What is Planck's constant dimensionally equal to?

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Answer 1 · 2014-10-04T01:05:27

The dimensions of Planck's constant are #ML^2T^-1#.

#E = hf#, so

#h = E/f#

#E = "energy" = "force × distance" = "mass × acceleration × distance"#

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

#f = "frequency"#, so #[f] = T^-1#

Then #[h] = (ML^2T^-2)/ T^-1 = ML^2T^-1#.

In SI base units, #[h] = "kg·m"^2"s"^-1#.

In SI derived units, #[h] = "J·s"#.