How tall is the roof? Roof Height Calculator works out peak height, mean roof height, and roof rise from building span, wall height, and roof pitch.
Roof Height Calculator finds the peak height of a gable roof from building span, plate height, and pitch. It also gives mean roof height, roof rise, and fascia height.
Roof Height Calculator: Peak Height
Roof height starts with the rise. The rise is how far the roof climbs above the top of the wall. On a gable roof the run is half the building span.
$$Rise=\frac{Span}{2}\times\frac{P}{12}$$
P is the pitch written as inches of rise per 12 inches of run. A 6/12 pitch has P = 6.
Peak height adds the wall to the rise.
$$H_{peak}=H_{plate}+Rise$$
Hplate is the top plate height measured from grade. With the default inputs the span is 24 ft, the plate is 10 ft, and the pitch is 6/12. The rise is 12 × 0.5 = 6 ft. The peak is 10 + 6 = 16 ft above grade.
The overhang does not change the peak. It lowers the roof edge. The eave drops by the overhang times the pitch.
$$H_{fascia}=H_{plate}-Overhang\times\frac{P}{12}$$
A 1.5 ft overhang at 6/12 drops 0.75 ft. The fascia sits at 9.25 ft.
Mean Roof Height
Mean roof height is the midpoint between the eave and the highest point of the roof. ASCE 7 and the IRC define it as the average of the roof eave height and the height to the highest point on the roof surface.
$$H_{mean}=\frac{H_{peak}+H_{fascia}}{2}$$
For the default roof this is (16 + 9.25) ÷ 2 = 12.63 ft.
The same definition has one exception. For a roof angle of 10 degrees or less, the eave height is used as the mean roof height. A 2/12 pitch is 9.46°, so it falls under that exception. For wind design on a 2/12 roof, use the Exterior Fascia Elevation card instead of the Mean Roof Height card.
Some reviewers take the eave at the wall line, not at the end of the overhang. Set the overhang to 0 to get that version. The default roof then has a mean height of 13.00 ft.
Roof Rise Chart
The chart gives roof rise in feet above the top plate for a gable roof. Add your plate height to get peak height from grade.
| Span | 3/12 | 4/12 | 6/12 | 8/12 | 10/12 | 12/12 |
|---|---|---|---|---|---|---|
| 12 ft | 1.50 | 2.00 | 3.00 | 4.00 | 5.00 | 6.00 |
| 16 ft | 2.00 | 2.67 | 4.00 | 5.33 | 6.67 | 8.00 |
| 20 ft | 2.50 | 3.33 | 5.00 | 6.67 | 8.33 | 10.00 |
| 24 ft | 3.00 | 4.00 | 6.00 | 8.00 | 10.00 | 12.00 |
| 28 ft | 3.50 | 4.67 | 7.00 | 9.33 | 11.67 | 14.00 |
| 30 ft | 3.75 | 5.00 | 7.50 | 10.00 | 12.50 | 15.00 |
| 32 ft | 4.00 | 5.33 | 8.00 | 10.67 | 13.33 | 16.00 |
| 36 ft | 4.50 | 6.00 | 9.00 | 12.00 | 15.00 | 18.00 |
| 40 ft | 5.00 | 6.67 | 10.00 | 13.33 | 16.67 | 20.00 |
Pitch to Angle Chart
The pitch multiplier converts a horizontal run to the length along the slope. Rafter line equals run times the multiplier.
| Pitch | Angle | Pitch multiplier |
|---|---|---|
| 2/12 | 9.46° | 1.014 |
| 3/12 | 14.04° | 1.031 |
| 4/12 | 18.43° | 1.054 |
| 5/12 | 22.62° | 1.083 |
| 6/12 | 26.57° | 1.118 |
| 7/12 | 30.26° | 1.158 |
| 8/12 | 33.69° | 1.202 |
| 9/12 | 36.87° | 1.250 |
| 10/12 | 39.81° | 1.302 |
| 12/12 | 45.00° | 1.414 |
For the default roof the run is 12 ft. The rafter line is 12 × 1.118 = 13.42 ft from plate to peak. That is a geometry line. It is not a cut length for a rafter.
Height Limit Example
A two-story house is planned in a zone with a 35 ft height limit. The span is 36 ft. The top plate is 20 ft above grade. The pitch is 12/12 and the overhang is 2 ft.
The rise is 18 × 1 = 18 ft. The peak is 38 ft above grade. The fascia is at 20 − 2 = 18 ft. The mean roof height is (38 + 18) ÷ 2 = 28 ft.
The answer depends on how the local code measures height. The IBC and IRC define building height as the vertical distance from grade plane to the average height of the highest roof surface. Under that definition this house measures 28 ft and passes. A zoning code that measures to the highest point would read 38 ft and fail.
Check the definition in your own ordinance before you submit. Dropping the pitch to 8/12 brings the peak down to 32 ft, which passes either way.
Roof Height in Meters
Set each unit selector to m. The results follow the span unit.
Metric drawings often give the roof angle in degrees, not as a pitch. Convert the angle to a rise on a 12 run with the tangent.
$$P=12\times\tan\theta$$
A 30° roof gives P = 12 × 0.5774 = 6.93. Choose Custom Pitch, then enter a rise of 6.93 and a run of 12.
Example: a gable roof spans 8 m with a 2.7 m wall and a 30° slope. The run is 4 m. The rise is 4 × 0.5774 = 2.31 m. The peak is 2.7 + 2.31 = 5.01 m above grade.
What the Result Leaves Out
The peak is the point where the two roof lines meet above the plate line. A finished ridge sits a little higher. Rafter depth above the plate, sheathing, roofing, and a ridge vent all add height. On a typical house that is several inches.
Plate height must be measured from grade, not from the floor. Add the foundation height above grade to the wall height. On a sloped lot, codes use an averaged grade plane. Use that value as your zero point.
The math assumes a symmetrical gable with the ridge at the center of the span.
Frequently Asked Questions
How do you calculate roof height from pitch?
Halve the building span to get the run. Multiply the run by the pitch divided by 12. That is the roof rise. Add the wall height to get the peak height from grade. Example: a 30 ft span with an 8/12 pitch has a run of 15 ft. The rise is 15 × 8 ÷ 12 = 10 ft. On a 9 ft wall the peak is 19 ft above grade.
What is mean roof height?
Mean roof height is the average of the eave height and the height of the highest point on the roof. It is the value ASCE 7 uses for wind loads. A roof with a 9 ft eave and a 19 ft peak has a mean roof height of 14 ft. For a roof angle of 10 degrees or less, the eave height is used instead. Many codes also measure building height to this midpoint for sloped roofs.
Is building height measured to the peak or the mean?
It depends on the code. The IBC and IRC measure building height from grade plane to the average height of the highest roof surface. For a gable roof that is the midpoint between eave and ridge. Many local zoning codes follow that rule. Others measure to the highest point of the roof. The two methods can differ by 5 to 10 ft on a steep roof, so read the definition in your own ordinance.
What is a standard roof height?
There is no single standard. Roof height depends on span, wall height, and pitch. A one-story house with 8 ft walls, a 24 ft span, and a 4/12 pitch peaks at 12 ft. The same house type with 9 ft walls, a 30 ft span, and a 6/12 pitch peaks at 16.5 ft. A second story adds about 9 to 10 ft to either number.
Does the overhang change roof height?
It does not change the peak. It lowers the fascia, because the roof keeps sloping down past the wall. A 2 ft overhang at 8/12 drops the roof edge by 1.33 ft. That lowers the mean roof height by half that amount, or 0.67 ft. A wider overhang can help a design that is close to a mean-height limit.
Does it work for a hip roof or a shed roof?
A hip roof with the same pitch on all sides reaches the same peak height as a gable. Use the shorter building dimension as the span. A shed roof slopes one way, so its run is the full width. Enter twice the real width as the span. A 12 ft wide shed at 4/12 with an 8 ft low wall then shows a rise of 4 ft and a high side of 12 ft.
References
- ASCE 7, Minimum Design Loads for Buildings and Other Structures, definition of mean roof height.
- International Building Code Section 202 and International Residential Code Section R202, definitions of building height and mean roof height.