Slope Calculator | Degrees to Percent | Average Slope

Convert Degrees to Percent

Calculator for converting an angle in degrees to a percentage value, or vice versa. Angles are usually expressed in degrees, but in the context of gradients or slopes, they are often stated as a percentage. The percentage value represents the ratio of the vertical rise to the horizontal length. The conversion is non-linear and relies on the tangent function, so it cannot easily be performed mentally.
Please enter an angle in degrees between -90 and 90, or any percentage value. The corresponding other value will be calculated.

Degrees:
Percent:

Round to   0 1 2 3 4 5 6 7 8 9   decimal places.

The formulas for the conversion are:
Percent = 100% * tan ( degrees * π / 180° )
Degrees = arctan ( percent / 100% ) / π * 180°

tan is the tangent, sine divided by cosine, while arctan is the arctangent, the inverse function of the tangent. The angle increases linearly. Two degrees is twice as much as one degree, and so on, with each additional degree representing a constant increment. This does not apply to the percentage value, which increases non-linearly. The tangent rises approximately linearly at low values ​​and steeply at high values. Near 90 degrees (plus or minus), the rise becomes extreme, in other words tangential.
The percentage value can be any real number. Zero degrees corresponds to zero percent, this is the only value shared by both. A vertical line, an angle of 90 degrees, corresponds to an infinite percentage value. This is because the calculation involves dividing by the horizontal length, which is zero at such an angle. A gradient of 100 percent corresponds to an angle of 45 degrees, as the rise and the horizontal length are equal in this case.
Negative values ​​indicate a different direction. When moving from left to right, a positive value represents an upward slope (incline), while a negative value represents a downward slope (decline). Consequently, the corresponding lines look like / for positive values ​​and \ for negative values.

This is a simple calculator for converting between degrees and percentages. A more comprehensive calculator that takes specific lengths and heights into account is the slope calculator.

Last updated on 08/23/2026. Author: Jürgen Kummer

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