Slope Calculator: Gradient, Percent Grade, Angle in Degrees and Ratio for Ramps, Roofs and Roads

Convert a slope between every way of writing it.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose what you know: the rise and run, the percent grade, the angle or the ratio.

Enter the value.

The calculator gives the percent grade, the angle, the decimal gradient, the ratio, the slope length and the rise over a distance.

Formulas used

  • \text{grade} = \frac{\text{rise}}{\text{run}}\times100
  • \theta = \arctan\frac{\text{rise}}{\text{run}}
  • L = \sqrt{\text{run}^2 + \text{rise}^2}

Worked example

With the default numbers in the calculator above:

  1. Percent grade (the rise for every 100 of run): 8.3333 %
  2. Angle above the horizontal: 4.7636 degrees
  3. Gradient as a decimal (rise over run): 0.0833333
  4. Run for every 1 of rise (the ratio 1 in n): 12 (a ratio of 1 in 12)
  5. Rise over the horizontal distance of 12: 1
  6. Length along the slope for that run: 12.0416

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What you know The angle in degrees; The angle above the horizontal 30 degrees.

  1. Percent grade (the rise for every 100 of run): 57.735 %
  2. Angle above the horizontal: 30 degrees
  3. Gradient as a decimal (rise over run): 0.57735
  4. Run for every 1 of rise (the ratio 1 in n): 1.7321 (a ratio of 1 in 1.732)
  5. Rise over the horizontal distance of 12: 6.9282
  6. Length along the slope for that run: 13.8564

Common questions

How do I convert a percent grade to degrees?

Take the inverse tangent of the grade divided by 100. A 10 percent grade is 5.71 degrees.

Is a 100 percent grade vertical?

No. A 100 percent grade rises as much as it runs, which is 45 degrees.

What does a slope of 1 in 12 mean?

It rises 1 unit for every 12 units of horizontal run, which is a grade of 8.33 percent or 4.76 degrees.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Basic trigonometry. Check the slope limits for ramps, roads and drains in the code or standard that applies.

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