Stair Calculator: Rise, Run, Stringer Length & Angle

Stair diagram

  Total Rise
  +-----------------------------+
  |                             |
  |     +--+                    |
  |     |  +--+                 |
  |     |  |  +--+              |
  |     |  |  |  +--+           |
  |     |  |  |  |  +--+        |
  |     |  |  |  |  |  +-------+  <- Landing (optional)
  +-----+--+--+--+--+--+
  ^              ^
  Riser (H)     Tread (D)

  Stringer = sqrt(rise^2 + run^2)  <- diagonal board
  Angle = arctan(rise / run)

The stringer (diagonal board) supports the treads (horizontal) and risers (vertical). The total rise is floor-to-floor height; the total run is the horizontal span of all treads.

How to calculate stairs: step by step

1. Measure total rise — the vertical distance from the lower floor to the upper floor.
2. Divide by desired riser height — typical comfortable risers are 7 in (17.8 cm). The calculator rounds to the nearest whole number of steps.
3. Recalculate actual riser height — divide total rise by the step count so the stairs land exactly flush.
4. Multiply tread depth by step count to get the total horizontal run.
5. Stringer length = √(totalRise² + totalRun²) — the hypotenuse of the stair triangle. This is the board you cut.
6. Stair angle = arctan(totalRise ÷ totalRun) × (180 ÷ π). Comfortable stairs land between 30° and 37°.
7. Concrete volume (for poured stairs) is estimated using a stacked-prism method: each step adds tread × width × cumulative height, plus any landing volume.

Key stair formulas

Frequently asked questions