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Stair Angle Calculator

The rise and the tread in; the angle and the stringers out.

Your building department's riser and tread limits win; type them under Assumptions.

7' · 84 in · 7 ft · 2.1336 m

3' · 36 in · 3 ft · 0.9144 m

11" · 11 in · 0.9167 ft · 0.2794 m

7" · 7 in · 0.5833 ft · 0.1778 m

12 risers

Nothing is added unless you add it: boards are bought whole and long enough. Waste is added once, to every board and piece on the list.

This page recalculates as you type. There is no Calculate button.

Answer

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Angle

32.47 °

11 treads of 11" over 10' 1" of run, at 32.47°.

How many risers 12 risers of 7"
Each riser 7"
Total run 10' 1"
Stringer length, top tread a riser below the floor 11' 11 7/16"
Stringers, 18" apart at most 3 stringers
More numbers
How many treads 11 treads of 11"
Hung flush instead 13' 7/16"
Each stringer board, at least 12' 2 3/8" cut from a 14 ft board
Stringer left under the notches 5 3/8"
Twice the riser plus the tread 25"
Cost of what is ticked $544.48
DrawingThe project drawn to scale. Stair 1: 7" × 11" × 7' × 10' 1".7"11"7'10' 1"Stair 1

Breakdown

Flight Measurements Qty Risers Share
Stair 1 7' × 3' × 11" × 7" Add ×1 12 risers

What to buy

Shopping list

3 boards $113.94 Reference price $37.98. Type your store's.
11 pieces $274.78 Reference price $24.98. Type your store's.
12 pieces $155.76 Reference price $12.98. Type your store's.
Ticked items $544.48

Untick what you have, and the riser boards for open risers.

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Standards

We hold the criteria and the clause, not the wording of the standard.

Meets IRC 2021 · R311.7.5.1

Every riser is 7", within the 7 3/4" the code allows.

Meets IRC 2021 · R311.7.5.1

The finished risers differ by 0", within 3/8": the bottom riser is cut for the tread and the flooring.

Meets IRC 2021 · R311.7.5.2

Treads of 11" are at least the 10" the code asks.

Meets IRC 2021 · R311.7.5.3

Not required: every tread is at least 11" deep.

Meets IRC 2021 · R311.7.3

The flight rises 84", within the 151" the code allows between floors or landings.

Meets IRC 2021 · R311.7.1

36" wide, at least the 36" the code asks above the handrail.

Not checked IRC 2021 · R311.7.2

The code asks 80" of headroom over the nosings; measure the flight as a stair under an opening to check it.

Not checked IRC 2021 · R311.7.8

Required: a handrail on at least one side. The flight has 12 risers, and the code asks for one from 4.

Not checked IRC 2021 · R312.1.1

Required along any open side: the stair climbs 84", more than 30" above the floor below.

How this was worked out

Every number below is yours. Each constant links to the row where you can change it.

Stair 1: risers 7' ÷ 7" = 12, rounded up 12
Stair 1: each riser 7' ÷ 12 7"
Stair 1: total run 11 × 11" 10' 1"
Stair 1: angle atan(7" ÷ 11") 32.47°
Stair 1: stringer, marked along its edge 11 steps of 13 1/16", the square set at 7" and 11" 11' 11 7/16"
Stair 1: bottom riser, as cut 7" − 1 1/2" tread + 0" flooring to come 5 1/2"

Change:Tread thicknessFlooring still to go down, at the bottom

Stair 1: top tread's cut, below the upper floor 7" + 1 1/2" tread − 0" flooring to come 8 1/2"

Change:Tread thicknessFlooring still to go down, at the top

Stair 1: every riser cut the same instead every riser 7": first step 8 1/2", last 5 1/2" 3" apart; a flight may differ 3/8"
Stair 1: board for each stringer 11' 11 7/16" + 5 1/2" × 7" ÷ 13 1/16" 12' 2 3/8" → 14 ft
Stair 1: stringer under the notches 11 1/4" − 7" × 11" ÷ 13 1/16" 5 3/8"

Change:Dressed, 8 in and wider

Stair 1: stringers 36" ÷ 18" = 2, rounded up, + 1; at least 3 3
12 risers of 7" 2 × 7" + 11" = 25", against 25" 10' 1" of run

Change:Comfortable step, 2 × riser + tread

13 risers of 6 7/16" 2 × 6 7/16" + 11" = 23 15/16", against 25" 11' of run

Change:Comfortable step, 2 × riser + tread

14 risers of 6" 2 × 6" + 11" = 23", against 25" 11' 11" of run

Change:Comfortable step, 2 × riser + tread

Cost 3 × $37.98 + 11 × $24.98 + 12 × $12.98 $544.48

Assumptions

Every one of these is editable. Change one and the answer changes with it.

Assumption Value Confidence
Dressed, 8 in and widerNIST PS 20-20, Table 3: 8 in nominal and wider is dressed dry ¾ in under it - 8 to 7¼, 10 to 9¼, 12 to 11¼. in From a data sheet or an agency document
Tread thicknessMyCarpentry's default tread, a 2× board 1½ in thick; a 5/4 tread is 1 in. The bottom riser is cut shorter by it. ≈ in Trade convention
Nosing1 in, the middle of the ¾–1¼ in nosing the code allows. ≈ in Trade convention
Flooring still to go down, at the bottomFlooring still to go down at the foot of the stair; 0 when that floor is finished. The stringer stands under it, so its bottom riser is cut taller by it. ≈ in Trade convention
Flooring still to go down, at the topFlooring still to go down at the top of the stair; 0 when that floor is finished. It moves where the stringer hangs, not how it is cut. ≈ in Trade convention
Stringer spacing under wood treadsAWC DCA 6-15, p. 20 and Figure 29: cut stringers no more than 18 in apart on center under 2× or 5/4 treads. in From a data sheet or an agency document
Fewest stringersAWC DCA 6-15, p. 20: where only cut stringers are used, at least three. stringers From a data sheet or an agency document
Least stringer to keep under the notchesAWC DCA 6-15, Figure 28 (p. 21): a cut stringer keeps at least 5 in below its notches. MyCarpentry and Blocklayer say the same. in From a data sheet or an agency document
Comfortable step, 2 × riser + treadTwice the riser plus the tread. Riser counts are ranked by how near they come to 25 in, inside the 60–65 cm Omni's calculator calls comfortable. ≈ in Trade convention
Lowest riser before a warningBlocklayer's stair calculator warns below a 4 in riser. ≈ in Trade convention
Deepest tread before a warningBlocklayer's stair calculator warns above a 14 in tread. ≈ in Trade convention
Tallest riser the code allowsIRC 2021 R311.7.5.1 (R318.7.5.1 in IRC 2024): a riser is not more than 7¾ in, measured between the leading edges of the treads. in From a data sheet or an agency document
Most two risers of a flight may differIRC 2021 R311.7.5.1 (R318.7.5.1 in IRC 2024): the tallest riser of a flight is no more than ⅜ in taller than the shortest. in From a data sheet or an agency document
Shallowest tread the code allowsIRC 2021 R311.7.5.2 (R318.7.5.2 in IRC 2024): a tread is at least 10 in deep, measured nosing to nosing. in From a data sheet or an agency document
Least nosing, where one is requiredIRC 2021 R311.7.5.3 (R318.7.5.3 in IRC 2024): a nosing projects at least ¾ in. in From a data sheet or an agency document
Most nosingIRC 2021 R311.7.5.3 (R318.7.5.3 in IRC 2024): a nosing projects no more than 1¼ in. in From a data sheet or an agency document
A tread this deep needs no nosingIRC 2021 R311.7.5.3 (R318.7.5.3 in IRC 2024): no nosing is required where the tread is at least 11 in deep. in From a data sheet or an agency document
Least headroomIRC 2021 R311.7.2 (R318.7.2 in IRC 2024): at least 6 ft 8 in of headroom, measured up from the sloped line of the nosings. in From a data sheet or an agency document
Narrowest stairIRC 2021 R311.7.1 (R318.7.1 in IRC 2024): at least 36 in of clear width above the handrail. in From a data sheet or an agency document
Tallest flight between floors or landingsIRC 2021 R311.7.3 (R318.7.3 in IRC 2024): a flight rises no more than 12 ft 7 in between floors or landings. in From a data sheet or an agency document
Risers that call for a handrailIRC 2021 R311.7.8 (R318.7.8 in IRC 2024): a handrail on at least one side of a flight with four or more risers. risers From a data sheet or an agency document
Open-side drop that needs a guardIRC 2021 R312.1.1 (R321.1.1 in IRC 2024): a guard along an open side more than 30 in above the floor or grade below. in From a data sheet or an agency document

How steep a stair is

The angle of a stair is the angle of a step: atan(riser ÷ tread). Twelve risers of 7 in on 11 in treads, a stair 7 ft high, climb at atan(7 ÷ 11) = 32.47°. Steeper risers or shallower treads make it steeper; the page works the angle out from the risers it counts, so changing the rise or the treads moves it.

The IRC sets no angle. It sets the riser and the tread, and the steepest stair it allows follows from them: 7¾ in risers on 10 in treads, 37.78°. Blocklayer's calculator warns past 40°.

Two stringer lengths, and which is which

The same stair has two stringers, depending on how it is hung. With the top tread a riser below the floor it carries 11 treads and is 143.42 in long; with the top tread level with the floor it carries 12 and is 156.46 in. A popular calculator's worked example gives both numbers; this page prints the one for the way you hang it, and names the other beside it.

The board for the shorter one is not a 12 ft board, although 143.42 in is under 144: the cuts at the top and the foot take it to 12 ft 2⅜ in, so a 14 ft 2×12.

A comfortable angle

Twice the riser plus the tread comes to 2 × 7 + 11 = 25 in on this stair, inside the 60 to 65 cm one calculator calls comfortable. The working weighs 13 and 14 risers as well, each with the run it takes.