Dimension of Spring Force Constant

Theorem

The dimension of a spring force constant is $\mathsf {M T}^{-2}$.

Proof

From Hooke's Law, we have:

$\mathbf F = -k \mathbf x$

where:

$\mathbf F$ is a force, of dimension $\mathsf {M L T}^{-2}$

$k$ is the spring force constant

$\mathbf x$ is a displacement, of dimension $\mathsf L$.

Let the dimension of $k$ be $D$.

Then we have:

$\mathsf {M L T}^{-2} = D \mathsf L$

from which the result follows immediately:

$D = \mathsf {M T}^{-2}$

$\blacksquare$