Best practices for stair layout & design:

Here we describe the recommended measurements for stair building that give a good starting point from which you can adapt the stairs to your specific need in total stair rise or height and run or length.

We describe how to translate the stair rise and run into a specific number of stair treads and risers that will be uniform and of proper (safe) dimension.

Ideal Stairway Rise, Run, Slope, Riser Height Tread Depth

On this page we include a table giving standard access ramp, ladder, and stair specifications for slope, angle, and rise/run measurements for stair treads for various types of stairs, ramps, and ladders.

We also provide Conversion Formulas for Stair Rise/Run, Percent Slope & Angle Degrees Calculations.

These notes describe an ideal stairway slope or angle and in a table we give the stairway as well as access ramp "steepness" expressed as stair or ramp angle, slope, and as typical step riser height and tread depth dimensions.

By "ideal stairway" we mean a stair that complies with building codes and recommended stair construction standards and that produce a stair that is comfortable to climb or descend.

We also refer readers to a companion article on designing comfortable stairways for people of limited mobility or seniors.

At STAIRWAY SLOPE or ANGLE & STAIR TREAD SLOPE we describe the maximum as well as recommended stairway angles or slopes and we explain how individual step dimensions (step rise and step tread depth or "horizontal run") translate into stairway angle.

Illustration above: adapted from California Title 8, Ch. 7, §3231. Stairways [PDF] Fig. E, Authority cited: Section 142.3, Labor Code. Reference: Section 142.3, Labor Code; and Section 18943(c), Health and Safety Code. Retrieved 2018/07/04, original source: https://www.dir.ca.gov/title8/3231.html

Stair Building Rules of Thumb

Our photo illustrates stair step tread run or depth and stair step rise or riser height; this particular stair is not a good one, sporting uneven riser heights and too-small tread run depth.

Ideal Stair Rule of Thumb

• Perfect stair (for most users): Rise = 7", Run = 11"
  
  The sum of one stair or step tread or "run" and one step height or "riser" should always be about 17" or 18" in total
• As the step rise gets shorter
  
  the step run must get longer

Stair Tread Rules of Thumb - the "rule of 28"

• The sum of two treads plus one riser
  
  should add up to around 28" or 29"
  
  A few readers mis-remembered this as "the rule of 25" but that number is a bit too small. Consider that if we have two 11-inch treads and one 7-inch riser that adds up to 28 inches.
  
• Stair step or tread "depth" or run -
  
  the horizontal walking surface of an individual step. It should be no less than 10". (IRC)
  
  or >= 8 1/4" to 9" in some codes or circumstances.
• Stair tread nosing:
  
  required, 1" to 1 1/2" projection beyond the riser face
  
• Stair tread thickness: 1" or greater;
  
  tread is supported by the riser.

Stair Riser Rules of Thumb

• Maximum stair step riser height -
  
  not more than 7.75" or in some codes <= 7.0" or in Canada <=8.25"
  
• Minimum stair step riser height: -
  
  not less than 4"
  
• Step riser height uniformity -
  
  no more than 3/8" variation between successive step surfaces, or in some codes <= 3/16" / 4.8 mm.

And because the combination of stair riser height and stair tread depth or run determines the overall slope of the stairway, here we include:

• Stairway slope: 7" of rise over 11" of horizontal travel, or a slope of 7/11 (personal preference)
  
  Stairway slope or angle of about 37° which equals approximately a 75% slope
  
  The stairway angle or slope should be between 30° and 50°, ideally around 37°
  
  I prefer a 33° stair that is approximately a 66% slope as is given by a 7/11 step rise/run ratio.
• Step riser slope  out of vertical: <= 30 deg measured from horizontal surface of the tread
  

Stair Handrails & Guardrails Rules of Thumb

• Stair handrail required:
  
  3 risers or more; 36" or more in some jurisdictions.
• Stairway handrailings should be continuous,
  
  graspable, and enclosed at ends
  
• Stair center handrail required:
  
  no more than 36" horizontal distance to a handrail on any stairway
  
• Stair guardrail required:
  
  3 risers or more; 36" or more in some jurisdictions.
  
• Stair guard baluster spacing:
  
  4" for solid balusters. 3 1/4" spacing between horizontal cables used in stair guards (3" in some sources)
  

Stair Landing Platform Rules of Thumb

• Minimum recommended stair landing length:
  
  36" in the direction of travel
• Minimum stair landing width:
  
  of the entry or width sufficiently greater than the swing of the door if a wider or slider door is present
• Door shall not swing out over a stairway;
  
  a platform or landing is required at same level as the adjacent walking surface

Stair lighting

• Lighting is required over stairs
  
  and shall have controls operable from top and bottom of stairway

 

Find the Total Rise, Run, & Slope of an Ideal Stairway

Using the numbers suggested above in the green range of the chart of dimensions for stairs, and looking at the slope or angle of a stairway represented by a single step (rise & run) we have the following:

• Step Rise in inches = 7"
• Step Run in inches = 11"
• 7" / 11" = 0.64 or about a 64% grade or percent slope

Let's convert % grade to angle:

To convert a % grade to slope we convert the percent slope to a decimal by dividing by 100, then find the inverse tangent of that value to convert to degrees. The inverse tangent is also called arctan or Arc Tan.

We had 7" / 11" = 0.64 or about a 64% grade or slope

64% grade / 100 = 0.64

Using any online or textbook trigonometry tables we look up the arctan value of 0.64 (as that's easier than re-learning the trigonometry to calculate it).

Arctan (0.64) = 32.6 deg stair angle, or about 33 degree angle or slope for our ideal stair

Watch out: for seniors or others of limited mobility, other stair dimensions are ideal.

See STAIR DESIGN for SENIORS

Find the rise and run of a 37° sloped stairway or a 37° angled stair

[Click to enlarge any image]

If stairs are built with a 37° stairway slope, what would be the step rise (Rise-X) if we use an 11-inch deep stair tread?

37° slope converts to 75.3 % or in decimal form a slope of 0.7535

Tangent or "Tan" is the reverse of Arctan.

Rise-X / 11 = 0.7535

Using simple algebra we re-arrange the formula above to read

Rise-X = 0.7535 x 11

Rise-X = 8.2" - too big

Watch out: at STAIR RISER SPECIFICATIONS and

at STAIR DIMENSIONS, WIDTH, HEIGHT you'll read that stair risers should be 7 inches (178 mm) maximum and 4 inches (102 mm) minimum.

We would need change the stair tread depth to make a 37° slope stair that has an acceptable 7-inch riser height.

7" Riser Height / Tread-Depth-Y = 0.7535 = 37° slope

Again using Mrs. Revere's elementary school algebra instructions, we can re-write the formula as

7" Riser Height = 0.7535 x Tread-Depth-Y

Tread-Depth-Y = 7" Riser Height / 0.7535

Notes to the table above

OPINION: among common stair dimensions, angles, or slopes, we prefer the 32.6° angle or 64% rise stairway built using stair treads that are 11" deep and stair risers of 7" in height.

Going to a lower rise can also work as you'll see in the table above, but at stair steps with higher rise, to keep the stairway within acceptable overall angle the tread depths become more shallow, making the stairs more-difficult to use.

Conversion Formulas for Stair Rise/Run, Percent Slope & Angle Degrees Calculations

How to Convert Total Stair or Individual Step Rise & Run to Percent Slope

Rise / Run = Decimal slope

Decimal slope x 100 = % Slope.

or

(Rise / Run ) x 100 = % Slope

Eg: 7" rise / 11" run = 0.636 decimal slope

(0.636 x 100) decimal slope = 64% slope

How to Convert Percent of Slope to Angle° or Degrees of Slope

Degrees of Slope = [ArcTan (% Slope / 100)]

Eg: [ArcTan (64% slope / 100)] = [ArcTan .64] = 32.6° slope

How to Convert Degrees of Slope to Percent Slope

Percentage Slope = [ Tan ( Degrees of Slope ) ] x 100

Eg: [Tan 32.6° Slope] x 100 = 63.9 or about 64% slope

Note: a tangent is a ratio of two sides of a triangle - in our case the stair triangle shown above.

Tan (θ) = opposite / adjacent

Percent slope can also be written as

% Slope = Tan (θ) * 100

Where Tan (θ) = rise/run

Example using a tangents table: If we round our slope up to 33° and look in a typical tangents table we'll see that Tan 33° = 0.6494. Multiplying that x 100 to give us slope in pecent we have

100 * 0.6494 = 64.9%

Special thanks to William Bye for pointing out errors previously in this section. 2024/04/18 - DF.

How to Convert Stair Angle to Stair Rise & Run or Step Rise & Tread Depth Dimensions

See BUILD a STAIR to a SPECIFIC ANGLE or SLOPE

and CALCULATE stair tread depth or riser height from stairway slope in degrees

...

Continue reading at STAIR ANGLE & SLOPE or select a topic from the closely-related articles below, or see the complete ARTICLE INDEX.

Or see these

Recommended Articles

• SLIP TRIP & FALL HAZARD LIST, STAIRS, FLOORS, WALKS
• STAIR CONSTRUCTION IDEAL DIMENSIONS - stair building rules of thumb
• STAIR CONSTRUCTION, LOW ANGLE SLOPE
• STAIR CONSTRUCTION, SPECIFIC ANGLE or SLOPE
• STAIR CONSTRUCTION, SPECIFIC TOTAL RISE & RUN
• STAIR DESIGNS for UNEVEN / SLOPED SURFACES
• STAIR RISE & RUN CALCULATIONS
• STAIR DIMENSIONS, WIDTH, HEIGHT
• STAIR ANGLE & SLOPE
• STAIR DESIGN for SENIORS
• STAIR DESIGNS for UNEVEN / SLOPED SURFACES
• STAIR CONSTRUCTION IDEAL DIMENSIONS
• STAIR CONSTRUCTION, LOW ANGLE SLOPE
• STAIR CONSTRUCTION, SPECIFIC ANGLE or SLOPE
• STAIR CONSTRUCTION, SPECIFIC TOTAL RISE & RUN
• STAIR HEADROOM
• STAIR PLATFORMS & LANDINGS
• STAIR RISE & RUN CALCULATIONS
• STAIR RISER SPECIFICATIONS
• STAIR STRINGER SPECIFICATIONS
• STAIR STRINGER DEFECTS
• STAIR TREAD DIMENSIONS
• STAIR TREAD - HALTING WALK STUTTER STEP
• STAIR TREAD NOSE SPECIFICATIONS
• STAIR USER FOOT & HAND PLACEMENT
• TANGENT & SLOPE CALCULATIONS

Suggested citation for this web page

STAIR CONSTRUCTION IDEAL DIMENSIONS at InspectApedia.com - online encyclopedia of building & environmental inspection, testing, diagnosis, repair, & problem prevention advice.

Or see this

INDEX to RELATED ARTICLES: ARTICLE INDEX to STAIRS RAILINGS LANDINGS RAMPS

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