Question 1

How do you convert slope percentage to degrees?

Accepted Answer

To convert slope percentage to degrees: θ = arctan(slope% ÷ 100). For example, a 10% slope equals arctan(0.10) = 5.71°. Conversely, degrees to percent: slope% = tan(θ) × 100. A 45° slope is exactly 100%.

Question 2

What is the maximum ADA-compliant ramp slope?

Accepted Answer

Per ADA Standards for Accessible Design 2010 §405.2, the maximum running slope for an accessible ramp is 1:12 (one unit of rise for every 12 units of horizontal run), which equals 4.76° or 8.33%. Cross slopes must not exceed 1:48 (2.08%). Maximum rise per ramp run is 30 inches (760 mm), requiring a level landing every 30 inches of rise.

Question 3

What is roof pitch and how is it measured?

Accepted Answer

Roof pitch is the ratio of vertical rise to horizontal run, expressed as "X-in-12" in the US (e.g., 6:12 means 6 inches of rise per 12 inches of run). Metric equivalent is rise per 1000mm of run. A 6:12 pitch equals 26.57°. Pitches below 2:12 (9.46°) are considered low-slope and require special roofing materials per IRC R905.

Question 4

What stair angle is required by the International Building Code?

Accepted Answer

IBC 2021 §1011.5 requires stair risers between 4 inches (min) and 7 inches (max), and treads of at least 11 inches (measured as going). This produces a stair angle range of approximately 29.7° to 36.4°. The Blondel formula (2R + G = 24–25 inches) checks ergonomic comfort — the calculator uses this formula to evaluate your stair geometry.

Question 5

How do you calculate a right triangle when you only know two sides?

Accepted Answer

Given two legs (a, b): hypotenuse c = √(a² + b²); angle A = arctan(a ÷ b). Given one leg and the hypotenuse (e.g., a, c): b = √(c² − a²); angle A = arcsin(a ÷ c). Given one leg and one angle (e.g., a, A): b = a ÷ tan(A); c = a ÷ sin(A). The calculator handles all four input combinations automatically.

Question 6

What is the difference between bevel angle and miter angle?

Accepted Answer

A bevel angle is the tilt of the blade from vertical (perpendicular to the workpiece face). A miter angle is the rotation of the fence/workpiece from 90° (perpendicular to the blade). For flat crown molding joints at a 90° corner with a 45° spring angle, the miter saw setting is approximately 35.26° miter and 30° bevel. The calculator uses the compound miter formula: miter = arctan(cos(bevel) × tan(corner ÷ 2)).

Question 7

How do you calculate the length of a hip or valley rafter?

Accepted Answer

Hip and valley rafters run diagonally at 45° to the building corners. Their unit run (per foot of common rafter run) is √(12² + 12²) = 16.97 inches. Hip rafter length = (unit rise² + 16.97²)^0.5 × (span ÷ 12). For example, a 6:12 pitch over a 20ft span has a hip unit length of √(6² + 16.97²) = 17.99 per 12 inches of run.

Question 8

What is the optimal solar panel tilt angle?

Accepted Answer

According to NREL PVWatts research, the optimal annual fixed tilt for a solar panel is approximately latitude × 0.87 + 3.1° for maximising annual energy output. For seasonal optimisation: summer tilt ≈ latitude − 15°, winter tilt ≈ latitude + 15°. For a location at 40° latitude, the annual optimal tilt is about 37.9°.

Question 9

How do you find the interior angle of a regular polygon?

Accepted Answer

Interior angle of a regular polygon = (n − 2) × 180° ÷ n, where n is the number of sides. Examples: triangle (n=3) = 60°; square (n=4) = 90°; hexagon (n=6) = 120°; octagon (n=8) = 135°; dodecagon (n=12) = 150°. The sum of all interior angles = (n − 2) × 180°. Each exterior angle = 360° ÷ n.

Question 10

How do you convert between degrees, radians, and percent grade?

Accepted Answer

Degrees to radians: multiply by π ÷ 180. Radians to degrees: multiply by 180 ÷ π. Degrees to grads: multiply by 10 ÷ 9 (400 grads = 360°). Degrees to percent grade: percent = tan(degrees) × 100. Percent grade to degrees: degrees = arctan(percent ÷ 100). Rise:Run ratio to degrees: degrees = arctan(rise ÷ run).

Question 11

What is the maximum slope for a parking structure ramp?

Accepted Answer

IBC 2021 §406.2.5 and most local codes limit parking structure ramps to 20% (11.3°) for straight ramps and 12.5% (7.1°) for curved transitions. AASHTO recommends highway design grades of 5–8% on flat terrain, up to 12% in mountainous terrain. Transition zones at the top and bottom of ramps should be flattened to ≤5% to prevent bottoming out.

Question 12

What stair angle is considered comfortable for residential use?

Accepted Answer

The most comfortable residential stair angle is between 30° and 35°. The Blondel formula (2 × riser + going = 24–25 inches / 610–635mm) predicts ergonomic comfort for average adult stride. A 7-inch riser with 11-inch tread gives 2(7)+11=25 — ideal. IRC R311.7 allows risers up to 7¾ inches and treads at least 10 inches for one/two-family dwellings, which produces angles up to approximately 37.8°.

Máy tính góc: Complete Guide with Formulas and Real-World Applications

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