How to Calculate Stair Rise and Run — Complete Design Guide
Introduction
Designing a safe, comfortable, and code-compliant staircase is one of the most rewarding—and challenging—aspects of any building project. Whether you're finishing a basement, building a deck, or constructing a new home, getting the stair dimensions right is non-negotiable.
Why Stair Calculations Matter
- Safety first: Prevent tripping hazards and accidents
- Code compliance: Pass building inspections and regulations
- Comfort: Create stairs that feel natural to use
- Professional results: Achieve construction-quality outcomes
- Cost efficiency: Avoid costly rebuilds and corrections
Consequences of Poor Stair Design
A poorly designed staircase can:
- Create tripping hazards and safety risks
- Fail building inspection and delay projects
- Feel awkward to use daily
- Reduce property value and appeal
- Require expensive corrections and rebuilds
What Makes Stairs Feel Right
Proper stair design ensures:
- Consistent step rhythm for natural movement
- Ergonomic proportions based on human gait
- Code-compliant dimensions for safety
- Comfortable daily use for all ages
- Professional appearance and craftsmanship
What You'll Master
This comprehensive guide covers the entire stair design process:
- Total rise measurement and calculations
- Optimal step number determination
- Riser height and tread depth calculations
- Comfort and safety verification methods
- Common DIY mistake avoidance
Using time-tested ergonomic formulas and current residential building standards, you'll learn to calculate, verify, and build stairs with confidence.
Step 1: Measure Total Rise Accurately
The foundation of every staircase is the total rise—the vertical distance from the finished floor at the bottom to the finished floor at the top.
⚠️ Critical Tip: If flooring (e.g., tile, hardwood, carpet) isn’t installed yet, add its thickness to your measurement. For example:
- Concrete basement floor (0") + 3/4" hardwood upstairs → measure to subfloor, then add 0.75".
Example:
- Subfloor-to-subfloor = 105"
- Upstairs finish = 3/4" hardwood
- Basement finish = 1/2" tile
- Total Rise = 105" + 0.75" – 0.5" = 105.25"
Step 2: Determine Number of Risers
Use a target riser height (typically 7–7.5" for comfort) to estimate the number of steps.
Formula:
Number of Risers = Total Rise ÷ Target Riser Height
→ Always round UP to the next whole number. This ensures no riser exceeds code limits.
Example:
- Total Rise = 105.25"
- Target = 7.5"
- 105.25 ÷ 7.5 = 14.03 → Round up to 15 risers
Now calculate exact riser height:
Exact Riser = Total Rise ÷ Number of Risers = 105.25 ÷ 15 = 7.017" (≈7 1/16")
✅ This is within the typical code max of 7.75".
Step 3: Calculate Treads and Total Run
- Number of Treads = Number of Risers – 1
(The top floor acts as the final tread.) - Tread Depth: Standard is 10–11" (min 10" per many codes).
- Total Run = Number of Treads × Tread Depth
Example:
- Risers = 15 → Treads = 14
- Tread Depth = 10.5"
- Total Run = 14 × 10.5" = 147" (12' 3")
Step 4: Validate with Ergonomic Formulas
Two key rules ensure comfort and safety:
1. Comfort Formula:
2 × Riser + Tread ≈ 24–25 inches
→ Ideal for natural stride.
Check:
2 × 7.017" + 10.5" = 24.53" → ✅ Excellent.
2. Safety Formula:
Riser + Tread ≈ 17–18 inches
→ Prevents overly steep stairs.
Check:
7.017" + 10.5" = 17.52" → ✅ Safe.
Step 5: Calculate Stringer Length
The stringer is the diagonal support beam. Use the Pythagorean Theorem:
Formula:
Stringer Length = √(Total Rise² + Total Run²)
Example:
√(105.25² + 147²) = √(11,077 + 21,609) = √32,686 ≈ 180.8" (15' 0.8")
→ You’ll need 16-foot 2×12 lumber (standard stringer material).
Step 6: Verify Building Code Compliance
While formulas guide comfort, local codes are law. Common residential requirements (always confirm with your authority):
| Parameter | Typical Code Limit | |---------|-------------------| | Max Riser Height | 7.75" (197 mm) | | Min Tread Depth | 10" (254 mm) | | Riser Uniformity | ±3/8" max variation | | Headroom | ≥80" (2032 mm) above any tread | | Max Vertical Rise | ≤12' (3658 mm) before a landing |
Headroom Check:
- Measure from nosing of tread upward at a 45° angle.
- Must be ≥80". If not, reduce riser height (increase step count) or raise the upper floor.
Step 7: Plan for Landings (If Needed)
For rises >12', a landing is required:
- Landing Depth ≥ tread depth (usually ≥36")
- Landing Width ≥ stair width
- Treat each flight separately (calculate rise/run for each segment)
Pro Tips & Common Mistakes
✅ Use a story pole: Mark exact riser heights on a straight board to test fit in the stairwell.
✅ Account for tread thickness: When cutting stringers, the horizontal cut depth = tread thickness (e.g., 1.5" for 2×10).
✅ Dry-fit stringers before permanent installation.
❌ Don’t ignore finish flooring in total rise.
❌ Don’t average riser heights—they must be identical.
❌ Don’t assume headroom is adequate—measure it!
Practical Applications
- Basement stairs: Most common DIY project; precision prevents head bumps.
- Deck stairs: Often open (no risers); tread depth still critical.
- Loft ladders: Steeper, but still bound by max riser rules.
- Renovations: Existing openings constrain total run—adjust tread/riser accordingly.
Worked Examples & Practice Problems
Example 1: Standard Interior Stairs
Given: Total Rise = 108", ample run space.
Goal: Design comfortable, code-compliant stairs.
- Risers: 108 ÷ 7.5 = 14.4 → 15 risers
Exact Riser = 108 ÷ 15 = 7.2" - Treads: 15 – 1 = 14 treads
Use 10.5" tread → Total Run = 14 × 10.5 = 147" - Comfort Check: 2×7.2 + 10.5 = 24.9" → ✅
- Stringer: √(108² + 147²) = √(11,664 + 21,609) = √33,273 ≈ 182.4" (15' 2.4")
Example 2: Deck Stairs with Limited Run
Given: Total Rise = 48", max Total Run = 60".
Find: Feasible tread depth.
- Risers: 48 ÷ 7.5 = 6.4 → 7 risers
Exact Riser = 48 ÷ 7 ≈ 6.86" - Treads: 7 – 1 = 6 treads
- Max Tread Depth: 60" ÷ 6 = 10"
- Comfort Check: 2×6.86 + 10 = 23.72" → Slightly low, but acceptable.
Example 3: Headroom Issue
Given: Total Rise = 110", floor-to-ceiling height = 86".
Problem: Headroom = 86" – (riser height × tread position). At mid-flight (7th tread), height ≈ 86" – (7 × 7.3") = 86 – 51.1 = 34.9" → ❌ Fails!
Solution: Increase riser count to 16 → Riser = 6.875"
At 8th tread: 86 – (8 × 6.875) = 86 – 55 = 31" → Still fails.
→ Must raise ceiling or lower basement floor.
Practice Problems
- Total Rise = 96". Design stairs with 11" treads. What’s the riser height?
- You have 120" of run space and 102" rise. What’s the max tread depth?
- A staircase has 13 risers of 7.5". What’s the total rise?
Answers
- Risers = 96÷7.5=12.8→13; Riser=96÷13≈7.38"
- Risers=102÷7.5=13.6→14; Treads=13; Tread=120÷13≈9.23" → Fails code (min 10")
- Total Rise = 13 × 7.5 = 97.5"
How do I measure total rise for basement stairs?
Measure from the finished basement floor (e.g., concrete or tile) to the finished first-floor surface (e.g., hardwood). If finishes aren’t installed, measure to subfloors and add the thickness of planned flooring at the top and subtract at the bottom (since you’re standing on it).
What if my calculated tread depth is less than 10 inches?
You have three options:
- Increase total rise (not usually possible).
- Reduce number of risers (but this increases riser height—may exceed 7.75").
- Extend total run (if space allows).
If none work, you may need a steeper staircase (e.g., for a loft) or consult a professional.
Can I use metric units?
Yes! The formulas are unit-agnostic. Common metric targets:
- Riser: 170–190 mm
- Tread: 250–280 mm
- Comfort: 2R + T ≈ 630–650 mm
How do I cut the stringers?
- Use a framing square with stair gauges set to riser and tread dimensions.
- Mark the top of the stringer (first riser is full height; first tread is full depth).
- Step down the board, marking each riser and tread.
- Cut along the lines with a circular saw (finish corners with a handsaw).
- Test-fit before cutting all stringers—use the first as a template.
Do deck stairs need risers?
Not always—many are open riser for aesthetics and drainage. However:
- Riser height still applies (vertical distance between treads).
- Tread depth must still meet code.
- Spacing between open risers must be below 4" (child safety).
What’s the minimum headroom, and how do I measure it?
- Minimum: 80" (2032 mm) in most residential codes.
- How: From the nosing (front edge) of any tread, measure vertically upward. The clearance must be ≥80" along the entire path of travel. Use a story pole to simulate.
Can I build stairs without a calculator?
Yes, but it’s error-prone. The calculator ensures:
- Precise riser uniformity
- Code compliance checks
- Accurate stringer length
- Headroom validation
For safety-critical structures, always double-check with a reliable tool.
What if my stairs feel “off” after building?
The most common cause is inconsistent riser heights—even 1/4" variation disrupts gait. Always:
- Use the exact same riser height on every step.
- Verify with a story pole before cutting.
- Never “eyeball” measurements.