A slope can be quoted three ways, and every trade prefers a different one. Roads and drainage use percent. Geotechnical drawings and embankment sections use H:V ratios. Machine control, clinometers and safety rules use degrees. You will be handed all three on the same job, sometimes on the same page.

Percent grade: $G = \dfrac{100\,\Delta h}{L}$, where $\Delta h$ is the vertical rise in metres, $L$ is the horizontal run in metres, and $G$ is a bare number wearing a percent sign. Rearranged for the rise it is $\Delta h = \dfrac{G L}{100}$ — delta-h equals G L over one hundred — which is the form that sets out a ramp.

Slope ratio to grade: $G = \dfrac{100}{n}$, where $n$ is the number of horizontal units per one vertical unit. See where the inversion comes from: n:1 means the rise-over-run is $1/n$, and the percent is a hundred times that. So the larger $n$ gets, the gentler the slope — a 5:1 batter is 20 %, a 2:1 is 50 %.

Grade to angle: $\theta = \arctan\!\left(\dfrac{G}{100}\right)$, read aloud theta equals arctan of G over one hundred. $\theta$ — theta — is the angle from horizontal in degrees. Divide the percent back to a decimal, because a tangent is a bare ratio, then take the arctangent. Backwards it is $G = 100\tan\theta$.

Now the fact this lesson exists for. A grade and an angle are not the same scale, and they diverge fast. Near zero they nearly agree — 1 % is 0.57°, close enough that a surveyor will let it pass in conversation. By 100 % the grade has run away from the angle completely: 100 % is 45°, not 100°, because a hundred percent means rise equals run. And a grade has no ceiling — a vertical face is an infinite percent — while an angle stops politely at 90.

Carry the triangle out with you: 3:1 = 33.3 % = 18.4°. Three numbers that share nothing, describing one embankment. Every one of the three appears somewhere on a real set of drawings, and mixing any two of them builds the wrong slope.