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newSchoolWorks.com › VoTechWorks › Building & Construction › Carpentry › Layout: Site, Structural, and Finish Carpentry Layout Techniques › Lesson 9
BLD-CARP03-08 · Lesson 9 · 15 clock hours · lab

Laying Out Stairs: Stringers, Treads, Risers, and Nosing

Objective. Using a stair framing square and a set of stair gauges, students will lay out a closed-stringer stair for a given total rise and run, marking cut lines for all treads and risers within 1/16 inch of calculated positions before any cuts are made.

Why Stair Layout Matters

A stairway that is built even slightly out of proportion is uncomfortable to climb, creates a tripping hazard, and may violate the building code. The key to a safe, code-compliant stair is accurate layout on the stringer before any saw touches the wood. In this lab you will lay out a closed stringer — one that carries both treads and risers and is notched to receive them — using a framing square and stair gauges.

The Vocabulary of a Stair

Before you touch a square, know what you are measuring. Total rise is the vertical distance from finish floor to finish floor. Total run is the horizontal distance the stair travels. Unit rise is the height of one riser; unit run is the horizontal depth of one tread, not counting the nosing. The nosing is the rounded or beveled overhang of the tread that extends past the riser face, typically about 1-1/4 inches for residential work — it increases tread depth for comfort without increasing total run. A stringer (also called a stair horse or carriage) is the diagonal structural member that supports the treads and risers. A closed stringer is notched so treads and risers sit in the notches; the outside face of the stringer still shows the full board profile.

Calculating Unit Rise and Unit Run

Start with the total rise in inches. Divide by the number of risers to find unit rise. A common target is 7 inches; the general residential guideline is a maximum of about 7-3/4 inches per riser and a minimum of about 4 inches, though you must always verify the applicable code for the project.

A useful rule of thumb: unit rise + unit run should equal roughly 17 to 18 inches. Once you choose your unit rise, subtract it from 17 or 18 to get a starting unit run, then verify the total run fits your floor plan. Remember: the number of treads is always one less than the number of risers because the upper floor acts as the top landing.

Example outline (not the worked example below): if total rise = 105 inches and you try 15 risers, unit rise = 7 inches. Using the 17-inch rule, unit run = 10 inches. Total run = 14 treads × 10 inches = 140 inches. Always round unit rise to the nearest 1/16 inch if the division does not come out even, then check that all risers still add up exactly to the total rise.

Setting Up the Framing Square

A stair framing square is an L-shaped steel tool with a body (the long leg, 24 inches) and a tongue (the short leg, 16 inches). Stair gauges are small brass clamp-on buttons that lock onto the square's edges at the exact unit-rise and unit-run dimensions so you can repeat the same position at every step without re-measuring.

1. Set one gauge on the tongue at the unit rise measurement.

2. Set the other gauge on the body at the unit run measurement.

3. Lay the 2×12 stringer stock flat on sawhorses with the crown (slight bow) facing up.

4. Mark the plumb cut at the top first: hold the square so both gauges touch the top edge of the board; draw along the tongue — this is your top plumb cut.

5. Step the square: slide it along the board so the unit-run gauge aligns with the mark you just made. Draw the next unit-rise line and unit-run line. This tread-riser intersection is your first step notch.

6. Continue stepping until you have marked every tread and riser. The last mark at the bottom gives you the bottom plumb cut, which defines how the stringer rests on the floor.

The Tread-Thickness Reduction (Bottom Riser)

Because treads add thickness at every step, the bottom riser is shorter than all others by the thickness of one tread board. If tread stock is 1-1/2 inches thick, cut 1-1/2 inches off the bottom of the stringer at the floor cut. This keeps every visible riser height equal once treads are installed.

Nosing

The nosing is added to the tread after the stringer is cut. It does not change the unit-run layout on the stringer; it simply extends the tread surface. Mark the nosing dimension on your calculation form for reference during tread installation.

Dimensional Tolerance

Your marks must be within 1/16 inch of calculated positions. Use a sharp pencil (not a crayon or marker) for accuracy. Verify each interval with a tape and combination square before moving on.

Safety During This Lab

Checking Your Work

When layout is complete, your partner measures every tread interval (horizontal) and every riser interval (vertical) with a tape and records the values on the check sheet. Compare each to your calculated unit rise and unit run. Any interval outside 1/16 inch must be corrected by re-marking — not by erasing and guessing. Recalculate and re-step that section of the square. Submit the stringer and the completed check sheet together.

Key terms8

Total riseThe full vertical distance from the lower finish floor to the upper finish floor that the stairway must climb.
Unit riseThe vertical height of a single riser step, found by dividing total rise by the number of risers.
Unit runThe horizontal depth of a single tread, measured from riser face to riser face, not including the nosing.
Stringer (carriage)The diagonal structural member, typically a 2×12, that is notched to support the treads and risers of a stairway.
NosingThe rounded or beveled overhang of a tread that projects past the riser face, typically about 1-1/4 inches, providing additional tread depth without increasing total run.
Stair gaugesSmall brass clamp-on buttons secured to a framing square at the unit-rise and unit-run dimensions so the same position can be repeated consistently at each step along the stringer.
Plumb cutA vertical cut made at the top or bottom of a stringer so it bears properly against the header or floor; laid out along the tongue of the framing square.
Tread-thickness reductionThe amount — equal to the thickness of one tread board — subtracted from the bottom of the stringer so that all visible riser heights remain equal once treads are installed.

Worked examples4

1. A floor-to-floor total rise is 91 inches. Find the number of risers, unit rise, and verify the unit rise is reasonable.
  1. Step 1 — Try a target unit rise near 7 inches. Divide total rise by trial unit rise: 91 ÷ 7 = 13.0 exactly. So 13 risers is a whole number — ideal.
  2. Step 2 — Confirm unit rise: 91 ÷ 13 = 7.000 inches per riser. No rounding needed.
  3. Step 3 — Check that 7 inches falls within typical limits (roughly 4 inches minimum, 7-3/4 inches maximum). 7 inches is well within range.
  4. Step 4 — State the answer: 13 risers at 7 inches each, totaling 91 inches.
Answer: 13 risers; unit rise = 7 inches exactly.
2. Using the result above (unit rise = 7 inches), find unit run using the 17-inch rule, then calculate total run for 12 treads.
  1. Step 1 — Apply the rule: unit rise + unit run ≈ 17 inches. So unit run = 17 − 7 = 10 inches.
  2. Step 2 — Number of treads = number of risers − 1 = 13 − 1 = 12 treads.
  3. Step 3 — Total run = 12 treads × 10 inches = 120 inches.
  4. Step 4 — Convert to feet for a plan check: 120 ÷ 12 = 10 feet of horizontal travel.
Answer: Unit run = 10 inches; total run = 120 inches (10 feet).
3. Total rise is 98 inches. Determine unit rise when using 14 risers, rounded to the nearest 1/16 inch, and confirm all 14 risers add up to exactly 98 inches.
  1. Step 1 — Divide: 98 ÷ 14 = 7.000 inches exactly. No rounding needed in this case.
  2. Step 2 — Verify: 14 × 7.000 = 98.000 inches. ✓
  3. Step 3 — Had the division produced a decimal, you would round to the nearest 1/16 inch (0.0625 inch), then multiply back and compare to the total rise to make sure the accumulated error is acceptable.
Answer: Unit rise = 7 inches exactly; 14 × 7 = 98 inches confirmed.
4. Tread stock is 1-1/2 inches thick. After stepping the stringer with 13 risers at 7 inches each, how much must be removed from the bottom of the stringer, and what will the bottom riser height be after the tread is installed?
  1. Step 1 — The bottom riser as laid out = 7 inches (one full unit rise).
  2. Step 2 — Once a 1-1/2-inch tread is installed on the first step, it raises that tread surface by 1-1/2 inches, making the effective first riser 7 + 1.5 = 8.5 inches — too tall.
  3. Step 3 — To equalize, trim 1-1/2 inches from the bottom of the stringer at the floor cut before installation.
  4. Step 4 — After trimming, bottom riser = 7 − 1.5 = 5.5 inches from floor to bottom of tread? No — reconsider: the tread sits on the notch. The cut reduces the stringer height at the floor, so the first riser measured from floor to top of first tread = (7 − 1.5) + 1.5 = 7 inches. The subtraction of tread thickness from the stringer bottom and the addition of tread thickness on top cancel exactly, giving the correct unit rise of 7 inches at every step.
Answer: Remove 1-1/2 inches from the bottom of the stringer; all risers — including the bottom — will measure 7 inches once treads are in place.

The math in this lesson2

Learners compute risers and unit rise for 91 in and 98 in, unit run by the 17 in rule, and stringer drop for tread thickness.
A-SSE.1N-Q.3
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor calculates a stair from a given floor-to-floor height, demonstrates placing framing square with gauges set to unit rise and unit run, stepping the square along a 2×12 stringer, and marking the top and bottom plumb cuts; students annotate each step on a reference sheet. · Students calculate their own unit rise and unit run from a different total-rise scenario, set gauges on a framing square, and step a full stringer on a 2×12, marking all tread-riser intersections and the top and bottom cuts. · Dimensional verification: partners measure every tread and riser interval on each other's stringer using a tape and combination square and record results on a check sheet; any interval outside 1/16 inch requires the student to re-mark before the lesson ends.
Materials: 2×12 lumber (stringer stock), stair framing square, stair gauges (clamp-on buttons), combination square, 25-ft tape, pencil, stair calculation forms, NCCER Carpentry Level 3 — Stairways and Ladders module
Check: Check sheet reviewed by instructor; all tread and riser marks within 1/16 inch of calculated positions; top and bottom plumb cuts correctly oriented; completed check sheet and stringer submitted together as a pass.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NCCER Carpentry — Stairways and Layout
1. A stair has a total rise of 84 inches. The carpenter chooses 12 risers. What is the unit rise?
NCCER Carpentry — Stairways and Layout
2. If the unit rise is 7 inches and the 17-inch rule is applied, what is the unit run?
NCCER Carpentry — Stairways and Layout
3. A stair has 13 risers. How many treads does it have?
NCCER Carpentry — Tools and Layout
4. When setting stair gauges on a framing square, where is the unit-rise gauge clamped?
NCCER Carpentry — Stairways and Layout
5. Why is 1-1/2 inches subtracted from the bottom of a stringer when the tread stock is 1-1/2 inches thick?
NCCER Carpentry — Stairways and Layout
6. During stringer layout, what is the maximum allowable deviation from a calculated tread or riser position before a mark must be corrected?
NCCER Carpentry — Stairways and Layout
7. What does the nosing on a stair tread affect in terms of stringer layout?
OSHA 10 — Personal Protective Equipment
8. Which PPE is required during stringer layout on shared sawhorses in this lab, even though no cutting occurs?
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