Chaining step count into stringer length
A 3000mm floor height with a 175mm desired riser needs 17 steps at a 277mm tread depth. Since the top step is the landing itself, there are only 16 actual treads along the run — 16 × 277mm = 4,432mm, or 4.432m of total horizontal run. Feeding that real 4.432m run, alongside the same 3m total rise, into the stringer length formula gives a stringer of 5.3519m at a 34.09° angle.
Why the tread count is one less than the step count
Each riser lifts you up to the next tread, but the very last "step" up is onto the landing itself — which isn't a tread you walk across horizontally as part of the run. A staircase with 17 steps therefore only has 16 physical tread surfaces contributing to the total horizontal distance.
Why this chained result differs from a stringer picked independently
Choosing a stringer's rise and run without first working out how many treads actually fit risks a mismatch — the earlier stringer example (3m rise, 4m run, a 5m stringer) assumed a 4m run as a starting point, not one derived from an actual number of steps. The 4.432m run computed here comes from a real staircase design (17 steps at 277mm each), making the resulting 5.3519m stringer the length that specific staircase actually needs.
The practical takeaway for planning a staircase
Before ordering stringer lumber, working out the step count and tread depth first — then deriving the total run from them — ensures the stringer length ordered matches the staircase actually being built, rather than a run guessed independently of the step design.