Stair Calculator: Rise, Run, Riser Height and Stringer Length
Last updated: October 19, 2026
Short Answer
Enter your total floor-to-floor rise and desired maximum riser height. The calculator returns the number of risers, exact riser height, number of treads, total run, step angle, stringer length (two conventions), and a 2R+T comfort value — plus reference IRC residential limit checks. This stair risers calculator also functions as a stair rise and run calculator and stair tread calculator. Local code adoption and amendments are not verified; confirm all values with your building department before cutting lumber.
Stair Calculator
Results
Reference IRC Residential Limit Checks Estimate with limitations JURISDICTION_REQUIRED
These checks use reference IRC 2021 values. Local amendments, adopted edition, and commercial/accessibility rules are NOT verified. NEEDS USER VERIFICATION
| Check | Reference Limit | Your Value | Status |
|---|
Stair Geometry Diagram
This stair calculator with diagram shows a side view of a straight-run stair with all key dimensions labeled.
Side view of a straight-run stair. The stringer runs from bottom left to top right. Each step consists of a vertical riser and horizontal tread. The total rise is the vertical distance from the lower floor to the upper floor. The total run is the horizontal distance from the first riser to the last riser. The step angle is the angle between the stringer and horizontal (arctan of riser height divided by tread depth). Nosing projections extend past each riser face.
Reference Limit Comparison
The table below compares reference IRC 2021 residential limits with common user inputs. These are reference values only — local amendments and adopted edition govern compliance.
| Parameter | Reference IRC 2021 Limit | Your Input | Status |
|---|---|---|---|
| Maximum Riser Height | 7 3/4 in (7.75 in) | — | — |
| Minimum Tread Depth | 10 in | — | — |
| Riser Uniformity Tolerance | 3/8 in (0.375 in) max difference | Calculated equal | ✓ Equal by design |
| Headroom (not calculated) | 6 ft 8 in minimum | — | Not checked |
| Maximum Vertical Rise per Flight (candidate) | 12 ft 7 in (151 in) — | — | Rule not verified |
Stringer Length Convention Comparison
Two conventions exist for measuring stringer length. The calculator shows both; the primary result uses Convention 1. For a 108 in total rise with 13 treads at 10 in depth (130 in total run):
✓ Convention 1: Total Hypotenuse (Primary)
- Formula: √(total rise² + total run²)
- Example: √(108² + 130²) = √(11,664 + 16,900) = √28,564 = 169.01 in
- Measures straight line from bottom of first riser to top of last riser
- Used for: overall stringer stock length estimation
✗ Convention 2: Along Nosing Line
- Formula: treads × √(riser² + tread²)
- Example: 13 × √(7.714² + 10²) = 13 × 12.630 = 164.19 in
- Follows the stair nosing line (sum of each step's hypotenuse)
- Difference: ~4.8 in shorter for this example
- Used for: layout along the stringer edge
How to Use This Calculator
- Enter Total Rise: Measure the vertical distance from the finished lower floor to the finished upper floor. Enter as decimal inches (e.g., 108), feet and inches (e.g., 9 ft 0 in), or centimeters (e.g., 274.32).
- Enter Maximum Riser Height: Input the maximum riser height you want. The reference IRC residential limit is 7 3/4 in (7.75 in). You can enter fractions like 7 3/4, decimals like 7.75, or centimeters.
- Enter Tread Depth: Input your desired tread depth. The reference IRC residential minimum is 10 in.
- Optional — Nosing: Enter nosing projection if desired (typical 3/4 in to 1-1/4 in). This does not affect stringer length calculations.
- Optional — Stair Width: Enter for reference only; does not affect calculations.
- Choose Stringer Convention: Select Convention 1 (total hypotenuse) or Convention 2 (nosing line). Convention 1 is the primary result.
- Click Calculate: Results appear instantly with code-limit checks.
Tip: The calculator uses the ceiling of (total rise ÷ maximum riser) to determine the number of risers. This ensures no riser exceeds your maximum. Treads always equal risers minus one because the upper floor acts as the final tread.
Calculation Method and Formula Logic
Core Formulas
- Riser Count (n)
n = ceiling(total_rise / max_riser)— Round up to the next whole number. Never round before the ceiling.- Riser Height
riser = total_rise / n— Exact division; displayed to 3 decimals (inches) and nearest 1/16 in.- Tread Count
treads = n - 1— The upper floor is the last tread.- Total Run
run = treads × tread_depth- Step Angle
angle = atan(riser / tread_depth)— Degrees, rounded to 1 decimal (half up).- Stringer Length (Convention 1)
stringer₁ = √(total_rise² + total_run²)- Stringer Length (Convention 2)
stringer₂ = treads × √(riser² + tread_depth²)- Comfort Check (2R + T)
comfort = 2 × riser + tread_depth— Guideline: 24–25 in is comfortable.
Rounding Rules
- Riser height: 3 decimal places in inches; fractional display to nearest 1/16 in.
- Run and lengths: 2 decimal places.
- Angle: 1 decimal place (half up).
- Never round before the ceiling operation.
Code Reference Values (Candidate — NOT VERIFIED)
- Maximum riser: 7 3/4 in (7.75 in) — IRC R311.7.5
- Minimum tread: 10 in — IRC R311.7.5
- Uniformity tolerance: 3/8 in (0.375 in) max difference between any two risers or treads — IRC R311.7.5
- Maximum vertical rise per flight: 12 ft 7 in (151 in) —
- Minimum riser: Conflicting sources —
All code values are reference IRC 2021 only. Local amendments, adopted edition, commercial rules (IBC), and accessibility rules are OUTSIDE SCOPE and NOT VERIFIED. JURISDICTION_REQUIRED NEEDS USER VERIFICATION
Worked Examples
These fixtures were computed with exact decimal arithmetic (60 digits) using the candidate IRC residential values. They test arithmetic, not law.
| Output | Value |
|---|---|
| Risers | 14 |
| Riser Height | 7.714286 in (7 11/16 in) |
| Treads | 13 |
| Total Run | 130.00 in (10.83 ft) |
| Step Angle | 37.6° |
| Stringer (Conv. 1) | 169.01 in |
| Stringer (Conv. 2) | 164.19 in |
| 2R + T Comfort | 25.43 in |
| Output | Value |
|---|---|
| Risers | 13 |
| Riser Height | 7.692308 in (7 11/16 in) |
| Treads | 12 |
| Total Run | 120.00 in (10.00 ft) |
| Step Angle | 37.5° |
| Stringer (Conv. 1) | 156.20 in |
| Stringer (Conv. 2) | 151.84 in |
| 2R + T Comfort | 25.38 in |
| Total Rise | Risers | Riser Height |
|---|---|---|
| 93.00 in | 12 | 7.750000 in (equal to max, allowed) |
| 93.01 in | 13 | 7.154615 in |
Common Mistakes and Key Conditions
✗ Counting Treads = Risers
- Wrong: 14 risers → 14 treads → 140 in run
- Right: 14 risers → 13 treads → 130 in run (upper floor is the last tread)
- Some secondary guides incorrectly count treads equal to risers
✗ Rounding Before Ceiling
- Wrong: Round total_rise / max_riser first, then ceiling
- Right: Apply ceiling to the exact quotient
- Example: 93.01 / 7.75 = 12.00129 → ceiling = 13, not 12
✗ Mixing Units
- Enter all values in the same unit system or use the unit selectors
- 9 ft 0 in = 108 in = 274.32 cm exactly
- 7 3/4 in = 7.75 in = 19.685 cm exactly
✗ Assuming Reference IRC = Local Code
- IRC is a model code; each jurisdiction adopts a specific edition with amendments
- Some states use older editions; some have stricter limits
- Commercial (IBC) and accessibility rules differ entirely
Frequently Asked Questions
- How many risers and treads will my stair have?
- Enter your total rise (floor-to-floor height) and the maximum riser height you want. The calculator divides total rise by the maximum riser and rounds up to the next whole number for the riser count. Treads equal risers minus one because the upper floor acts as the final tread.
- What are the reference IRC residential limits for riser height and tread depth?
- The 2021 International Residential Code (IRC) Section R311.7.5 sets a maximum riser height of 7-3/4 inches and a minimum tread depth of 10 inches for residential stairs. These are reference values only — your local building department adopts a specific IRC edition with amendments. Always verify with your local authority before building.
- Why does the calculator show two different stringer length values?
- Stringer length can be measured in two ways: (1) the straight-line hypotenuse from the bottom of the first riser to the top of the last riser (sqrt(rise² + run²)), or (2) the sum of each step's hypotenuse along the nosing line. The difference can be several inches. The calculator shows both and states which convention is used for the primary result.
- Can I use this calculator for deck stairs?
- Yes, the arithmetic works for any straight-run stair including deck stairs. However, deck stairs may have additional local requirements for landings, guardrails, and footing depth that are outside this calculator's scope. Check with your local building department.
- What is the 2R + T comfort check?
- The 2R + T formula (two times riser height plus tread depth) is a traditional comfort guideline. Values between 24 and 25 inches are generally considered comfortable. This is a guideline, not a code requirement.
- Does this calculator handle landings or winders?
- No. This calculator is for straight-run stairs only. Landings, winders, spiral stairs, and curved stairs are outside the scope.
- What IRC edition does this calculator reference?
- The reference values shown are from the 2021 IRC Section R311.7.5. Your local jurisdiction may have adopted a different edition (2018, 2015, 2012, etc.) with amendments. The adopted edition and its effective date must be verified locally.
- How do I enter fractions like 7 3/4?
- Type 7 3/4 (with a space between the whole number and fraction) in the Maximum Riser field. The calculator parses fractions automatically. You can also enter decimals like 7.75.
Glossary
- Total Rise
- The vertical distance from the finished lower floor to the finished upper floor.
- Riser
- The vertical board between two treads; also the height of that board.
- Tread
- The horizontal board you step on; also the depth of that board (nosing to nosing or nosing to riser).
- Nosing
- The projection of the tread beyond the riser face below.
- Total Run
- The horizontal distance from the face of the first riser to the face of the last riser.
- Stringer
- The angled structural member that supports the treads and risers.
- Step Angle
- The angle between the stringer and horizontal (arctan of riser ÷ tread).
- 2R + T
- A comfort guideline: two times riser height plus tread depth.
- IRC
- International Residential Code, a model building code.
- Ceiling Function
- Rounds a number up to the next whole number (e.g., ceiling(12.001) = 13).
Related Calculators
Official References and Last Checked
- International Residential Code Section R311.7 Stairways — Candidate source: https://codes.iccsafe.org/ (verify edition and free-access terms).
- Local Building Department — Find your city/county building department page stating its adopted IRC edition. Record the exact URL. NEEDS USER VERIFICATION
Limitations, Exclusions, and Assumptions
- Straight-run stairs only. No landings, winders, spiral, or curved stairs.
- Reference IRC residential limits only. Commercial (IBC), accessibility (ADA), and local amendments are not applied.
- No structural sizing. Stringer material, dimensions, and connection design are outside scope.
- No handrail/guard design. Separate code requirements apply.
- No permit advice. Confirm all requirements with your local building department.
- Maximum vertical rise per flight (12 ft 7 in) is NOT VERIFIED and not enforced.
- Minimum riser height has conflicting sources and is not enforced.
- Uniformity tolerance (3/8 in) is reported but the calculator produces equal risers by design.
- Arithmetic uses exact decimal (60 digits) with display rounding per the rules above.
Summary and Next Steps
This calculator gives you a buildable straight-stair layout with exact arithmetic and reference IRC limit checks. Before cutting any lumber, verify every value with your local building department. The reference IRC 2021 values shown (max riser 7-3/4 in, min tread 10 in, uniformity 3/8 in) are candidates — your jurisdiction's adopted edition and amendments control.
