When you need to reproduce an existing roof, pergola or canopy, one of the first questions is: what angle is the sloping beam? You do not need an expensive digital angle finder. With two carpenter’s triangles, a spirit level and a tape measure, you can calculate the angle accurately in a few minutes.
What you need
- Two carpenter’s triangles or speed squares
- A spirit level
- A tape measure or ruler
- A calculator or smartphone
The basic idea
The two triangles help you create a small right-angled measuring frame against the sloping beam. You measure:
- Run — the horizontal distance
- Rise — the vertical height difference over that distance
These two measurements form a right triangle. The beam angle is then calculated from the ratio between rise and run.
Step-by-step method
- Place the first triangle against the underside or side of the beam. One edge must sit firmly along the sloping surface.
- Use the second triangle to create a vertical reference. Hold it against the first triangle so that the two tools form a clear right angle.
- Level the horizontal reference. Use a spirit level to make sure the line you are treating as horizontal is truly level.
- Measure the horizontal run. For easier calculation, use 100 mm, 200 mm, 500 mm or 1,000 mm.
- Measure the vertical rise. Measure how much the beam rises over the selected horizontal run.
Formula for the angle
Angle = arctan(rise ÷ run)
Use the inverse tangent function, shown as tan⁻¹ or atan, on a calculator.
Example 1
If the beam rises 87 mm over a horizontal run of 1,000 mm:
Angle = arctan(87 ÷ 1,000) = approximately 5°
Example 2
If the beam rises 140 mm over a horizontal run of 1,000 mm:
Angle = arctan(140 ÷ 1,000) = approximately 8°
Quick reference table
| Angle | Rise over 1,000 mm | Slope percentage |
|---|---|---|
| 5° | 87 mm | 8.7% |
| 8° | 141 mm | 14.1% |
| 10° | 176 mm | 17.6% |
| 15° | 268 mm | 26.8% |
| 30° | 577 mm | 57.7% |
Do not confuse degrees with percent
A slope of 10% is not the same as 10°. A 10% slope rises 100 mm over 1,000 mm and is approximately 5.7°. This is one of the most common mistakes when ordering connectors or cutting roof beams.
How to improve accuracy
- Measure over the longest practical horizontal distance.
- Check the result in at least two different places.
- Make sure the timber is not twisted or bowed.
- Measure the actual structural beam, not roof tiles or decorative cladding.
- Round only after completing the calculation.
Why the exact angle matters
The correct angle affects the beam cuts, connector selection, roof drainage, final height and the alignment of the entire structure. Even a difference of two or three degrees can create visible gaps and assembly problems.
LuxShade produces metal connectors for timber pergolas and canopies in standard and custom angles. Before ordering sloped connectors, measure the rise and run carefully or send us a clear sketch with the dimensions.
Need help choosing the correct connector angle? Send us the horizontal run and vertical rise of your structure, and we will help you identify the required angle.
Important: This method determines geometry only. Beam dimensions, spans, snow loads, wind loads and fastening details should be checked separately by a qualified structural professional when required.