This elevation grade calculator determines and expresses, in four different ways, the slope of an earthen surface. It may be given in terms of the angle of elevation from the horizontal plane, in terms of the percentage of deviation from the horizontal line, or simply in terms of the ratio of its "rise to run" or "unit rise in run". To calculate the slope of a line and to learn more about slopes in general, you can check our slope calculator. To learn more about how to find the slope of the terrain (or of the ground in general), keep reading.
What is elevation grade?
Elevation grade (or slope) is the steepness, or degree of inclination, of a certain area of land. It can simply be the steepness between two specific points in a given area, the average of an area's gradual change in steepness, or an erratic variation in the elevation of the ground. We usually measure the ground's elevation as its altitude above sea level. Land surveyors and engineers are generally the ones who measure and record these elevations using surveying equipment and tools.
Why do we need to know a particular terrain's elevation grade?
Knowing an area's elevation grade offers many advantages over not knowing it at all. It may also be a requirement to proceed with other activities, such as construction or irrigation. Here are some examples of the importance and advantages of knowing the grade of a particular area:
- Knowing the area's elevation grade helps in the construction of roads. We use it, for example, in the vertical curve formula. Very steep terrain may require roads to be laid out in a zig-zag pattern for safer ascending and descending. Engineers can design a cutting-and-filling procedure for less steep terrain to decrease the slope. Cutting-and-filling is where soil from the higher part of the slope is transferred to the lower part to reduce its grade.
- Determining the elevation grade also helps when building retaining walls. Retaining walls support the earth above it to keep it from eroding downhill. Therefore a retaining wall can be constructed against a cliff to avoid landslides.
If you wish to learn more about retaining walls, retaining walls check out our retaining wall calculator. - Knowing the terrain's angle of elevation also helps when assessing a land's ability to support a structure. Building structures on a sloping area may require some additional foundation to avoid failing.
- Elevation grade also helps when examining the flow of water from higher elevations to see if the land can be irrigated without pumps.
- and so much more. :)
How to calculate for the elevation grade and angle of elevation?
We calculate terrain grade in the same way we calculate the slope of a line. The slope of a given line requires the coordinates of its endpoints. The slope is the quotient of the change in the values of y and the change in the values of x. As an equation, it looks like this:
slope=x2−x1y2−y1
In the mathematical community, these changes in x and y values have nicknames. We call the change in the values of y "rise", since it is along the vertical axis. On the other hand, we call the change in the x values the "run", since it runs along the horizontal axis. This relationship gives us the popular equation that you might have already heard before: "slope is equal to rise over run." Or:
slope=runrise
Aside from this, we can also express grade in terms of angles. With this, we would need the help of trigonometry to obtain the angle. We are interested in getting the angle between the horizontal plane and the plane of incline. We call an angle that goes up from the horizontal line an "angle of elevation", while those that go down are the "angle of declination." We can determine this angle using the arctan function. The arctan function is the inverse of the tangent function with the slope as its article. In equation form, it looks like this:
Grade(angle)=arctanrunrise
If you don't have a calculator with this trigonometric function, don't worry, we already have it incorporated into our elevation grade calculator above. If you want to learn more about the other essential trigonometric functions, you can check our trigonometric functions calculator and play around with angles.
Aside from expressing grade using ratios and angles, we can also determine it in terms of percentages - we only have to multiply its ratio value by 100 to get it. That is where the equation below comes from. A grade of one hundred percent means that the slope's rise equals its run. The resulting slope for this value is considered neither steep nor flat but instead of an average grade. Here is its equation form:
Grade(percentage)=runrise⋅100%
We equipped our elevation grade calculator with all these equations, so it can give you all the answers you need every time you input a value for any variable. You can set the grade and determine the horizontal distance required to obtain the required change in a vertical distance, as well as obtain the angle of elevation.
Understanding elevation grade values
Grade values are pretty easy to understand. Terrain grades less than 1 (terrain grade <1) mean the slope is gentle. On the other hand, terrain grades that are greater than one (terrain grade >1) indicate that the terrain is steep. In terms of angle of elevation, angles above 45 degrees are the steep ones, whereas angles below 45 degrees are relatively flat.
How to determine the "rise" and "run."
We can get the "run", or the change in the horizontal distance, by using a measuring tape. We will have to pull the tape taut to get a precise measurement. However - not pulling it tight will provide a higher value than this actual value because the tape will sag due to gravity.
On the other hand, we can get the vertical distance by using optical devices, such as a surveyor's transit paired with a leveling rod. A surveyor's transit has an inbuilt telescope that can be rotated laterally or vertically over a tripod. Focusing it on the leveling rod (which is like a huge ruler) will give a reading. We can translate this reading into the elevation between the leveling rod and the transit. A surveyor's transit also has distinctive markings on its view that make it also able to measure horizontal distances when paired with a leveling rod.
We can also use a tool like a clinometer, which can directly provide the angle of elevation between two points. A clinometer is like a mini telescope with a protractor attached to its side. Other more sophisticated digital gadgets can now help obtain the slope of a particular surface. A smartphone, if equipped with adequate hardware like gyroscopic sensors, can accurately provide you with a surface's slope when you lay your it on the slope.
More about terrains
We can plot the averages of the terrain grades to compose a contour map. A contour map is a topographic map that gives viewers an overview of what a specific area's terrain is like. Vertical exaggeration is often needed to emphasize certain terrain features, such as the height of the mountains or volcanoes.
To learn more about vertical exaggeration, check out our vertical exaggeration calculator.
FAQ
What's the elevation grade of the steepest road in the world?
Baldwin Street, New Zealand, has an impressive grade of about 0.35, corresponding to a horizontal length of 2.86 m for each vertical meter. The short 350 m long street is a real challenge to walk up!
A grade of 0.35 correspond to an angle of:angle = arctan(rise/run) = arctan(1/2.86) = 19.27°.
What's the difference between slope as an angle and slope as a percentage?
The formula gives the slope defined as an angle:slope (angle) = arctan(rise/run)
Where the rise is the vertical distance and the run is the horizontal distance of a slope.
To calculate the slope as a percentage, take the argument of the arctangent function and multiply it by 100:slope (percentage) = rise/run × 100
Which angle corresponds to a slope of 100%?
Rather counterintuitively, a slope of 100% corresponds to an angle of 45°. However, consider that the slope is the result of the equation:slope = rise/run
Where
riseis the vertical distance; andrunis the horizontal one.
A slope where each horizontal meter corresponds to a vertical meter has slope 1, which multiplied by 100 returns the value 100%.
How do you calculate the grade of a road?
Let's assume that the road has 12 meters of rise for every 200 meters of run. The grade would be 0.06. To calculate the grade of a road with:
rise = 12 m; andrun = 200 m:
- Compute the ratio between rise and run:
grade = rise/run = 12/200 = 0.06 - If you want to know the angle of the slope, input the value in the arctangent function:
slope (angle) = arctan(rise/run) = arctan(12/200) = 3.43° - If you want to know the slope as a percentage, multiply the ratio by
100:slope (percentage) = 100 × rise/run = 6%.
FAQs
How do you calculate elevation grade? ›
An easy-to-remember equation for finding change in elevation as a decimal is “rise over run,” meaning the rise (the change in vertical distance) divided by the run (the change in horizontal distance).
What is a 2% grade? ›A 100 percent grade would be equivalent to a 45-degree angle. The elevation grade calculator can be used to determine the vertical percentage grade change on highways located in mountain terrains or an inclined plane.
How steep is a 20 percent grade? ›In surveying 20% is interpreted as 20% of a right angle (i.e. a brick wall) and so would be 18 degrees.
How steep is a 3 percent grade? ›| Degrees | Percentage (%) | Permillage (‰) |
|---|---|---|
| 0.2865° | 0.5% | 5‰ |
| 0.1719° | 0.3% | 3‰ |
| 0.1146° | 0.2% | 2‰ |
| 0.0868° | 0.1515% | 1.515‰ |
Moderate slopes: 10 - 15 % gradient. Steep slopes: 16 - 30 % gradient. Extremely steep slopes: 31 - 60% gradient. Excessively steep slopes: > 60% gradient.
How many inches per foot is a 1% slope? ›1% as a decimal is 0.01 and hence the slope is 0.01. That means for a run of pipe of a certain length the rise must be 0.01 times the length. Thus for you example, since the length of the run is 80 feet which is 80 × 12 = 960 inches the rise must be 0.01 × 960 = 9.6 inches.
Is a 6% grade steep? ›The slope distance is 100.2 ft. for a run of 100 ft. As you can see from this example, in a forest, a six percent slope would be considered a gentle slope.
How many degrees is a 6% grade? ›A road with a 6% grade rises at an angle of 3.43∘ relative to the horizon.
How to calculate a grade? ›To calculate your current letter grade, divide the points earned by the points possible. Using the example, 380 divided by 536 equals 0.71. To turn this into a percentage multiply the answer by 100 or move the decimal point over two places. This equals 71 or 71%.
What is a 40% grade? ›
| Letter Grade | Percentage Range | Mid-Range |
|---|---|---|
| D+ | 55% to 59% | 57.5% |
| D | 50% to 54% | 52.5% |
| E | 40% to 49% | 45% |
| F | 0% to 39% | 20% |
| Letter Grade | Grade Points | Numerical Grade |
|---|---|---|
| A | 4.0 | 94–96 |
| A- | 3.7 | 90–93 |
| B+ | 3.3 | 87–89 |
| B | 3.0 | 84–86 |
A+ (90% and above): Outstanding work that demonstrates independent thought and critical reflection and has an excellent research question as well as systematic and persuasive answers to this question.
Is a 15% slope steep? ›Less than 10% incline is considered slight and is the easiest to build on. Around 11-20% is considered moderate and gradients above 20% are considered “steep”.
Is a 30% slope steep? ›Article content. 30 Degrees: This has enough drop to cause you to slip and slide if you fall. It's average for a steep section in a blue (intermediate) run. Will cause adrenaline increases in most average skiers.
What is the steepest road grade allowed? ›While federal law requires interstate highways to have a maximum grade of six percent, state highways are a different story. Pennsylvania maintains a highway with a 14.5-degree slope, and California is even steeper, with a highway at a whopping 26-degree grade.
Is a 5% gradient steep? ›1-3%: Slightly uphill but not particularly challenging. A bit like riding into the wind. 4-6%: A manageable gradient that can cause fatigue over long periods. 7-9%: Starting to become uncomfortable for seasoned riders, and very challenging for new climbers.
Is a 4% grade steep? ›Steep grade means a grade exceeding seven percent (7%).
How much fall is in a 2% slope? ›The fact that the pipe is installed with a 2% grade means that the drop is 2% of the length.
Is a 12% slope steep? ›
Steep Slope: 10/12 and above
Any pitch that's at least 10/12 (39.81 degrees) is considered steep slope. This includes 10 over 12, 11 over 12, 12 over 12, and pitch where the rise is greater than the run.
How Steep of a Driveway Is Too Steep? You shouldn't have a driveway slope grade greater than 20%, but ideally, it shouldn't go over 12%. What that means is the incline shouldn't be higher than 12 feet for every 100 feet of length.
How steep is a 30 degree grade? ›30 degrees is equivalent to a 58% grade which is another way to describe the magnitude of a slope.
How much is a 2% slope? ›Answer and Explanation: A 2% slope means that a surface (such as a road or a train track) change in elevation by 2 units over a run of 100 units. This means that a 2% slope is present when the rise changes by 2 meters (or feet) over a run of 100 metres (or feet).
How many inches per foot is a 4 slope? ›Slope Ratio
A roof that rises 4 inches for every 1 foot or 12 inches of run is said to have a “4 in 12” slope. If the rise is 6 inches for every 12 inches of run, then the roof slope is “6 in 12.”
Related: Welsh street named steepest in world, edging out Pittsburgh's Canton Ave. Canton Avenue in Pittsburgh's Beechview neighborhood is a monster hill with a 37% grade -- a struggle for walkers and drivers alike.
How steep is a 7% grade? ›If you climb or descend 370 feet, that's a 7% grade, or if you climb or descend 264 feet that's a 5% grade. Carried to it's extreme, a 30% grade means you go up or down almost 1600 feet in a mile.
What is the steepest road in the United States? ›Pittsburgh is a city known for its many incredibly steep streets, but one stands above them all as the steepest street in the United States: Canton Avenue. Canton Avenue is located in the Beechview neighborhood, only a couple of miles south of downtown Pittsburgh in Allegheny County, PA.
How do you find a 2% slope? ›To calculate percent slope, divide the difference between the elevations of two points by the distance between them, then multiply the quotient by 100. The difference in elevation between points is called the rise. The distance between the points is called the run. Thus, percent slope equals (rise / run) x 100.
What is a 2% slope? ›Answer and Explanation: A 2% slope means that a surface (such as a road or a train track) change in elevation by 2 units over a run of 100 units. This means that a 2% slope is present when the rise changes by 2 meters (or feet) over a run of 100 metres (or feet).
What is the slope of 1 8 inch per foot? ›
Just over 1%. Tiers are expressed as a percentage of ascents divided by miles. Dividing 1/8 by 12 (inches per foot) is 0.0104, which is 1.04%.
How do I calculate my grade manually? ›To calculate your current letter grade, divide the points earned by the points possible. Using the example, 380 divided by 536 equals 0.71. To turn this into a percentage multiply the answer by 100 or move the decimal point over two places. This equals 71 or 71%.
How is a grade Calculated? ›The course grade is determined by the sum of the student's item scores divided by the total points possible. Categories only - Categories are used to group gradebook items, where items are assigned a relative weight.
What is a grade calculation? ›A grade calculation is a formula used to determine grades, based on other grade items. Note that this is not the same as Calculated question types.
What does 1 in 20 slope mean? ›Minimum slope: 1:20, meaning you will have 20 units of horizontal length (run) by 1 unit of vertical length (rise).
What does a 3 to 1 slope mean? ›- are expressed as "1 in x". And "1 in 3" does one unit vertically for every three horizontally. 1 in 1 would be 45 degrees.
What does 1 in 10 slope mean? ›In geometry, in means for every ten units of horizontal distance crosses there is unit of vertical drop or rise.
How steep is 8 grade? ›Suppose you climb eight feet as you go forward 100 feet. That's an 8% gradient. Or suppose you go up 100 feet as you go forward 100 feet. That's a 100% gradient, and is also going to be pretty hard to get your tires to not slip a little bit.
What is 4 to 1 slope grading? ›With a 4 to 1 slope, usually expressed as 4:1, the pond extends 4 feet for every 1 foot of depth, regardless of the pond's size.