# How do I convert a gradient to degrees?

Hello...

I am curious as to how I convert a gradient (in the form 1:10) into degrees.

For example, if a road is to have a slope of 1:10, then how to I convert this into degrees?

Thanks for all answers

### 9 Answers

- mikeoxley242Lv 51 decade agoFavourite answer
On the roads, the gradient or grade is the vertical rise divided by the horizontal run. So the angle from the horizontal is the arctangent of the (rise divided by the run).

For trains, the gradient is the verical rise divided by the length of the slope, so the angle from the horizontal is the arcsin of the (rise divided by the slope).

For small angles, the difference is negligible.

Source(s): http://www.bookrags.com/research/grades-highway-mm... http://www.ordnancesurvey.co.uk/oswebsite/educatio... http://math.colorado.edu/~rmg/roads/records.html - 5 years ago
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RE:

How do I convert a gradient to degrees?

Hello...

I am curious as to how I convert a gradient (in the form 1:10) into degrees.

For example, if a road is to have a slope of 1:10, then how to I convert this into degrees?

Thanks for all answers

Source(s): convert gradient degrees: https://bitly.im/gP1HM - rrabbitLv 41 decade ago
A gradient of 1 : 10 means that as you travel 10 units along the road you rise 1 unit vertically. From basic trigonometry, this means that sin(a) = 1/10 where a is the angle to the horizontal.

So to convert gradient g to degrees

a = arcsin(1/g)

(you can use any scientific calculator, where arcsin may be called inv sin or sin^-1).

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- 1 decade ago
Very simple: The gradient given in the form a:b means simply that the RATIO of the vertical component to the horizontal component is a: b or a/b. Therefore, the tangent of the angle made by this slope to the horizontal is also given by the ration a/b. To find the angle in degrees, all you have to do is read the value arc(tan) of a/b or in your example 1/10 = 0.1

which gives an angle of 5.71 deg

- Anonymous5 years ago
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In road terms the grade is the percent rise, so a grade of 22 is a 22% rise. This means the rise/run is 22/100= .22, which is the tangent of the angle. So tan ^-1(.22)=12.4 degrees

- Anonymous1 decade ago
Simply find the arctangent (inverse tangent) of the ratio. E.g. for your question, find arctan(1/10). This is written as tan^-1 on your calculator.