Stair geometry calculations: BCIN Calculation Lab

Last updated October 22, 2026

When this shows up on the exam

Stair geometry is a favourite on the House exam and on the Small Buildings exam. A typical question gives a floor-to-floor height and a stair type, then asks for the minimum number of risers, the rise, the total run, or whether a landing is needed. Others give measured risers or treads and ask if the flight meets the tolerances, or give a beam height and ask if the headroom works.

Two traps cause most wrong answers. First, the 2024 code uses a minimum run of 255 mm for private stairs; do not trust run values from older editions or other sources. Second, Part 9 does not use a combined rise plus run formula. You check rise and run separately against the limits in OBC Div. B Table 9.8.4.1. and nothing else.

The method

Classify the stair. Read the notes under Table 9.8.4.1.. Stairs inside a house or a single dwelling unit, and exterior stairs serving it, are private stairs. Everything that is not private or service is a public stair.
Find the maximum rise in the table row for that stair type (column "Max. Rise, mm, for All Steps"). Rise is measured nosing to nosing (9.8.4.1.).
Minimum number of risers = total rise divided by the maximum rise, always rounded UP. If the division is exact, do not add one.
Actual rise = total rise divided by the number of risers. Check it is not below the 125 mm minimum.
Treads in a flight = risers in that flight minus 1, because the floor or landing at the top is not a tread.
Minimum total run = number of treads times the minimum run from the table ("Min. Run" column). Tread depth may be from the run up to the run plus 25 mm (9.8.4.2.).
Landing check. No flight may rise more than 3.7 m (9.8.3.3.). If the total rise is higher, split the stair with a landing (9.8.6.2.). A straight landing need not be longer than the lesser of the required stair width and 1,100 mm; a landing that turns 90° or more must be at least as long and wide as the stair (9.8.6.3.).
Width and headroom. Width comes from 9.8.2.1.: 860 mm for exit stairs serving a single dwelling unit and for at least one stair between each floor level within a dwelling unit, 900 mm for residential public and exit stairs, and for other occupancies the greater of 900 mm or 8 mm per person. Headroom comes from 9.8.2.2.: 1,950 mm for stairs serving a single dwelling unit, 2,050 mm otherwise, measured vertically from a line through the nosings.
Tolerances. Risers and rectangular treads may differ by at most 5 mm between neighbours and 10 mm between the largest and smallest in the flight (9.8.4.4.).

Worked example 1: house stair, 2,790 mm floor to floor

A straight interior stair in a detached house rises 2,790 mm. Find the minimum risers, the rise and the minimum total run.

Step	Working	Result
Stair type	Interior stair in a single dwelling unit	Private
Max. rise	Table 9.8.4.1., "Private stairs" row, Max. Rise column	200 mm
Risers	2,790 / 200 = 13.95, round up	14
Rise	2,790 / 14	199.3 mm
Min. rise check	199.3 is not less than 125	OK
Treads	14 - 1	13
Min. run	Same row, Min. Run column	255 mm
Total run	13 x 255	3,315 mm
Landing?	2,790 mm is not more than 3,700 mm	Not needed

Answer: 14 risers of about 199.3 mm and a minimum total run of 3,315 mm (OBC Div. B 9.8.4.1., 9.8.4.2., 9.8.3.3.). If the stairwell opening is shorter than about 3.3 m plus room at the top, the stair needs a turn or winders.

Worked example 2: office stair, 4,200 mm floor to floor

A Part 9 office building has a straight interior stair, 1,100 mm wide, serving 100 persons. Floor to floor is 4,200 mm.

Step	Working	Result
Stair type	Office stair, not private or service	Public
Max. rise	Table 9.8.4.1., "Public stairs" row	180 mm
Risers	4,200 / 180 = 23.33, round up	24
Rise	4,200 / 24	175 mm
Landing?	4,200 mm is more than 3,700 mm	Required
Flights	Two flights of 12 risers, 12 x 175 = 2,100 mm each	OK
Treads	(12 - 1) + (12 - 1)	22
Total tread run	22 x 280 (public Min. Run)	6,160 mm
Required width	Greater of 900 mm and 100 x 8 = 800 mm	900 mm
Landing length	Lesser of 900 mm and 1,100 mm (straight landing)	900 mm
Overall	6,160 + 900	7,060 mm

Answer: 24 risers of 175 mm in two flights, with a straight landing at least 900 mm long (9.8.3.3., 9.8.2.1., 9.8.6.3.). Note the landing length uses the required width, not the 1,100 mm actual width.

Worked example 3: headroom under a bulkhead

A house stair has 195 mm risers. A duct bulkhead crosses the stair. Its lowest point (the bottom corner on its uphill side) is 2,900 mm above the lower floor and sits directly over the nosing at the top of the 5th riser.

Step	Working	Result
Nosing height	5 x 195	975 mm
Clear height	2,900 - 975	1,925 mm
Required	Stair serving a single dwelling unit	1,950 mm
Shortfall	1,950 - 1,925	25 mm

Answer: the bulkhead fails by 25 mm (OBC Div. B 9.8.2.2.(3)). The reduced 1,850 mm value in Sentence (4) applies only to stairs under beams and ducting in secondary suites.

Worked example 4: winders in a house

A house stair turns 90° with winders. Each winder tread must turn between 30° and 45°, all winders in the set turn the same angle, and the set turns no more than 90° (9.8.4.6.). So 90° can be 2 treads of 45° or 3 treads of 30°. A 180° turn needs two sets (at least 4 winders), and the sets must be at least 1,200 mm apart in plan.

Common mistakes

Rounding the riser count down, or adding an extra riser when the division is exact.
Counting treads equal to risers instead of risers minus 1.
Using a minimum run from an older edition or another source instead of the 255 mm private stair value.
Using the public row (180 mm rise, 280 mm run) for a house stair, or the private row for an office stair.
Forgetting the 3.7 m flight limit, so no landing is shown.
Using the actual stair width, instead of the required width capped at 1,100 mm, for a straight landing.
Applying 8 mm per person to a residential stair; residential stairs use a flat 900 mm.
Taking 1,850 mm headroom for a normal house stair, or measuring headroom from the wrong nosing.
Checking only the 10 mm overall riser or tread spread and missing the 5 mm limit between neighbours.
Forgetting that interior flights outside a dwelling unit need at least three risers (9.8.3.2.), which together with the 125 mm minimum rise rules out very small level changes.

Find it fast in the code PDF

Bookmark path: Division B > Part 9 > Section 9.8 Stairs, Ramps, Handrails and Guards. Useful Ctrl+F terms:

"nosing-to-nosing" for the rise rule and Table 9.8.4.1.
"Private stairs" for the table notes that classify the stair.
"not more than its run plus 25 mm" for tread depth.
"vertical height of any flight" for the 3.7 m limit.
"length of the landing need not be more than" for straight landings.
"clear height over stairs" for headroom.
"deepest and shallowest treads" for tolerances.
"converge to a centre point" for winders.

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Code cited in this method

Based on the official 2024 Building Code Compendium on ontario.ca.

OBC Div. B Table 9.8.4.1. Rise for Rectangular Treads, Tapered Treads and Winders and Run for Rectangular Treads — Forming Part of Sentences 9.8.4.1.(1) and 9.8.4.2.(1)
Table 9.8.4.1 — Rise for Rectangular Treads, Tapered Treads and Winders and Run for Rectangular Treads — Forming Part of Sentences 9.8.4.1.(1) and 9.8.4.2.(1) Stair Type | Max. Rise, mm, for All Steps | Min. Rise, mm, for All Steps | Max. Run, mm, for Rectangular Treads | Min. Run, mm, for Rectangular Treads Private stairs[1] | 200 | 125 | 355 | 255 Public stairs[2] | 180 | 125 | no limit | 280 Service stairs[3] | no limit | 125 | 355 | no limit Stairs to unoccupied attic space[4] | no limit | 125 | 355 | no limit Stairs to crawl spaces | no limit | 125 | 355 | no limit Stairs that serve mezzanines not exceeding 20 m² within live/work units | no limit | 125 | 355 | no limit Notes to Table 9.8.4.1.: (1) Private stairs are: (a) interior stairs within a house with a secondary suite or an individual dwelling unit, (b) exterior stairs serving a house with a secondary suite or an individual dwelling unit, and (c) exterior stairs serving a garage that serves a house with a secondary suite or an individual dwelling unit. (2) Public stairs are all stairs not described as service stairs or private stairs. (3) Service stairs are stairs that serve areas used only as service rooms or service spaces. (4) Stairs to unoccupied attic space are stairs that serve attics containing no storage or living space.
Open OBC Div. B Table 9.8.4.1. in the code viewer
OBC Div. B 9.8.4.1. Dimensions for Risers
(1)Except as provided in Article 9.8.4.7., the rise, which is measured as the vertical nosing-to-nosing distance, shall conform to Table 9.8.4.1.
Open OBC Div. B 9.8.4.1. in the code viewer
OBC Div. B 9.8.4.2. Dimensions for Rectangular Treads
(1)The run for rectangular treads shall conform with Table 9.8.4.1.
(2)The depth of a rectangular tread shall be not less than its run and not more than its run plus 25 mm.
Open OBC Div. B 9.8.4.2. in the code viewer
OBC Div. B 9.8.3.3. Maximum Height of Stairs
(1)The vertical height of any flight of stairs shall not exceed 3.7 m.
Open OBC Div. B 9.8.3.3. in the code viewer
OBC Div. B 9.8.6.2. Required Landings
(1)Except as provided in Sentences (2) to (4) and Sentence 9.9.6.6.(2), a landing shall be provided
(a)at the top and bottom of each flight of interior and exterior stairs, including stairs in garages,
(b)at the top and bottom of every ramp with a slope greater than 1 in 50, and
(c)where a doorway opens onto a stair or ramp.
(2)Where a door at the top of a stair within a dwelling unit swings away from the stair, no landing is required between the doorway and the stair. (See Note A-9.8.6.2.(2))
(3)A landing may be omitted at the top of an exterior flight serving a secondary entrance to a single dwelling unit or a house with a secondary suite, provided
(a)the stair does not contain more than three risers,
(b)the principal door is a sliding door or swings away from the stair, and
(c)only a storm or screen door, if any, swings over the stair and is equipped with hardware to hold it open.
(3.1)Sentence (3) does not apply to an exterior stair serving a secondary entrance to a house with a secondary suite that is also a main entrance to a dwelling unit in the house.
(4)A landing may be omitted at the bottom of an exterior stair or ramp provided there is no obstruction, such as a gate or door, within the lesser of the width of the stair or ramp or
(a)900 mm for stairs or ramps serving a single dwelling unit, and
(b)1,100 mm for stairs or ramps not serving a single dwelling unit.
Open OBC Div. B 9.8.6.2. in the code viewer
OBC Div. B 9.8.6.3. Dimensions of Landings (See also Articles 9.9.6.1. and 9.9.6.6. regarding landings in exits)
(1)Except as provided in Sentences (2) to (7), landings shall be at least as wide and as long as the width of the stair or ramp in which they occur.
(2)Where the landing in a stairway or ramp does not turn or turns less than 90° , the length of the landing need not be more than the lesser of
(a)the required width of the stair or ramp, or
(b)1,100 mm.
(3)The length of a landing shall be measured perpendicular to the nosings of adjacent steps or to the end of the ramp, at a distance equal to half the length required in Sentence (2) from the narrow edge of the landing.
(4)Where stair flights or ramps of different widths adjoin a single landing, the minimum width of the landing shall be
(a)where one or more of the stair or ramp widths do not exceed their respective required widths, not less than the greater required stair or ramp width, or
(b)where all of the widths of the stairs or ramps exceed their respective required widths, not less than the lesser actual stair or ramp width.
(5)Where a door swings toward a stair, the full arc of the swing shall be over the landing.
(6)The slope of landings shall not exceed 1 in 50.
(7)Where a doorway or stairway opens onto the side of a ramp, the landing shall extend for a distance of not less than 300 mm on either side of the doorway or stairway, except on a side abutting an end wall.
Open OBC Div. B 9.8.6.3. in the code viewer
OBC Div. B 9.8.2.1. Stair Width
(1)Except as provided in Sentence (2) and Article 9.8.4.7., required exit stairs and public stairs serving buildings of residential occupancy shall have a width of not less than 900 mm.
(2)Exit stairs serving a single dwelling unit or a house with a secondary suite including their common spaces shall have a width of not less than 860 mm.
(3)Except as provided in Article 9.8.4.7., required exit stairs and public stairs serving buildings of other than residential occupancy shall have a width of not less than the greater of
(a)900 mm, or
(b)8 mm per person based on the occupant load limits specified in Table 3.1.17.1.
(4)Except as provided in Article 9.8.4.7., at least one stair between each floor level within a dwelling unit, and exterior stairs serving a single dwelling unit except required exit stairs, shall have a width of not less than 860 mm.
Open OBC Div. B 9.8.2.1. in the code viewer
OBC Div. B 9.8.2.2. Height Over Stairs
(1)The clear height over stairs shall be measured vertically, over the clear width of the stair, from a straight line tangent to the tread and landing nosings to the lowest point above. (See Note A-3.4.3.4.)
(2)Except as provided in Sentences (3) and (4) and Article 9.8.4.7., the clear height over stairs shall not be less than 2,050 mm.
(3)Except as provided in Article 9.8.4.7., the clear height over stairs serving a single dwelling unit or a house with a secondary suite including their common spaces shall not be less than 1,950 mm.
(4)The clear height over stairs that are located under beams and ducting in secondary suites shall not be less than 1,850 mm.
Open OBC Div. B 9.8.2.2. in the code viewer

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OBC Div. B 9.8.4.4. Uniformity and Tolerances for Risers, Runs and Treads
(1)Except as provided in Sentence (2), risers shall be of uniform height in any one flight with a maximum tolerance of
(a)5 mm between adjacent treads or landings, and
(b)10 mm between the tallest and shortest risers in a flight.
(2)Except for required exit stairs, where the top or bottom riser in a stair adjoins a sloping finished walking surface such as a garage floor, driveway or sidewalk, the height of the riser across the stair shall vary by not more than 1 in 12.
(3)Rectangular treads shall have a uniform run with a maximum tolerance of
(a)5 mm between adjacent treads, and
(b)10 mm between the deepest and shallowest treads in a flight.
(4)Tapered treads in a flight shall have a uniform run in accordance with the construction tolerances stipulated in Sentence (3) when measured at a point 300 mm from the centre line of the handrail as described in Sentence 9.8.7.1.(5).
(5)The slope of treads shall not exceed 1 in 50.
Open OBC Div. B 9.8.4.4. in the code viewer
OBC Div. B 9.8.4.6. Winders
(1)Stairs within dwelling units are permitted to contain winders that converge to a centre point provided
(a)the winders turn through an angle of not more than 90°,
(b)individual treads turn through an angle of not less than 30° or not more than 45°, and
(c)adjacent winders turn through the same angle.
(2)Where more than one set of winders described in Sentence (1) is provided in a single stairway between adjacent floor levels, such winders shall be separated in plan by at least 1,200 mm.
Open OBC Div. B 9.8.4.6. in the code viewer
OBC Div. B 9.8.3.2. Minimum Number of Risers
(1)Except for stairs within a dwelling unit, at least three risers shall be provided in interior flights.
Open OBC Div. B 9.8.3.2. in the code viewer