The method
Before using the result
- Straight geometry only. The selected known pair controls the calculation; unselected values are ignored. No accessibility or drainage-code approval.
Worked examples
These original training examples illustrate the method for Architect Registration Examination (ARE) - United States. Use the matching “Load example” button above to explore a variation; example values are not equipment settings or prescribed criteria.
1. Worked example
Explore the space required by a chosen ramp rise and slope in a building-design study. Geometry alone does not establish accessibility compliance.
- Known pair
- Rise and run
- Vertical rise
- 0.5 m
- Horizontal run
- 6 m
- Known pair: Rise and run; rise = 0.5 m; run = 6 m.
- Grade = 0.5/6 × 100%; angle = atan(0.5/6).
- Rise: 0.5 m
- Horizontal run: 6 m
- Grade: 8.333333 %
- Angle: 0.08314123 rad
- Slope length: 6.020797 m
- Horizontal units per unit rise: 12
2. Comparison example
Compare a different supplied condition using the same method. For Archi Conquer, the important check is that the input meaning, units and method assumptions still match the problem.
- Known pair
- Rise and run
- Vertical rise
- 0.75 m
- Horizontal run
- 6 m
- Known pair: Rise and run; rise = 0.75 m; run = 6 m.
- Grade = 0.75/6 × 100%; angle = atan(0.75/6).
- Rise: 0.75 m
- Horizontal run: 6 m
- Grade: 12.5 %
- Angle: 0.124355 rad
- Slope length: 6.046693 m
- Horizontal units per unit rise: 8
Check your understanding
1. Which relationship is used?
Grade = rise/run × 100; angle = atan(rise/run); slope length = hypot(rise, run).
2. Which assumption should you check first?
Straight geometry only. The selected known pair controls the calculation; unselected values are ignored. No accessibility or drainage-code approval.
3. How should you verify a different unit system?
Convert every input to the displayed calculation units first. Equivalent physical inputs must give equivalent results; a unit label alone does not convert a number.
Continue with the matching exam topic
This tool connects to Architect Registration Examination (ARE) - United States free practice. Work through a question independently, then use the calculation steps to identify where your method differs. The tool stays free whether or not you choose paid preparation.