there are different ways of doing this but the following way will work.
The method revolves around knowing the horizontal distance between the lower and upper newel posts. Since the regulation of 100mm relates to a horizontal (parallel to the floor), not pitch (parallel to the rise of the stairs) distance between balusters.
(This measurement might equate to whats known as the 'total going' of your stairs,the total distance the stair structure travels horizontally, as it also rises to the floor above.)
To find this measurement you can drop a plumb line from the inside edge of the upper newel to the floor below and simply measure the distance from this to the inner edge of the lower newel ( a little crude but it will work).
Alternatively, if the above method won't work for any reason, you can measure the distance between the newel posts going with the pitch along the 'stair string' that connects them, and, if you know the degree pitch of your stairs, calculate the 'total going' distance using trigonometry.
Once you have the horizontal distance between the newel posts, you must then measure the horizontal width of the balusters/spindles you intend on using.
At this point, multiply the width measurement of the spindles by an acceptable multiple (perhaps use two spindles per tread, so if you have 10 treads use 20 spindles). Then subtract the multiple spindle measurement from your total going measurement. This will give you the fresh air measurement!
At this point divide the fresh air measurement by the number of spindles plus 1 (remember to add 1). The figure you now have is the distance between two spindles. If its greater than 100mm add more spindles (remembering to add 1 when dividing the number of spindles in the fresh air measurement). If the distance is too low, work on fewer spindles. However, consider appearance as well as regs. Sometimes too few spindles, even though within the regs, can end up looking too few.
[quote="piperjim"]is there a quick formula for working out the amount of spindles required and the spacing of these spindles? I know that the spacings cannot be more than 100mm apart.Any help would be appreciated.[/quote]
Allow 2 Spindles for every tread and you won't go wrong.
I spent some time writing a very satisfying spreadsheet for just this purpose involving all that trigonometry you thought you'd never use at school. In practice it was of limited use.
If my web surfing is accurate the 100mm rule says that no gap anywhere in the ballustrades should allow the passage of a 100mm sphere. So in my case a 95mm gap between the base of the spindles still broke the rule because the spindles were thinner in the middle.
I've settled on fillets on about 120mm long, which with a stair pitch of 45 degrees means the gaps between the square part at the base of the spindles (easiest to measure) is 85mm. At the thinner parts this just passes the 100mm rule.
The reason my spreadsheet was of limited use was because it didn't account for the shape of the newel posts at the beginning and end of each run. So my advice is to work out the first and last gap first, then divide the remaining space by a guessed number of spindles. If the gap is too big add a spindle to the calculation, and if its too small take one away and see if the gap still passes the 100mm rule.