Calculate Spearman and Pearson correlation on variables of different units If for example I have the following data
X     Y
3.2   0
1.5   0
6.5   3
2.4   1
6.2   3

where X is a value between 1 (best case) and 7 (worst case)
and Y is a value between 0 (best case) and 3 (worst case)
and I would like to compute Spearman or Pearson correlation between X and Y.
Do I need to convert into values with similar units?

Dave is already correct in his answer. The formula for the correlation is a unitless measure. Here I use R for illustration. If you scale your x and y values and run a correlation on them:
#### Correlation of Raw Units ####
x <- c(3.2,1.5,6.5,2.4,6.2)
y <- c(0,0,3,1,3)
scale.x <- scale(x)
scale.y <- scale(y)
cor(scale.x,scale.y)

This gives you $r = .93$:
         [,1]
[1,] 0.929868

If you run a correlation of the raw values using cor(x,y) instead, you get the same result:
> cor(x,y)
[1] 0.929868

So you do not need to worry about the items being on different scales. You can simply run the correlation as is.
