Construction Angle Converter
Convert between degrees, radians and grads, while also showing the equivalent positive slope ratio and grade percentage for an angle measured from the horizontal.
Angle input
Conversion result
| Representation | Value |
|---|---|
| Radians | — |
| Degrees | — |
| Grads | — |
| Slope ratio rise/run | — |
| Grade | — |
How construction angle conversion works
One horizontal-referenced angle can be represented in several useful ways. Degrees, radians and grads are angular units. Slope ratio and grade are geometric representations derived from the tangent of the angle.
Grade % = tan(θ) × 100
Degrees = radians × 180 ÷ π
Example
A 5° angle has a slope ratio of about 0.0875 and a grade of about 8.75%. Conversely, an 8.33% grade corresponds to an angle of roughly 4.76°.
Important limitation
Slope conversion here assumes the angle is measured from horizontal. A site angle measured from vertical is a different reference and must be converted before applying these formulas.
Frequently Asked Questions
Can the input be a slope ratio?
Yes. Enter rise/run such as 0.125.
Can grade exceed 100%?
Yes mathematically. A 100% grade corresponds to a 45° slope.
What is a grad?
A full circle contains 400 grads.