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Theoretical stair design (C) Daniel Friedman Ideal Stair Rise & Run Specifications
Stair Building Rules of Thumb & Standard Measurements

  • POST a QUESTION or COMMENT about measuring and calculating to build stairways & low slope or low angle stairways, treads, risers, stairway run, stairway landings & platforms


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.

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.

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

Stair slope rise and run for stairs, ramps, ladders (C) InspectApedia.com adapted from CA Titel 8  Ch 7  §3231. Stairways cited in detail in this articleThese 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: 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

[Click to enlarge any image]

 

Stair Building Rules of Thumb

Our photo below 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.

Undersized stair tread depth (C) Daniel Friedman

Ideal Stair Rule of Thumb

Stair Tread Rules of Thumb

Stair Riser Rules of Thumb

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

Stair Handrails & Guardrails Rules of Thumb

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

 

Articles Detailing Each of these Stair Construction Rules of Thumb

 

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

Theoretical stair design (C) Daniel Friedman

[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

Common Ramp, Stair & Ladder Angle, Slope, Rise / Run Dimensions

Angle in Degrees° Slope %

Example Rise / Run

Ramp Slope  
0 - flat 0 0 / 12
12% 1.44 / 12
18° 32% 3.84 / 12
Stairway Slope
30° 58% 6.4 / 11
32.6° 64% 6.4 / 10 or 7 / 11
37° 75% 6.75 / 9 or 7.5 / 10
45° 100% 7 / 7 or 7.5 / 7.5
50° 102% 7.14 / 7
Fixed Ladder
50° 102%  
75° 373%  
Runged Ladder
75° 373%  
90° N/A  

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 a stair aingle to rise & run using tangent (C) Daniel Friedman

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 = Angle in degrees / 360 x 100

Note: that divisor of 360 is the number of degrees in a full circle.

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


...

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


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

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