Calculation of roof slope: formula, conversion to degrees and minimum slope

The roof slope calculation is based on a formula: divide the elevation of a slope by its horizontal distance, then multiply by 100 to obtain a percentage. The angle in degrees is derived from the arctangent. The difficulty lies elsewhere: determining the correct angles, not confusing percentage and degrees, and then verifying that the obtained slope is suitable for the intended coverage.

Here you will find the formula, recalculated conversion tables, ways to measure the slope of an existing roof, and the reading of a minimum slope. Last step: measure the slope on a PDF cut with MeasureAll, without having to climb on the roof.

Calculating the roof slope: the formula based on your measurements

A gradient compares two lengths taken on the same slope, or basin, in its line of greatest gradient, that followed by the water that flows:

• the H vertical gradient, that is, the difference in height between two points on the slope, for example between the gutter, its lower edge, and the parapet, its upper line;
• the horizontal distance D between these two same points, measured horizontally and not along the roof.

Slope (%) = 100 × H ÷ D, and angle = arctan(H ÷ D)

Let’s take the elevation of a ridge: the bottom of the slope is at 2.95 m, the face of the cliff at 5.80 m, and 4.75 m separate these two horizontal points. The elevation is 5.80 − 2.95 = 2.85 m, the slope is 100 × 2.85 ÷ 4.75 = 60%, and the angle arctan(0.60) = 30.96°. Taking the elevation of the face of the cliff, 5.80 m, instead of the elevation would give 122.11%, a slope of more than 45° that the drawing does not show: the discrepancy indicates an error in the starting point.

You do not always have these two coefficients at hand. The following table shows how to perform the roof slope calculation based on the data available:

You know	Calculation of the slope in %
H gradient and horizontal distance D	100 × H ÷ D
Increase in centimeters for every 1 m horizontally	The slope is this number of centimeters
Inclined length R and elevation H	D = √(R² − H²), then 100 × H ÷ D
Inclined length R and horizontal distance D	H = √(R² − D²), then 100 × H ÷ D
Angle read on an instrument	100 × tan(angle)

The inclined length, or ramped length, never replaces the horizontal distance in the division. In the example, the ramped length measures √(2.85² + 4.75²) = 5.54 m: dividing 2.85 by this ramped length would give approximately 51.4% instead of 60%. For a slope of terrain or staircase, the same formula applies with other references, detailed in our article on’application to calculate a slope.

Slope calculation in percentage: centimeters per meter

A slope percentage is expressed in centimeters per meter: 60% means that the slope increases by 60 cm for every meter traveled horizontally. The calculation of the percentage slope remains the same in any unit, provided that H and D are expressed in the same unit: 285 cm for 475 cm gives the same result as 2.85 m for 4.75 m. Dividing centimeters by meters, on the other hand, multiplies the result by 100.

Converting a roof slope into degrees or percentages

Not all plans, instruments and manufacturers use the same unit. To switch from one to the other:

• Angle in degrees = arctan(slope in % ÷ 100) ;
• slope in % = 100 × tan(angle in degrees).

Set your calculator to degrees mode; in radians mode, multiply the result of the arctangent by 180 and then divide by π, and before taking a tangent, multiply the angle by π and then divide by 180. Above all, the two units are not proportional. A slope of 45% equals 24.23°, not 45°; an angle of 45° corresponds to a slope of 100%, or a rise of 1 m for 1 m. At 90°, the horizontal distance becomes zero: a vertical wall has no infinite slope in percentage terms.

For a quick calculation of the roof slope, here are the most useful correspondences, recalculated and rounded to the hundredth:

Slope in %	Increase by 1 m horizontally	Angle in degrees
5 %	5 cm	2,86°
10 %	10 cm	5,71°
15 %	15 cm	8,53°
20 %	20 cm	11,31°
25 %	25 cm	14,04°
30 %	30 cm	16,70°
35 %	35 cm	19,29°
40 %	40 cm	21,80°
45 %	45 cm	24,23°
50 %	50 cm	26,57°
60 %	60 cm	30,96°
70 %	70 cm	34,99°
80 %	80 cm	38,66°
100 %	100 cm	45,00°
120 %	120 cm	50,19°
150 %	150 cm	56,31°

Conversely, start from the angle read on a plan or on a instrument:

Angle in degrees	Slope in %
5°	8,75 %
10°	17,63 %
15°	26,79 %
20°	36,40 %
25°	46,63 %
30°	57,74 %
35°	70,02 %
40°	83,91 %
45°	100,00 %
50°	119,18 %
55°	142,81 %
60°	173,21 %

The arrondis count towards a limit. A document that announces «70%, or 35°» rounds it down: 70% is 34.99°, and 35° is 70.02%. To compare a measurement to a threshold, convert it to the unit of the reference document, without rounding it to your advantage.

How to calculate the slope of an existing roof?

On a built building, several methods provide for a slope, more or less reliable. A principle of prevention guides the choice:’INRS recommends First try to remove the access from the roof when the task allows it. For a roof slope calculation, a reliable plan, accessible attics, or the ground can avoid having to climb onto the roof for this single measure.

Method	What you measure	Points of attention
Cutting or scaling up	H and D, or the angle drawn	Cut perpendicular to the siding or elevation of the ridge, same scale horizontally and vertically, plan view
Rules and level, in the attic	The increase of one chevron for 1 m horizontally	Shelves accessible safely, measured on the structure and not on a tile
Inclination meter or electronic level	The angle of the support on which it rests	Announced precision, dedicated support, several measurements
Laser rangefinder, from the ground	The heights of the slope on the ridge and its horizontal spacing	Well-defined target points, overlapping measurements
Ordinary photo	An image in perspective	No reliable measure of the angle

On an old building, the actual slope may differ from that of the original plan if the structure has been deformed or modified: then check the plan by measuring it in situ.

In the attic, If a plinth allows safe passage, press a rule of at least 1 m, level, against the bottom of a chevron in its axis. Then measure the vertical gap between the rule and the chevron at 1 m from the point of contact, on the side of the rafter. A gap of 42 cm gives 42%, or 22.78°. A reading error of 0.5 cm shifts the slope by 0.5 point; on a base of 50 cm, the same error costs 1 point. Measure the structure, whether chevron or arbaletier, rather than a tile: the slope that counts for installation is that of the support, distinct from the inclination of each element.

With an inclinometer applied against the chevron, you can read the angle directly. An electronic level like the GIM 120 from Bosch It indicates a precision of ±0.2° between 1° and 89°. A reading of 34.8°, or 69.50%, therefore covers the range from 34.6° to 35.0°, or 68.99% to 70.02%, even before taking into account the support and the condition of the support. Multiply the readings over several beams, because a deformed structural element distorts a local measurement.

From the ground, On the ridge, measure the height of the bottom of the slope and that of the screed using a laser distance meter, then the horizontal distance separating them: you then recalculate the roof slope using the example of the ridge. Cut several measurements, as errors on both heights can add up in the elevation difference.

On a photo, The perspective distorts the angles as soon as the device is not perfectly aligned with the spire, and nothing indicates the accuracy obtained: the image documents the state of the roof, without providing a reliable slope.

Do you have the PDF of the roof’s profile? Use MeasureAll to measure the slope of the side of the hill: a complete file is available for you to try it out.

Arretier and knot: a slope that is lower than that of the panels

On a four-sloped roof, do not measure the slope on a rafter. When two slopes of the same slope meet at a right angle on the plane, the rafter travels, for the same elevation, a horizontal distance √2 times longer, or approximately 1.41 times. Its slope in percentage, not in degrees, is therefore the same as the slopes divided by √2: for slopes of 60%, the rafter is at 60 ÷ 1.4142 = 42.43%, or 22.99° instead of 30.96°. A calculation of the roof slope on the rafter significantly underestimates the slope of the slopes. The joint at the angle of entry follows the same rule. For slopes of different slopes, return to the elevation and the horizontal distance of the measured line.

What minimum slope for a tiled roof?

The roof pitch calculation gives a measured slope. The minimum allowable slope, however, is not calculated: it is read from the document applicable to the roof model, and it depends on the context. There is no single minimum for all tiles. This question arises especially before changing the model on an existing roof: the roof pitch does not change, but the minimum of the new model may be different. Proceed in the order:

1. Identify the exact model and its family, not just «mechanical tile»;
2. Identify the reference document: DTU for the family, Technical Information or Technical Documentation for Application if there is one, and the manufacturer’s fiche;
3. Determine the area of application, the location of the site, whether it is more or less exposed, and the altitude;
4. measure the horizontal projection of the ramp, that is the distance D from the gutter to the parapet, which the tables often involve, and not its inclined length;
5. note the presence of a screen under the roof and the installation conditions;
6. Keep the line of the table retained with your calculation.

Two examples show the difference between the cases. For its flat tile Pompadour MH, Terreal indicates a theoretical slope of 70% in zone 1, a normal situation, with a screen. Technical Document for the Application of the TFP Fault, A Wienerberger glazed tile with a dovetail joint admits 18% for the support. This value, specific to the process, is valid only in Zone 1, in a normal or protected site, for a horizontal projection of the eaves of no more than 6.50 m, with a roof-under-the-roof screen and under other conditions. None of these values is transferable to another model or context. number of tiles per m² It also depends on the model and its tread, which can vary with the slope.

A measurement close to the threshold calls for a check, not a favorable rounding. The reading of 34.8° viewed higher leaves the actual slope between 68.99% and 70.02%, with the instrument’s accuracy alone: it does not allow a conclusion regarding the 70% announced for the Pompadour MH. Repeat the measurement using another method, preferably on a plan, and consult the manufacturer. A geometric result can never, on its own, justify writing «compliant with the DTU.» The table of reference documents by cover type is included in our guide for calculating the roof surface area.

Modifying the slope of a roof also changes the exterior appearance of the building: Public Service indicates that a preliminary declaration may then be necessary, and the local urban planning regulations may set their own rules.

Zinc, steel beams, slate: one document per system

The reasoning applies to all covers. For the standing seam zinc, VMZINC In its design, it associates 5% with continuous or stepped sections, in certain configurations, and 20% with a transverse junction with double fixing points and a covering of 180 mm. For its COVEO steel bins range, Bacacier associates 5% with a cumulative case: a rib of at least 35 mm in height, no penetration, no light plate and a sheet as long as the rafter; outside this case, other values apply. For natural slate, the overlap table applies. CUPA Pizarras It connects the slope, the area and the horizontal projection of the ramp to the covering that is to be provided. The system therefore takes into account the material as much as the material itself.

Calculate the slope of a roof on a PDF plan with MeasureAll

When the building is designed, the roof slope calculation is done on the CAD model, without access to the roof. MeasureAll is a PDF plan measurement app for iPhone, iPad and Android: it measures on the drawing, not on the actual roof.

1. Import and calibrate. You load the cup or raise the pinion; you level the page scale to a known reference point, then you verify a second reference point.
2. Lift the side. On a line perpendicular to the retaining wall, at the same scale horizontally and vertically, you measure the slope of the hillside and its horizontal projection, or the angle drawn with the angle tool.
3. Convert. Starting from H and D, you apply 100 × H ÷ D; starting from an angle measured from the horizontal, 100 × tan(angle). You then convert to the unit of your reference document.
4. Reuse the slope. Once entered, the slope is taken into account in calculating the coverage area.
5. Classify and export. Each measure receives a name, is placed in its own worksheet, and is exported in a format readable by a spreadsheet.

Once the plans are loaded, the elevation reading also works offline. A top view does not allow for measuring the slope: without a cut, elevation or marked slope, the application cannot detect it. The accuracy depends on the plan, its scale and the care taken in the calibration. And the measurement does not constitute validation: the minimum slope is always verified in the document applicable to the model, DTU, Technical Information or the manufacturer’s datasheet.

Elevate the slope of your roofs in a PDF plan: a complete dossier is provided. MeasureAll is available on the’App Store for iPhone and iPad, and on Google Play for Android smartphones and tablets. After this first subscription, the subscription is purchased in the app.

For a roofing company, MeasureAll also offers annual subscriptions for teams, with activation by company code, a single invoice, and licensable licenses. The same measuring tool for the entire team: request a company quote.

Calculation of the roof slope: what you need to remember

• Slope calculation in percentage: 100 × elevation difference ÷ horizontal distance; never the slope; the angle is equal to arctan(slope ÷ 100).
• 45% is 24.23° and 45° is 100%: always compare a measurement in the unit of the reference document.
• Measure on the steepest line of a slope, never on a ridge or a knot.
• Without a plan, measure from accessible attic spaces that are secure or from the ground level, and then compare your measurements.
• The minimum slope is specified in the model documentation, depending on the area, the slope projection and the screen.

To make cutting PDFs easier, at the office or on the construction site, try MeasureAll: a complete package is provided, and then the subscription is purchased within the app.