Stair Calculator: Calculate Rise, Run & Stringer Dimensions
A stair calculator is an essential construction and carpentry tool that accurately computes stair dimensions including individual riser height, tread depth, total run, stringer length, and number of steps required for safe, code-compliant stairways. By inputting total rise (floor-to-floor height) and desired step configuration, this calculator determines optimal measurements that meet building codes, ensure comfortable climbing ratios, and provide precise cutting dimensions—helping homeowners, builders, carpenters, and DIY enthusiasts design and construct interior and exterior stairs, decks, porches, and multi-level structures with proper proportions and safety.
📐 Interactive Stair Calculator
Calculate stair dimensions, rise, run, and stringer length
Step 1: Enter Total Rise (Height)
💡 Measure vertical distance from finished floor to finished floor above
Step 2: Stair Configuration
Leave risers blank for automatic calculation based on codes (7-7.75" per riser)
Step 3: Stringer Specifications
Understanding Stair Terminology
Stair construction uses specific terminology that must be understood for accurate calculations and safe building.
Key Stair Components
- Total Rise: Vertical height from finished floor to finished floor above
- Riser: Vertical height of each individual step
- Tread (Going): Horizontal depth of each step where foot rests
- Total Run: Total horizontal distance stairs occupy
- Stringer: Diagonal support beam that treads and risers attach to
- Nosing: Tread overhang beyond riser (typically 1-1.25 inches)
- Headroom: Vertical clearance above stairs (minimum 6'8")
Essential Stair Formulas
Individual Riser Height
Riser Height Formula:
\[ R = \frac{H}{N} \]
Where:
\[ R = \text{Individual riser height (inches)} \]
\[ H = \text{Total rise (total height)} \]
\[ N = \text{Number of risers} \]
Number of Treads
Tread Count:
\[ T = N - 1 \]
Number of treads is always one less than number of risers
Example: 14 risers = 13 treads
Total Run Calculation
Total Run Formula:
\[ \text{Total Run} = (N - 1) \times G \]
Where:
\[ G = \text{Tread depth (going)} \]
\[ N = \text{Number of risers} \]
Stringer Length (Hypotenuse)
Stringer Length Formula (Pythagorean Theorem):
\[ L = \sqrt{H^2 + R_{\text{total}}^2} \]
Where:
\[ L = \text{Stringer length} \]
\[ H = \text{Total rise (height)} \]
\[ R_{\text{total}} = \text{Total run} \]
The 2R + G Rule
The most important formula for comfortable, safe stairs is the rise/run relationship.
Comfortable Stair Formula:
\[ 2R + G = 24 \text{ to } 25 \text{ inches} \]
Where:
\[ R = \text{Individual riser height} \]
\[ G = \text{Tread depth (going)} \]
Ideal: \( 2R + G = 25 \) inches
This formula represents natural human stride length
2R + G Examples:
Example 1: 7" rise, 11" tread
\[ 2(7) + 11 = 14 + 11 = 25 \text{ inches} \] ✅ Perfect
Example 2: 7.5" rise, 10" tread
\[ 2(7.5) + 10 = 15 + 10 = 25 \text{ inches} \] ✅ Perfect
Example 3: 8" rise, 9" tread
\[ 2(8) + 9 = 16 + 9 = 25 \text{ inches} \] ✅ Perfect
Complete Calculation Example
Detailed Example: Interior Staircase
Given Information:
- Total rise (floor to floor): 108 inches (9 feet)
- Desired tread depth: 10 inches
- Stringer width: 2×12 lumber (11.25" actual width)
- Stair width: 36 inches
Step 1 - Determine Number of Risers:
Target riser height: 7-7.75 inches per code
\[ N = \frac{108}{7.5} = 14.4 \rightarrow \text{Try 14 risers} \]
Step 2 - Calculate Actual Riser Height:
\[ R = \frac{108}{14} = 7.714 \text{ inches} \]
Rounds to 7.71" or 7-11/16" ✅ Within code
Step 3 - Verify with 2R + G Rule:
\[ 2(7.714) + 10 = 15.428 + 10 = 25.428 \text{ inches} \] ✅ Acceptable
Step 4 - Calculate Number of Treads:
\[ T = 14 - 1 = 13 \text{ treads} \]
Step 5 - Calculate Total Run:
\[ \text{Total Run} = 13 \times 10 = 130 \text{ inches} = 10' 10" \]
Step 6 - Calculate Stringer Length:
\[ L = \sqrt{108^2 + 130^2} = \sqrt{11664 + 16900} \]
\[ L = \sqrt{28564} = 169.01 \text{ inches} = 14' 1" \]
Step 7 - Check Stringer Depth:
Effective depth after cuts: 11.25" - 7.71" = 3.54" ✅ Adequate (minimum 3.5")
Building Code Requirements
🏛️ International Residential Code (IRC) Standards
| Requirement | IRC Minimum/Maximum | Notes |
|---|---|---|
| Maximum Riser Height | 7.75 inches (7-3/4") | Residential stairs |
| Minimum Tread Depth | 10 inches | Measured horizontally |
| Minimum Stair Width | 36 inches | Clear width between handrails |
| Maximum Riser Variation | 3/8 inch (0.375") | Between any two risers |
| Minimum Headroom | 80 inches (6'8") | Measured vertically |
| Nosing Projection | 0.75" to 1.25" | Tread overhang |
| Landing Depth | 36 inches minimum | At least stair width |
⚠️ Always check local building codes—requirements may be more restrictive
Optimal Stair Dimensions
Comfortable Residential Stairs
| Riser Height | Tread Depth | 2R + G Total | Use Case |
|---|---|---|---|
| 7" | 11" | 25" | Standard residential (ideal) |
| 7.5" | 10" | 25" | Standard residential (code minimum tread) |
| 7.75" | 10" | 25.5" | Maximum code-compliant riser |
| 6.5" | 12" | 25" | Comfortable, gradual stairs |
| 8" | 9" | 25" | Steep (allowed for certain applications) |
Stringer Layout and Cutting
Calculating Stringer Minimum Width
Required Stringer Width:
\[ W_{\text{min}} = R + 3.5 \text{ inches} \]
Where:
\[ R = \text{Riser height} \]
3.5" = Minimum effective depth after stair cuts
For 7.5" risers: 7.5 + 3.5 = 11" minimum (use 2×12)
Number of Stringers Required
- 36" stair width or less: 3 stringers minimum (2 outer, 1 center)
- 36-48" width: 3 stringers recommended
- 48-72" width: 4 stringers (spaced 16-18" apart)
- 72" and wider: 5+ stringers (maximum 16" spacing)
Material Calculations
Stringer Material
Stringer Lumber Needed:
Example: 14-riser staircase, 36" wide
- Stringer length: 169" (14' 1")
- Number of stringers: 3 (standard)
- Lumber needed: 3 pieces of 2×12 × 16'
Alternative for narrow stairs (30"): 2×12 × 14' (if available)
Tread Material
Tread Board Feet:
For each tread:
\[ \text{Board Feet} = \frac{T \times W \times t}{12} \]
Where:
\[ T = \text{Tread depth + nosing (11-12")} \]
\[ W = \text{Stair width (36")} \]
\[ t = \text{Thickness (typically 1" or 1.5")} \]
Safety Considerations
⚠️ Critical Safety Requirements
- Consistent dimensions: All risers within 3/8" of each other (code requirement)
- Handrails required: Stairs with 4 or more risers must have handrails
- Handrail height: 34-38 inches above nosing
- Graspable handrail: 1.25" to 2" diameter for proper grip
- Landing requirements: Top and bottom landings at least 36" deep
- Lighting: Adequate illumination at all stairs
- Slip resistance: Treads should not be slippery when wet
- Load capacity: Stairs must support 300 lbs concentrated load
Common Stair Types
Straight Run Stairs
- Description: Single straight flight from bottom to top
- Advantages: Simplest to build, easiest calculations, most economical
- Disadvantages: Requires long horizontal space
- Best for: Basement stairs, outdoor deck stairs
L-Shaped (Quarter Turn) Stairs
- Description: 90-degree turn with landing
- Advantages: Saves space, landing provides rest point
- Disadvantages: More complex construction
- Best for: Interior home stairs, split-level entries
U-Shaped (Half Turn) Stairs
- Description: 180-degree turn with landing
- Advantages: Compact footprint, landing provides rest
- Disadvantages: Most complex, requires precise calculation
- Best for: Multi-story buildings, tight spaces
Winder Stairs
- Description: Pie-shaped treads at turns instead of landing
- Advantages: Saves space compared to landing
- Disadvantages: Less safe, harder to navigate, complex cutting
- Best for: Tight spaces where landing won't fit
Installation Tips
Professional Stair Construction Guidelines:
- Double-check total rise: Measure from finished floor to finished floor (not subfloor)
- Use framing square: Layout stringers with stair gauges for accuracy
- Mark first riser correctly: Deduct one tread thickness from bottom riser
- Cut stringers identically: Use first as template for others
- Secure stringers properly: Use joist hangers or blocking at top, solid footing at bottom
- Install treads front to back: Start from bottom, work up
- Use construction adhesive: Plus screws for squeak-free stairs
- Check level and plumb: Each step during installation
- Install handrails securely: Must support 200 lbs force
- Final inspection: Walk stairs, check for squeaks or movement
Common Mistakes to Avoid
❌ Stair Construction Errors
- Measuring to subfloor: Always measure to finished floor height
- Inconsistent riser heights: Causes tripping hazard, fails inspection
- Forgetting nosing: Treads need 1-1.25" overhang for safety
- Wrong number of treads: Always one less tread than risers
- Inadequate stringer depth: Minimum 3.5" after cuts for structural integrity
- Improper stringer attachment: Must be securely fastened top and bottom
- Skipping the 2R + G check: Results in uncomfortable, unsafe stairs
- Not accounting for landing: Top landing must be at least 36" deep
Outdoor vs. Indoor Stairs
Key Differences
| Feature | Indoor Stairs | Outdoor Stairs |
|---|---|---|
| Maximum Riser | 7.75 inches | 8 inches (some codes) |
| Minimum Tread | 10 inches | 11 inches (deeper recommended) |
| Material | Any suitable lumber | Pressure-treated or composite |
| Drainage | Not required | Essential (1/4" per foot slope) |
| Footing | Floor attachment | Concrete footings below frost line |
Frequently Asked Questions
How do I calculate the number of steps I need?
Divide total rise by desired riser height (7-7.75 inches). Example: 108-inch total rise ÷ 7.5 inches = 14.4, round to 14 risers. Then calculate actual riser: 108 ÷ 14 = 7.714 inches per riser. Number of treads = risers - 1 = 13 treads. Always verify with 2R + G = 24-25 inches for comfortable stairs.
What is the 2R + G rule for stairs?
The 2R + G rule states that twice the riser height plus the tread depth (going) should equal 24-25 inches, ideally 25 inches. This represents natural human stride length. Example: 7-inch riser, 11-inch tread: 2(7) + 11 = 25 inches. This formula ensures comfortable, safe stairs that feel natural to climb.
How do I calculate stringer length?
Use Pythagorean theorem: Stringer length = √(total rise² + total run²). Example: 108-inch rise, 130-inch run: √(108² + 130²) = √(11,664 + 16,900) = √28,564 = 169 inches or 14 feet 1 inch. Add extra length for top and bottom attachment points when ordering lumber.
What size lumber do I need for stair stringers?
Minimum 2×12 (actual 11.25" width) for most residential stairs with risers up to 7.75 inches. Effective depth after cuts must be at least 3.5 inches. For higher risers or stronger construction, use 2×14 if available. Never use less than 2×10 for stair stringers as it leaves inadequate depth after notching.
How many stringers do I need for my staircase?
Minimum 3 stringers for stairs up to 36 inches wide (2 outer, 1 center). Add 1 stringer for every additional 16-18 inches of width. 48-inch stairs need 4 stringers, 60-inch stairs need 5, etc. Closer spacing (12-16 inches) provides stronger, quieter stairs and prevents tread bounce.
Can I build stairs steeper than code allows?
For residential occupancy, maximum riser is 7.75 inches per IRC. Steeper stairs (like ship ladders or alternating tread stairs) allowed only for limited applications like attic access or lofts with special approval. Steeper stairs significantly increase fall risk and fail inspections. Always follow local building codes for safety and resale value.
Key Takeaways
Calculating stair dimensions requires understanding rise/run relationships, building codes, and the critical 2R + G formula. Accurate calculations ensure safe, comfortable, code-compliant stairs that pass inspections and provide years of reliable service.
Essential principles to remember:
- Individual riser height = Total rise ÷ Number of risers
- Number of treads = Number of risers - 1 (always one less)
- 2R + G should equal 24-25 inches for comfortable stairs
- Maximum riser height: 7.75 inches (residential IRC code)
- Minimum tread depth: 10 inches (code requirement)
- Total run = (Number of risers - 1) × Tread depth
- Stringer length = √(Total rise² + Total run²)
- All risers must be within 3/8 inch of each other
- Minimum 3 stringers for stairs up to 36 inches wide
- Measure total rise from finished floor to finished floor
Getting Started: Use the interactive stair calculator at the top of this page to determine exact dimensions for your staircase project. Enter total rise (floor-to-floor height), configure number of risers and tread depth, and receive instant calculations for individual riser height, total run, stringer length, and verification that your design meets building codes and the 2R + G comfort formula.