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Slope / Grade Calculator

How do I calculate slope?

How it is calculated

Slope is expressed three ways from the vertical rise and horizontal run: grade = rise / run × 100, angle = arctan(rise / run) in degrees, and ratio = 1 : (run / rise). Rise and run must use the same unit. The run must be greater than zero, because it is the horizontal distance and not the length of the sloping surface. A negative rise means a downhill slope and gives a negative grade and angle, while the ratio is shown as an absolute value. If the rise is zero the slope is flat and the ratio is shown as a dash. Note that a 100% grade is 45°, not 90°, because the grade grows without limit as the slope approaches vertical.

Worked example

A ramp climbs 1 unit over a horizontal run of 12 units. Grade = 1 / 12 × 100 = 8.33%. Angle = arctan(0.0833) ≈ 4.76°. Ratio = 1 : (12 / 1) = 1:12.00. All three values describe the same incline.

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Common mistakes

  • Measuring along the sloping surface as the run instead of the horizontal distance.
  • Using different units for rise and run, such as rise in centimetres and run in metres.
  • Believing that a 100% grade is vertical; it is a 45° incline.
  • Reading a 1:12 ratio as 1/12 of an angle or as 12%, instead of about 8.33%.
  • Forgetting the sign: a negative rise is a descent and the grade and angle are negative.

About this calculator

This calculator turns a vertical rise and horizontal run into three equivalent ways of expressing slope: a percentage grade (rise divided by run, times 100), an angle in degrees (the arctangent of rise over run), and a simplified ratio. The three describe the exact same incline, but different fields default to different units, so being able to convert between them on demand avoids a lot of confusion.

Road signs and cycling apps typically show grade as a percentage, construction and engineering drawings often specify slope as a ratio (like 1:12 for a wheelchair ramp) or in degrees, and hikers comparing trail steepness may see either. Builders use it to check that a ramp, roof or drainage slope meets a code requirement expressed in a different unit than the one they measured on site.

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Comments (1)

  • Editorial team

    Roof pitch is usually quoted as rise in 12, and you can enter it directly: rise 6 and run 12 gives a 50% grade, an angle of 26.57° and a ratio of 1:2.00. The run is the horizontal distance, so if you measured along the sloping surface with a tape, convert it before typing. A negative rise shows a descent. Are you checking a roof, a ramp or a road, and what limit do you have to meet? Post your numbers and what you are building.

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