# What is Planck's constant dimensionally equal to?

Oct 4, 2014

The dimensions of Planck's constant are $M {L}^{2} {T}^{-} 1$.

$E = h f$, so

$h = \frac{E}{f}$

$E = \text{energy" = "force × distance" = "mass × acceleration × distance}$

So [E] = M × LT^-2 × L = ML^2T^-2, where the brackets mean "units of".

$f = \text{frequency}$, so $\left[f\right] = {T}^{-} 1$

Then $\left[h\right] = \frac{M {L}^{2} {T}^{-} 2}{T} ^ - 1 = M {L}^{2} {T}^{-} 1$.

In SI base units, $\left[h\right] = {\text{kg·m"^2"s}}^{-} 1$.

In SI derived units, $\left[h\right] = \text{J·s}$.