Slope to Degrees Calculator

A slope to degrees calculator is a tool that converts the slope of a line or surface, typically expressed as a ratio or percentage, into an angle measured in degrees.

The slope represents the steepness or incline of a line or surface, while the angle in degrees provides a more intuitive understanding of the slope’s magnitude. For example, a slope of 1:1 (or 100%) corresponds to an angle of 45 degrees, indicating that the line or surface rises at a 45-degree angle from the horizontal.

Sample Conversions

A slope of 0.5 (or 50%) is equivalent to approximately 26.57 degrees.
The slope of 2:1 (or 200%) corresponds to about 63.43 degrees.
A slope of 0.1 (or 10%) is equal to roughly 5.71 degrees.

Slope	Degrees	Conversion Equation	Usage Purpose
0.1 (10%)	5.71°	arctan(0.1) × (180/π)	Gentle ramps, drainage
0.25 (25%)	14.04°	arctan(0.25) × (180/π)	Moderate inclines, ski slopes
0.5 (50%)	26.57°	arctan(0.5) × (180/π)	Steep roads, advanced ski runs
1 (100%)	45.00°	arctan(1) × (180/π)	Very steep terrain, extreme sports
2 (200%)	63.43°	arctan(2) × (180/π)	Cliff faces, rock climbing
1:12 (0.0833)	4.76°	arctan(1/12) × (180/π)	ADA-compliant ramps
1:4 (0.25)	14.04°	arctan(1/4) × (180/π)	Embankments, roofing
3:1 (3)	71.57°	arctan(3) × (180/π)	Steep embankments, fortifications

Related Tools:

Slope to Degrees Calculation Formula

The formula to convert slope to degrees is:

Degrees = arctan(slope) × (180 / π)

Where:

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

This formula works for slopes expressed as decimal numbers or ratios. If the slope is given as a percentage, divide it by 100 first to convert it to a decimal.

Examples

For a slope of 0.5: Degrees = arctan(0.5) × (180 / π) ≈ 26.57 degrees
A slope of 2:1 (which is equivalent to 2): Degrees = arctan(2) × (180 / π) ≈ 63.43 degrees
For a slope of 25% (0.25): Degrees = arctan(0.25) × (180 / π) ≈ 14.04 degrees

How to Convert Slope to an Angle

Converting a slope to an angle involves several steps:

Ensure the slope is in the correct format: If the slope is given as a ratio (e.g., 2:1), convert it to a decimal by dividing the first number by the second (2 ÷ 1 = 2). If it’s a percentage, divide by 100 (e.g., 25% becomes 0.25).
Apply the arctangent function: Use the inverse tangent (arctan or tan^-1) function on the slope value. This gives you the angle in radians.
Convert radians to degrees: Multiply the result from step 2 by (180 / π) to convert from radians to degrees.
Round the result: Depending on the required precision, round the final answer to the appropriate number of decimal places.

For example, to convert a slope of 0.75 to degrees:

The slope is already in decimal form, so we can proceed.
arctan(0.75) ≈ 0.6435 radians
0.6435 × (180 / π) ≈ 36.87 degrees

Rounded to two decimal places, the final answer is 36.87 degrees.

How to Calculate a Slope in Degrees

Calculating a slope in degrees typically involves the following steps:

Measure the rise and run: The rise is the vertical distance, while the run is the horizontal distance.
Calculate the slope: Divide the rise by the run to get the slope as a decimal.
Use the arctangent function: Apply arctan to the slope value.
Convert to degrees: Multiply the result by (180 / π) to convert from radians to degrees.

For example, if you have a rise of 3 meters over a run of 4 meters:

Rise = 3m, Run = 4m
Slope = 3 ÷ 4 = 0.75
arctan(0.75) ≈ 0.6435 radians
0.6435 × (180 / π) ≈ 36.87 degrees

Thus, a slope with a rise of 3m and a run of 4m is approximately 36.87 degrees.

How Many Degrees is a 2% Slope?

To calculate the degrees of a 2% slope:

Convert the percentage to a decimal: 2% = 0.02.
Apply the formula: Degrees = arctan(0.02) × (180 / π).
Calculate: arctan(0.02) ≈ 0.0199 radians.
Convert to degrees: 0.0199 × (180 / π) ≈ 1.15 degrees.

Therefore, a 2% slope is equivalent to approximately 1.15 degrees.

This relatively small angle illustrates why percentages are often used for gentle slopes, as they provide a more precise and easily understood measure for slight inclines.

What Degree is a 5% Slope?

To find the degree equivalent of a 5% slope:

Convert 5% to a decimal: 5% = 0.05.
Use the formula: Degrees = arctan(0.05) × (180 / π).
Calculate: arctan(0.05) ≈ 0.0499 radians.
Convert to degrees: 0.0499 × (180 / π) ≈ 2.86 degrees.

Thus, a 5% slope corresponds to approximately 2.86 degrees. This angle is commonly encountered in road design, where a 5% grade is often the maximum allowed for highways to ensure safe driving conditions, especially in areas with frequent ice or snow.

How Many Degrees is a 1% Slope

For a 1% slope:

Convert to decimal: 1% = 0.01
Apply the formula: Degrees = arctan(0.01) × (180 / π)
Calculate: arctan(0.01) ≈ 0.0100 radians
Convert to degrees: 0.0100 × (180 / π) ≈ 0.57 degrees

A 1% slope is equal to about 0.57 degrees. This very gentle incline is often used in drainage systems or for slight grades in walkways to ensure proper water runoff while maintaining accessibility for all users, including those with mobility challenges.

3 to 1 Slope in Degrees

A 3 to 1 slope means that for every 3 units of horizontal distance, there is 1 unit of vertical rise. To convert this to degrees:

Express as a decimal: 1 ÷ 3 ≈ 0.3333
Use the formula: Degrees = arctan(0.3333) × (180 / π)
Calculate: arctan(0.3333) ≈ 0.3218 radians
Convert to degrees: 0.3218 × (180 / π) ≈ 18.43 degrees

A 3 to 1 slope is approximately 18.43 degrees. This slope is often used in landscaping and earthwork projects, as it provides a good balance between stability and space efficiency.

1:10 Slope in Degrees

A 1:10 slope indicates 1 unit of vertical rise for every 10 units of horizontal distance. To convert to degrees:

Express as a decimal: 1 ÷ 10 = 0.1
Apply the formula: Degrees = arctan(0.1) × (180 / π)
Calculate: arctan(0.1) ≈ 0.0997 radians
Convert to degrees: 0.0997 × (180 / π) ≈ 5.71 degrees

The 1:10 slope is equivalent to about 5.71 degrees. This gentle slope is often used in ramp designs for accessibility, as it provides a comfortable incline for wheelchair users and people with limited mobility.

1:100 Slope in Degrees

For a 1:100 slope:

Convert to decimal: 1 ÷ 100 = 0.01
Use the formula: Degrees = arctan(0.01) × (180 / π)
Calculate: arctan(0.01) ≈ 0.0100 radians
Convert to degrees: 0.0100 × (180 / π) ≈ 0.57 degrees

A 1:100 slope is approximately 0.57 degrees. This very slight incline is often used in large-scale drainage projects or in the design of airport runways, where even small slopes can have significant effects over long distances.

1:18 Slope in Degrees

To convert a 1:18 slope to degrees:

Express as a decimal: 1 ÷ 18 ≈ 0.0556
Apply the formula: Degrees = arctan(0.0556) × (180 / π)
Calculate: arctan(0.0556) ≈ 0.0555 radians
Convert to degrees: 0.0555 × (180 / π) ≈ 3.18 degrees

A 1:18 slope is about 3.18 degrees. This slope is often used in the design of accessible ramps for public buildings, as it provides a good balance between ease of use and space efficiency.

1:20 Slope in Degrees

For a 1:20 slope:

Convert to decimal: 1 ÷ 20 = 0.05
Use the formula: Degrees = arctan(0.05) × (180 / π)
Calculate: arctan(0.05) ≈ 0.0499 radians
Convert to degrees: 0.0499 × (180 / π) ≈ 2.86 degrees

A 1:20 slope is equivalent to approximately 2.86 degrees. This slope is commonly used in the design of wheelchair ramps and pedestrian walkways, as it provides a very gentle incline that is easy for most people to navigate, including those with mobility impairments.

Slope to Degrees Calculator – Calculate Slope Angle Percentage