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How steep the mansard's lower (near-vertical) roof segment is, measured from horizontal.
Mansard roofs are defined by a steep lower slope (often 60-75° from horizontal) that gives usable attic headroom, transitioning to a much shallower upper slope near the ridge.
The vertical rise of the steep lower segment, from the wall top to the break line.
A vertical RISE, not a rafter. On a true mansard the lower segment is close to vertical, so its rise and its rafter length are nearly equal — which is exactly what makes substituting one for the other so easy and so persistent, because every rafter comes out short by the same small amount and nothing looks obviously wrong until the break line does not meet the upper slope.
The shallow upper roof segment's pitch, expressed as inches of rise per 12 inches of run.
Both segments are described the same way here, rise over run — including the steep lower one, which builders more often quote as an angle because at that steepness a pitch reads oddly. Mixing the two conventions between the segments is the commonest mansard error: the geometry still closes, but it closes with the break line at the wrong height, and the roof is framed before anyone notices.
The overall width of the building, wall to wall.
OVERALL, wall to wall, because a mansard has to close all the way across: two steep lower slopes and two shallow upper ones must meet at a ridge that lands on the centreline. A width taken to the inside faces leaves the upper slopes short of one another by two wall thicknesses, and a ridge that does not close has to be made up on site with a flat that was never designed.
Total mansard rafter length
21.49 ft
- Lower segment length
- 6.92 ft
- Upper segment length
- 14.57 ft
They open the calculator with your figures already in it
Mansard Roof Rafter Geometry Calculator: 21.49 ft — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- The steep lower mansard segment is sized by its slope angle and vertical height (length = height/sin(angle), run = height/tan(angle)); the shallow upper segment uses the standard rise/12 rafter-length formula over the remaining half-width
Inputs used
- Lower Segment Slope Angle (° from horizontal)
- 70
- Lower Segment Vertical Height
- 6.5 ft
- Upper Segment Pitch (rise per 12)
- 3
- Building Width
- 33 ft
Intermediate steps
- Lower segment length
- 6.92 ft
- Upper segment length
- 14.57 ft
What this calculation does not cover
- The total is the sum of two segments that meet at the break line, not the length of one piece of timber. Cut from the two figures in the breakdown, not from the total: on the default 70 degree lower slope and 3-in-12 upper slope the two members meet at a change of direction of about 56 degrees, so a single rafter of the total length does not exist.
- The run is measured from the wall to the ridge centre line, so what you get is a theoretical line length. It excludes the eaves overhang, the half-thickness of the ridge board that has to come off each upper rafter, and the timber consumed by the birdsmouth seat cut and the plumb cuts at each end.
- This is the common rafter through one cross-section. A mansard is normally hipped on all four sides, and the hip rafters and the jack rafters running into them are longer and cut to compound angles that this page does not produce. No rafter spacing is asked for either, so there is no rafter count and no total timber quantity.
- Nothing here tests whether the roof stands up. The junction between a near-vertical lower slope and a shallow upper slope is a kink that pushes outwards under load and normally has to be restrained by a curb plate or purlin with a floor or collar behind it; the calculator returns no member depth, span limit or fixing detail for that transition.
- The upper pitch accepts 1 to 8 in (203 mm) 12, which is roughly 4.8 to 33.7 degrees, and the lower part of that range sits below the minimum pitch that slates and most interlocking tiles are rated for. Minimum pitch is set by the covering manufacturer and by local rules rather than by the geometry, so a shallow mansard top often has to become a membrane or standing-seam metal deck instead.
- The steep lower slope of a mansard is usually pierced by dormers, and the geometry here assumes it is unbroken. Each dormer opening cuts rafters that must be trimmed round with doubled trimmers and headers, none of which is reflected in the length or in the breakdown.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-02 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- The steep lower mansard segment is sized by its slope angle and vertical height (length = height/sin(angle), run = height/tan(angle)); the shallow upper segment uses the standard rise/12 rafter-length formula over the remaining half-width
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Your workspace
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Tools and safety for this job
To cut framing lumber. Generic types, no brands, no prices.
Protection this work requires
- Hardwood dust is a recognised carcinogen: extract at the tool and wear a P2/N95 respirator when cutting or sanding indoors.
- Saws, grinders and breakers run above 85 dB, where hearing damage accumulates and does not recover: defenders or plugs for every cut, not just the long ones.
Show the 5 tools this job needsHide tools
Essential
Circular saw
Combination or framing square
Tape measure
Recommended
Mitre saw
Optional
Hand saw
Also needed as materials: circular saw blades, mitre saw blades.
what each carpentry tool is for, and the spec that decides which to buy where one does.