*h = 6.6260693(11) x 10*^{-34}J swhere uncertain values in the decimal place are contained in brackets. Planck's constant has the units of action (

*energy*x*time*, which can be shown to be the same as*momentum*x*length*).Planck's constant was first identified as part of Max Planck's description of blackbody radiation. Later, it was shown by Albert Einstein to be the constant of proportionality between the energy (

*E*) and frequency (*f*) of photons:*E = hf*A closely-related quantity (usually pronounced "h-bar") is:

*ħ = h/2π = 1.054571596(82) x 10*^{-34}J sIn this form, Planck's (reduced) constant appears in the two uncertainty relationships:

*ΔxΔp ≥ ħ*and *ΔEΔt ≥ ħ*where we have uncertainties in the measurements of a particle's

or wave-packet's position*Δx*, momentum*Δp*, energy*ΔE*and lifetime*Δt*.In Planck units, or natural units,

*ħ = 1, c = 1*.