# How to Find Slope ( with all Calculations )

How to Find Slope. Find Slope or calculation is under several headings. The slope is called the slope where the surface is more or less inclined towards a horizontal plane. In fact, most of the days we used in the day have a bend. For example; we have a tendency to throw the fishing line we use when fishing in the sea. As another example, the adjustable screens of laptop computers can be described as a slope. The slopes of any non-oblique objects are shown as zero.

In a mathematical sense, the slope is expressed as the ratio of the horizontal change to the vertical change between any two points on a straight line. More specifically, slope is the ratio of elevation difference between two points to horizontal distance. The slope of a line on the coordinate plane is indicated by the letter “m”.

## How to Find Slope with Formula

Formula to Find Slope is used to calculate and find slope. The formula m = \ frac {y_2-y_1} {x_2-x_1} is used to find the slope of a straight line. By substituting the coordinates x1, x2, y1 and y2 of the direct coordinates in the form, the slope of the line expressed by the letter “m” is obtained.

Example: In the coordinate plane we find the slope of the straight line passing through the points A (0,1) and B (1,2).

Solution: In order to find the correct tilt, the direction of the line is obtained with the replacement of the points that the line passes through in the form.

Slope (m) = (y2 – y1) / (x2 – x1) = (2 – 1) / (1 – 0) = 1.

## How to Find Slope with Percentage

In some cases it may be necessary to find the value as a percentage. In this case, the percentage of slope must be calculated. In cases where the percentage value of the slope value should be found, the slope rate is multiplied by one hundred.

On the other hand, if the slope value is to be found, the value is multiplied by a thousand, and if it is found to be a degree, the desired value is calculated by multiplying by sixty. If we will formulate the calculation of the slope as a percentage, a degree or a degree;

Slope (m) = [Height (m) / Horizontal Distance (meters)] x (100, 1000 or 60) formula. Often, horizontal distances are given in kilometers (km). If the horizontal distance is given in kilometers (km), the length value is converted to kilometer (000) units by adding three zeros to the given value.

### Example:

If the altitude difference between two points is 50 m and the horizontal distance is 1 km (km), find the slope between two points as a percentage.

Solution: Using the formula given above, we can find slope as a percentage. However, as mentioned earlier, it is necessary to convert the horizontal distance in kilometers to meters.

After converting the value of the horizontal distance to 1 km = 1000 m from the kilometer meter, the data given in the example should be written in place of the form. According to this;

Slope (m) = (50/1000) x 100 = 5.

## How to Find Slope on the Map

Finding a slope in the map is also a fairly common calculation. The scale of the maps, the slope of the geographical shapes, the gradient between the seas and the elevations can be found by calculating the slope on the map. To calculate and find slope on the map, use Slope = Elevation (h) / Length (l) x 100 or 1000 formula.

Below are examples of the slope calculations used in map calculations.

### Example 1:

A person leaving the road by sea level has stopped at a point 2200 meters high. We know the percentage of inclination according to what is known to have traveled a total of 20 kilometers with the vehicle.

### Solution:

The height difference between two points (h) = 2200 – 0 = 2200 meters.

Horizontal distance (L) = 20 kilometers = 20,000 meters (km should be converted to m.)

The slope (m) is calculated as 11 percent of the operation of 2200 x 100/20000.

### Example 2:

A scale of 1/500000 is defined as the distance between two points is 30 cm. If the altitude difference between two points is 900 meters, what is the slope?

### Solution:

In order to solve the problem, firstly it is necessary to find the distance between two points. For this;

Actual Length = Map Length x Scale Share

Actual Length = 30 x 500 000

Actual Length = 15 000 000 cm = 150 000 m

GU = L = 150 000 m and the height (h) is 900 m,

The slope (m) is found to be 6 in the process of 900 x 1000/150 000.

### Example 3:

The ratio of elevation difference to distance between two points in a field gives the gradient between two points. As it is known that the distance between points A and B in the isohips map is 6 km, we can find the gradient between points A and B as a percentage.

### Solution:

For example the L value must first be found for the solution. Elevation differences in isohips are 200 meters. The A point is 0 meters and the B point is 1200 meters high. The altitude difference between points A and B is 1200 meters. The horizontal distance between the two points is 6 km, which is 6000 meters. We can calculate the tilt by typing the found and given values in the form instead.

Slope (m) = 1200 x 100/6000

Slope (m) = 120000/6000

Slope (m) = 20 percent.

### Example 4:

The horizontal distance from a sea level to a mountain peak is 5 km. According to the height of the mountain is 300 meters, we have a slope.

### Solution:

Height (h) = 300 – 0 = 300 meters

Horizontal distance (L) = 5000 meters

Slope (m) = 300 x 1000/5000

Slope (m) = 300000/5000

The slope (m) = 60 in.

### Example 5:

The distance between points A and B is shown as 8 cm on the map. The slope between these two points is 4 percent, the map scale is 1/400 000, and the B point is 200 meters high, we find the height of A point.

### Solution:

First, it is necessary to find the difference between the two points.

Actual Length = Map Length x Scale Share

Actual Length = 8 x 4 = 32 km

The slope is used after the actual length is found.

4 (slope) = Height x 100/32000 (meters)

128 000 = h x 100

Elevation difference (h) = 1280 meters

The height of point A is 200 + 1280 = 1480 meters.

## How to Find Slope of Geometric Slope

The slope (m) is found by dividing the vertical length of the geometry by the vertical triangle length.

Slope (m) = (vertical length) / (horizontal length) formula is calculated.

Here are some examples of finding the geometry tilt calculation.

### Example 1:

The length of a vertical upright triangle is 10 cm and the length of a horizontal side is 15 cm. According to this, what is the slope of the line drawn between two perpendicular edges?

### Solution:

The slope of the line drawn between two points is calculated by dividing the slope by the vertical edge length and the horizontal edge length. Accordingly, the slope of the slope is 10/15 = 0.66.

### Example 2:

If the slope of a ladder standing on a wall is 75 percent and the horizontal distance between the ladder and the wall is 8 meters, how many cm is the height of the point where the top of the ladder intersects the wall?

### Solution:

75% = 75/100. If we write this proportionally, we can express 3k / 4k.

3k = wall height and 4k = 8 m, the height of the point where the top of the ladder intersects the wall is 6 m.

Tangent is used to calculate tilt according to an angle in the triangle. The tangent is calculated by dividing the adjacent vertical edge by the opposite vertical edge.

### Example 3:

| AB | = 3 cm, | BC | = 5 cm and | AC | = 4 cm in length. If C is called α, we have a slope.

The inclination in the direction of the given information can be found with tanα. Accordingly, the slope is calculated by dividing the adjacent perpendicular edge of the opposite perpendicular edge seen by the angle α. As a result, the slope (m) = 75% of the 3/4 operation.

In addition to all this information, you can enter the calculation tool to calculate the tilt with the calculation tool, and then press the calculation button after writing the required information. After the necessary steps, the desired slope will be calculated easily.