Quick answer

Percent = tan(angle) x 100; angle = arctan(percent/100).

Formula

  • % = tan(angle) x 100
  • angle = arctan(% / 100)
  • rise/run = % / 100

Introduction

Plans may show 6% grade while the rotary laser speaks in degrees. The Slope Percentage Calculator displays both to reduce translation errors.

Ground definitions in what is slope percentage help before you convert.

Practice numbers in slope percentage examples after you read the conversion rules here.

Percent vs degrees in practice

Highway standards often cap percent grade. Operators still set blades using slope indicators that may read in degrees.

Roofing documents mix pitch-in-12, percent, and degrees depending on the audience. Conversions must be explicit.

Surveying exports may list percent slope from DEM processing while field crews discuss degrees at the instrument.

Small percent changes near level ground translate to tiny angle changes, but near 45 degrees both units climb quickly.

Formula and relationships

  • % = tan(angle) x 100
  • angle = arctan(%/100)

Roof contexts: roof pitch to percentage.

Road contexts: grade percentage calculator.

Rise-run basics: rise over run calculator.

Step-by-step guide

  1. Write the percent as a decimal. Divide by 100.
  2. Apply arctan. Result is angle in radians; convert to degrees.
  3. Or start from degrees. tan(angle) x 100 gives percent.
  4. Check with rise and run. Recompute percent from measurements to confirm.

Reference pairs

5% is about 2.86 degrees. 10% is about 5.71 degrees. 15% is about 8.53 degrees. 100% is 45 degrees.

Use slope percentage formula when you need rise solved from angle.