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How to convert a stair aingle to rise & run using tangent (C) Daniel Friedman Stair Angle or Slope Specifications
Stairway slope or angle calculations & designs

  • 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

Stair slope or angle specifications & limits:

What is the permitted angle or percent slope of stairs built indoors or outside? What stair angles are too steep or require special provisions for safety?

The question of stair angle or slope is just one calculation in constructing a stairway that meets safety, accessibility, and code specifications. For other stairway specifications besides angle and slope, see the Recommended Articles list at the end of this article.

This article series includes example stair building calculations, illustrations, and procedures. Page top stair dimension sketch courtesy of Carson Dunlop Associates, a Toronto home inspection, education & report writing tool company [ carsondunlop.com ].

InspectAPedia tolerates no conflicts of interest. We have no relationship with advertisers, products, or services discussed at this website.

Stairway Slope or Angle & Stair Tread Slope Allowed

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 articleRecommended & Code-Specified Stairway Angle or Slope

Stair codes and guidelines prefer an angle of around 37° for normal stairways (the green area in our illustration) and around 7° for ramps (the yellow area in our illustration).

Steeper slopes or angles are permitted for stepladders in certain applications as you can see in the illustration.

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

The sketch shows the recommended and allowable range of slope or "steepness" or angle for access ramps (yellow area), normal stairways (green), stepladders and fixed ladders with treads (beige) and runged or cleated ladders (pink).

Slope for each of these types of stair or ladder is given in degrees.

[Click to enlarge any image]

The maximum stair slope for the overall stairway for stairs used as a public passageway between levels is also implicit in the maximum step riser height - typically 8" or in some codes such as New York, 8.25" maximum riser height along with minimum tread depth (recommended 10").

Stair Tread Slope vs Stairway Slope or Angle

Stair codes talk about slope chiefly when discussing how much out of level a stair tread may be from front to rear or from side to side to avoid a slip and fall hazard.

Stair treads themselves must also be close to level, as you'll see in the following standards:

Question: how can I calculate stair tread rise & depth from stair slope measured in degrees?

How to convert a stair aingle to rise & run using tangent (C) Daniel FriedmanStairway at 38 degrees: what is the rise and foot? - George Tubb

[Click to enlarge any image]

Reply:

George we're back to plane geometry.

[Click to enlarge any image]

You are asking the rise and "run" of the treads. There is no single answer, since we could choose different tread depths or "runs" that would give different tread rises or heights.

E.g. we could make the stairs "one giant step" or "three little steps".

But to stay within reason we chose a stair tread depth (step run length) of 10" in the equation above to obtain an individual step rise of 7.8". That is, on a 38 degree sloped stairway, we will ascend 7.8" in height for every 10 inches of horizontal distance traveled.

Complete details about converting slope or angle to stair rise & run along with other neat framing and building tricks using triangles and geometry are found

at FRAMING TRIANGLES & CALCULATIONS.

And for a special use of right triangles to square up building framing,

also see USE the 6-8-10 RULE detailed explanation and examples for framing squarely and at right angles.

Where to Measure Stair Pitch or Angle

Stair pitch or slope calculation, Northern Ireland Code - at InspectaPedia.com

The proper lines to be used for calculating or measuring the pitch or slope of a stairway or the stair angle illustrated here are excerpted from Northern Ireland's stair, landing, ramp and guardrail code cited just below.

For UK readers we recommend this document as particularly lucid and easy to follow.

Question: what's the maximum-allowed or proper angle, height, and width of a stairway?

2018/07/04 rickburr_ecoquest@hotmail.com said:

My son wants to buy an old house, I don't know what the angle or slope the stairs are.

The stairs are at an angle that they seem to almost be straight up, awfully hard to climb.

What should the stairs angle be set at?

What is the height " and width " of the steps to be and what is the height from floor to ceiling be?

Reply: 37° slope, 36" wide stairway, & minimum headroom of 6'8" over any tread or landing

Rick

Thank you for a great question.

Most of our stair inspection, construction, and repair articles focus on choosing a proper step riser height and stair tread depth since choosing those properly will guarantee a stairway that is also at an acceptable overall angle or slope.

Here I'll translate some of those into degrees:

Stair tread/riser rule of thumb: the dimension in inches of one stair tread and one stair riser should always be about 17 or 18". That assumes a ten-inch tread depth

I prefer an 11-inch tread depth giving a rule of thumb of 18" overall.

Example: using a step rise of 7 inches and a step tread depth of 11 inches gives us a total of 18".

The slope of that step will be 7" of rise over 11" of horizontal travel, or a slope of 7/11.

That's an ideal stairway slope of about 37 degrees - the same as you'll see in our illustration above, adapted from CA code.

See details at STAIR BUILDING RULES of THUMB

Stair overall height Required

Stairway height requirements (C) InspectApedia.com

The second part of your question is described as STAIR HEADROOM REQUIREMENTS - indeed there is a recommended maximum total stair rise height as well as a requirement for landings on long stair runs.

Stair overall width Required

Required stairway width (C) InspectApedia.com

The stair width part of your question is answered in detail at

STAIRWAY WIDTH REQUIREMENTS

...

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

Or see these

Recommended Articles

Suggested citation for this web page

STAIR ANGLE & SLOPE 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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