Search for a tool
Slope Calculator

Tool/Calculator to find a slope/grade value (of a road, a roof, a construction, a frame, etc.) from its height or width or length or distance etc.

Results

Slope Calculator -

Tag(s) : Geometry

Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Slope Calculator' tool for free! Thank you!

# Slope Calculator

Please fill at least 2 items from this diagram
NB: Use the same unit (m, cm, etc.) for all distances (the result will be in this same unit)

### What is a slope? (Definition)

Slope is a measure of the inclination or decline of land, road or surface. It indicates the variation in height in relation to a distance traveled.

Slope is generally measured in percentage (a slope of 30%, or a rise/change of 30 units for a run horizontal distance of 100 units).

By extension, some call slope, the angle $a$ (a slope of 15 degrees).

### How to calculate a slope (in percentage)?

The slope $p_\%$ (in % percent) is calculated by the ratio of the height $h$ by the width $w$ (multiplied by 100 to get a percentage): $$p_\% = 100 \times \frac{h}{w}$$

Example: Calculate the slope for a vertical distance of 10m and a horizontal distance of 50m: $p = 10/50 = 0.2$ or $20%$

### How to calculate a slope (in degrees)?

The slope $p°$ (in ° degrees) is calculated by trigonometric functions: $$p° = \arctan \left( \frac{h}{w} \right) \times \frac{180}{\pi}$$

Example: Calculate the slope for a vertical distance of 10m and a horizontal distance of 50m: $p° = \arctan(10/50) \approx 0.19 \text{ rad} \approx 11.3°$ (multiply radians by $180/\pi$ to get a value in degrees)

### How to convert a slope (percentage <-> degrees)?

The formula for converting slope from degrees to percentage is:$$p° = \arctan \left( p_\% / 100 \right) \times \frac{180}{\pi}$$

The formula for converting slope from percentage to degrees is: $$p_\% = 100 \tan( p° \times \frac{\pi}{180} )$$

### What is a negative slope?

A positive slope (or grade) indicates that the land rise or is rising in the chosen direction (positive height difference), while a negative slope indicates that the land is falling or falling in the chosen direction (negative height difference).

### How to interpret a slope of 0%?

A grade/slope of 0% means that there is no significant vertical change in the distance traveled. This is equivalent to flat land (no elevation).

### What are the formulas for finding each value in a slope calculation?

The following equations allow us to find $d$, $h$, $w$ from the angle $a$ (in degrees)

$$d = w / \cos(a \pi/180)$$

$$h = d \sin(a\pi/180) = w \tan(a \pi/180)$$

$$w = h / \tan(a \pi/180)$$

From the slope $p_\%$ in percentage:

$$d = w / \cos(\arctan( p_\% / 100 ) )$$

$$h = d \sin( \arctan( p_\% / 100 ) ) = w \tan( \arctan( p_\% / 100 ) )$$

$$w = h / \tan( \arctan( p_\% / 100 ) )$$

## Source code

dCode retains ownership of the "Slope Calculator" source code. Except explicit open source licence (indicated Creative Commons / free), the "Slope Calculator" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Slope Calculator" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Slope Calculator" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

## Cite dCode

The copy-paste of the page "Slope Calculator" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Slope Calculator on dCode.fr [online website], retrieved on 2024-09-10, https://www.dcode.fr/slope-calculator

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!