Calculate rise, run, diagonal, angle, and slope from any two known measurements.
Free to use · No signup required
Enter rise and run to solve diagonal, angle, and slope.
Enter rise and run to calculate.
Rise, run, and diagonal form a right triangle. If any two compatible measurements are known, the remaining dimensions can be calculated using basic right-triangle geometry. Skoppe Calculator converts the results back into construction-friendly feet, inches, and fractions so the measurements can be used directly in the field.
Diagonal = √(Rise² + Run²)
Rise = √(Diagonal² − Run²)
Run = √(Diagonal² − Rise²)
Angle = atan(Rise ÷ Run)
Slope % = (Rise ÷ Run) × 100
Rise = tan(Angle) × Run
Run = Rise ÷ tan(Angle)
Any two compatible measurements are enough to solve the rest of the triangle.
A rise of 6 ft over a run of 12 ft:
√(6² + 12²) = √180
≈ 13.42 ft
Diagonal: ≈ 13 ft 5 inatan(6 ÷ 12)
Angle: ≈ 26.57°6 ÷ 12 × 100
Slope: 50%The vertical distance between the lower and upper points.
The horizontal distance between those points.
The straight-line distance connecting the two points.
The angle formed between the run and diagonal.
The rise-to-run relationship expressed as a percentage.
Framing: check diagonal dimensions and angled framing layouts.
Bracing: solve diagonal lengths from known rise and run.
Ramps: calculate geometry from rise, run, or angle.
Roof layout: solve geometric dimensions used during layout.
Site work: calculate slope relationships between measured points.
A 3-4-5 triangle is a common field method for checking a 90° corner. If one side measures 3 units and the other measures 4 units, the diagonal between them should measure 5 units.
3 ft × 4 ft → 5 ft diagonal. 6 ft × 8 ft → 10 ft diagonal. 9 ft × 12 ft → 15 ft diagonal.
Any proportional multiple of 3-4-5 works the same way.
| Relationship | Meaning |
|---|---|
| Rise² + Run² = Diagonal² | Pythagorean theorem for right triangles |
| Slope % | Rise ÷ Run × 100 |
| 45° angle | 100% slope — rise equals run |
| 3-4-5 | Right triangle — square corner check |
| 6-8-10 | Right triangle — square corner check |
| 9-12-15 | Right triangle — square corner check |
Square the rise and run, add the results, and take the square root. This gives the straight-line diagonal between the two points.
Square the diagonal, subtract the square of the run, and take the square root.
Square the diagonal, subtract the square of the rise, and take the square root.
Divide rise by run and take the inverse tangent of the result.
Divide the rise by the run and multiply by 100.
A 3-4-5 triangle is a right triangle with sides in a 3:4:5 ratio. It is commonly used in construction to check whether a corner is square.
Yes, it can calculate geometric rise, run, diagonal, angle, and slope relationships used in roof layout. It does not determine structural or roofing requirements.
Yes. Skoppe Calculator supports construction-style dimensional inputs and returns dimensional results in feet, inches, and fractions.
Join Skoppe for practical construction tools and a clearer way to manage scope, budgets, and project communication.