According to the Readers Digest Complete DIY manual, first measure from the front to the back of one tread (the part you walk on) and multiply the figure by the number of treads in the staircase.
In the case of a curving staircase, such as yours, take the larger measurement.
If the stairs turn a corner on a half-landing, measure the length of the half-landing and add it to the total. If you wish the carpet to run to the far end of any landing at the top of the stairs, add this measurement as well.
Now measure the height of the riser (the vertical part of each step) and multiply the figure by the number of risers.
Add this to the figure you already have. The total is the length of carpet needed to cover the stairs. But an allowance for moving the carpet to even out the wear is also needed, so add the depth of the bottom tread and the height of the bottom riser.
You will probably have to buy to the next metre or half metre.