What Is a Rise Over Run to Degrees Calculator?
This calculator converts a slope expressed as rise over run into an angle measured in degrees. Rise is the vertical change and run is the horizontal change. The ratio of the two defines the steepness of a line, ramp, roof, road, or staircase — and that steepness can be expressed equally well as an angle. The tool is universal: it works for any units (feet, meters, inches) as long as rise and run use the same units.
How to Use It
Enter the rise (how far it goes up) and the run (how far it goes across). The calculator returns the slope angle in degrees, the equivalent percent grade, and the run-to-rise ratio. For example, a wheelchair ramp limit of 1:12 (one unit of rise per twelve of run) corresponds to about 4.76°.
The Formula Explained
The angle is found with the arctangent function: $$\theta = \arctan\left(\frac{\text{Rise}}{\text{Run}}\right) \times \frac{180}{\pi}$$ Because \(\arctan\) returns radians, we multiply by \(\frac{180}{\pi}\) to convert to degrees. The percent grade is simply \(\frac{\text{Rise}}{\text{Run}} \times 100\). When the run is zero, the slope is vertical, giving a 90° angle.
Worked Example
Suppose a roof rises 4 units for every 12 units of horizontal run. Then \(\frac{\text{rise}}{\text{run}} = \frac{4}{12} = 0.3333\), and \(\arctan(0.3333) = 0.32175 \text{ rad}\). Multiplying by \(\frac{180}{\pi}\) gives 18.43°. The percent grade is \(33.33\%\) and the ratio is \(3 : 1\).
FAQ
What angle is a 1:1 slope? A rise equal to the run gives \(\arctan(1) = 45°\).
Does the unit matter? No — only the ratio of rise to run matters, so any consistent unit works.
What if the run is 0? The slope is vertical and the angle is 90°.
