Free Slope Percentage Calculator

The slope percentage, also known as grade or the rise‑over‑run ratio, is a convenient way to express the steepness of a surface—commonly used on road signs, in construction plans, and in mathematics. This calculator instantly converts between slope percentage and angle in degrees, and can compute any missing rise or run value from the other two inputs.

What Is Slope Percentage?

Slope percentage quantifies steepness as the vertical change (rise) relative to the horizontal distance (run), multiplied by 100. In practical terms, a slope percentage tells you how many units the terrain rises (or falls) for every 100 units of horizontal travel. For example, a 5 % grade means an ascent of 5 m (or 5 ft) over a horizontal run of 100 m (or 100 ft).

Formula and Step‑by‑Step Calculation

The core relationship is:

$$\text{Slope percentage} = \frac{\text{rise}}{\text{run}} \times 100$$

To apply it:

1. Measure the vertical distance the slope rises or drops (rise). Use a negative value if the slope goes downward.
2. Measure the horizontal distance covered (run).
3. Divide the rise by the run.
4. Multiply the result by 100 to obtain the percentage.

If you know the rise and the slope percentage, you can solve for the run, and vice versa.

Converting Between Degrees and Slope Percentage

Angles and slope percentages are two sides of the same steepness coin. The conversion relies on the tangent function:

• Degrees → percentage:
  $\text{Slope percentage} = \tan(d) \times 100$, where $d$ is the angle in degrees.

• Percentage → degrees:
  $d = \arctan\left(\dfrac{\text{slope percentage}}{100}\right)$.
  The resulting angle is given in degrees; if your input is in radians, convert it first (degrees = radians × 180 / π).

Quick‑Reference Table

Angle (degrees)	Slope percentage
0°	0 %
5°	≈ 8.75 %
10°	≈ 17.63 %
45°	100 %
60°	≈ 173.21 %
90°	→ ∞

Important Characteristics

• Slope percentage can be negative, indicating a downhill direction.
• It can exceed 100 %—anything above 45° produces a percentage greater than 100. For instance, a 60° slope returns about 173 %.
• As the angle approaches ±90°, the slope percentage tends toward infinity. For the tool to produce meaningful results, the input angle must be between −90° and 90° (exclusive).

Using the Slope Percentage Calculator

This tool accepts any two of the three variables (rise, run, angle) and instantly computes the third. You can also enter a slope percentage to get the corresponding angle. Whether you’re checking road grades, designing ramps, or solving homework problems, the calculator handles both positive and negative slopes and works in any consistent unit (meters, feet, etc.).

To get started, either input the rise and run or the angle in degrees. The slope percentage—and any missing variable—appears right away.