What it works out
Choose the two values you know from rise, run, diagonal and pitch, then enter them. The tool works out the other sides and the pitch angle, plus the triangle area, the rise per 12 of run and the grade. Rise and run meet at a right angle, and pitch is measured in degrees above the run. A diagonal must be longer than the rise or run it pairs with.
The formula
- Diagonal
- √(rise² + run²)
- Pitch
- atan(rise ÷ run)
- Area
- rise × run ÷ 2
In words: Diagonal = the square root of rise squared plus run squared; pitch = the arctangent of rise divided by run; area = rise times run divided by 2
Worked example
A rise of 3 ft over a run of 4 ft
- Rise 3 ft
- Run 4 ft
- Diagonal = √(3² + 4²) = √25 = 5 ft
- Pitch = atan(3 ÷ 4) = 36.87°
- Area = 3 × 4 ÷ 2 = 6 ft²
- Rise per 12 of run = 3 ÷ 4 × 12 = 9
The classic 3-4-5 triangle: a handy check for square corners.
Good to know
- Right triangles only.
- A diagonal must be longer than the rise or run it pairs with.
- A calculator, not a building-code check: confirm local rules with your building authority.
Questions
What is the 3-4-5 rule?
A triangle with sides 3, 4 and 5 has a right angle. Scale it up (6-8-10, 9-12-15) to square a large layout.
Which two values do I need?
Any two of rise, run, diagonal and pitch.