Slope to Degrees Calculator

This slope to degrees calculator helps convert the slope of a line, typically expressed as a ratio or percentage, into an angle measured in degrees.

Assume you're designing a wheelchair ramp for a building. The building code specifies that the ramp should have a slope of 1:12 (meaning it rises 1 unit for every 12 units of horizontal distance). To better visualize this incline, you can use this slope to degrees converter. In this case, a slope of 1:12 is equivalent to approximately 4.76 degrees.

Slope to Degrees Conversion Chart

Slope (as ratio)	Slope (as percentage)	Angle (in degrees)
1:1	100%	45°
1:2	50%	26.57°
1:3	33.33%	18.43°
1:4	25%	14.04°
1:5	20%	11.31°
1:6	16.67%	9.46°
1:8	12.5%	7.13°
1:10	10%	5.71°
1:12	8.33%	4.76°
1:20	5%	2.86°
1:50	2%	1.15°

Slope to Degrees Formula

The formula to convert slope to degrees is:

Angle (in degrees) = arctan(slope) × (180/π)

Where:

arctan is the inverse tangent function (also written as tan^-1)
π (pi) is approximately 3.14159

Suppose you have a slope of 0.5 (which can be expressed as a ratio of 1:2 or 50%). To convert this to degrees:

Calculate the arctangent of 0.5: arctan(0.5) ≈ 0.4636 radians
Multiply by (180/π) to convert radians to degrees: 0.4636 × (180/π) ≈ 26.57°

A slope of 0.5 (or 50%) is equivalent to an angle of approximately 26.57 degrees.

How to Convert a Slope in Degrees?

To convert a slope given in degrees back to a slope value (as a ratio or percentage), you can use the following steps:

Convert the angle from degrees to radians by multiplying by (π/180)
Calculate the tangent of this angle
The resulting value is the slope as a ratio
Multiply by 100 to get the slope as a percentage

Let’s use an example of a 30-degree angle:

Convert to radians: 30 × (π/180) ≈ 0.5236 radians
Calculate the tangent: tan(0.5236) ≈ 0.5774
The slope as a ratio is 0.5774:1
As a percentage: 0.5774 × 100 ≈ 57.74%

A 30-degree angle corresponds to a slope of approximately 0.5774:1 or 57.74%.