{
  "slug": "grade-degrees-converter",
  "title": "Grade to Degrees Converter",
  "category": "Conversions",
  "category_slug": "conversions",
  "tier": 2,
  "summary": "Convert incline between percent grade and degrees, with rise-over-run shown both ways.",
  "description": "This converter translates incline between its two common notations: percent grade (rise divided by horizontal run, times 100) and degrees of angle. Enter a grade to get the angle via degrees = atan(grade ÷ 100), or enter an angle — leave grade at 0 — to get the percent via grade = tan(angle) × 100. The result also reports the rise in metres per 100 m of horizontal run and the rise-to-run ratio. Treadmill incline displays, road signs, and trail gradients almost always use percent, while drawings and some equipment use degrees; the two scales are related through the tangent, not proportionally.",
  "page_url": "https://fitmetriclab.com/en/tools/conversions/grade-degrees-converter/",
  "api_url": "https://fitmetriclab.com/api/tools/grade-degrees-converter.json",
  "formula": {
    "id": "grade_degrees_converter",
    "expression": "\\theta = \\arctan\\!\\left(\\frac{g}{100}\\right), \\quad g = \\tan(\\theta) \\times 100",
    "variables": [
      {
        "symbol": "\\theta",
        "description": "Slope angle in degrees"
      },
      {
        "symbol": "g",
        "description": "Percent grade"
      }
    ]
  },
  "inputs": [
    {
      "id": "grade_pct",
      "label": "Grade",
      "type": "number",
      "unit": "%",
      "default": 10,
      "min": 0,
      "max": 100,
      "step": 0.1
    },
    {
      "id": "degrees",
      "label": "Angle",
      "type": "number",
      "unit": "°",
      "default": 0,
      "min": 0,
      "max": 45,
      "step": 0.1
    }
  ],
  "worked_example": {
    "inputs": {
      "grade_pct": 10,
      "degrees": 0
    },
    "expected_output": "5.71°"
  },
  "result_summary_template": "A grade of {grade_pct}% corresponds to an angle of approximately {result}, rising {grade_pct} m per 100 m of horizontal run.",
  "methodology": "Degrees = atan(grade ÷ 100) × 180 ÷ π, where grade is percent grade (rise ÷ horizontal run × 100). In the reverse direction, grade = tan(degrees × π ÷ 180) × 100. Rise per 100 m of horizontal run equals the percent grade read as metres; the rise-to-run ratio is 1 : (100 ÷ grade). A non-zero grade input takes precedence; a grade of 0 derives the conversion from the angle input.",
  "sources": [
    {
      "label": "ACSM's Guidelines for Exercise Testing and Prescription — metabolic equations using fractional treadmill grade. American College of Sports Medicine.",
      "url": "https://acsm.org/education-resources/books/guidelines-exercise-testing-prescription/"
    },
    {
      "label": "Compendium of Physical Activities — walking and running entries by grade. Accessed 2026.",
      "url": "https://pacompendium.com/"
    }
  ],
  "faqs": [
    {
      "question": "Is a treadmill incline of 10 the same as 10 degrees?",
      "answer": "No. Consumer and commercial treadmills display incline in percent grade, so a setting of 10 means a 10% slope — 10 m of rise per 100 m of horizontal run — which is an angle of only 5.71°. A true 10° tilt would be a 17.6% grade, beyond the maximum of most machines. The percent convention matches how road gradients are signed and how the ACSM metabolic equations expect incline to be entered."
    },
    {
      "question": "Why is 45 degrees equal to 100% grade and not 45%?",
      "answer": "Percent grade is the tangent of the angle times 100, and tan(45°) = 1, so rise equals run at exactly 100%. The two scales are not proportional: doubling the angle more than doubles the grade once slopes get steep. A 45% grade corresponds to 24.2°, and grades above 100% remain far from vertical — a 60° slope is a 173% grade, and the percent figure runs to infinity as the angle approaches 90°."
    },
    {
      "question": "Can I just multiply percent grade by 0.57 to get degrees?",
      "answer": "As a shortcut it holds up surprisingly well on shallow slopes. The small-angle approximation makes 1% ≈ 0.573°, so 10% estimates as 5.73° against a true 5.71°. By 20% the shortcut gives 11.46° against a true 11.31°, and at 45% it gives 25.8° against 24.2° — the error grows with steepness because the tangent curve bends away from linear. The converter applies the exact inverse tangent, so no approximation error is carried into the output."
    },
    {
      "question": "Should grade be measured against horizontal distance or distance travelled?",
      "answer": "The strict definition divides rise by horizontal run, which corresponds to the tangent of the slope angle. Many GPS devices and route profiles divide by distance along the slope instead, which corresponds to the sine and reads slightly lower. At typical road and treadmill grades the difference is a fraction of a percent of the value; on very steep trails it becomes noticeable — a 30% strict grade would read about 28.7% by the along-slope method."
    },
    {
      "question": "What does the rise-to-run ratio in the output mean?",
      "answer": "It expresses the slope as 1 unit of vertical rise per so many units of horizontal run — the notation used in building codes, ramp specifications, and railway engineering. A 10% grade is 1 : 10, meaning one metre up for every ten metres forward. Smaller second numbers mean steeper slopes: 1 : 6.7 for a 15% grade, 1 : 1 at 45°. The ratio carries the same information as percent grade, arranged for quick judgement of steepness."
    }
  ],
  "related_tools": [
    {
      "slug": "treadmill-pace",
      "title": "Treadmill Pace Converter",
      "api_url": "https://fitmetriclab.com/api/tools/treadmill-pace.json",
      "page_url": "https://fitmetriclab.com/en/tools/running/treadmill-pace/"
    },
    {
      "slug": "elevation-pace",
      "title": "Elevation-Adjusted Pace Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/elevation-pace.json",
      "page_url": "https://fitmetriclab.com/en/tools/running/elevation-pace/"
    },
    {
      "slug": "calories-walking",
      "title": "Calorie Burn — Walking",
      "api_url": "https://fitmetriclab.com/api/tools/calories-walking.json",
      "page_url": "https://fitmetriclab.com/en/tools/energy-expenditure/calories-walking/"
    }
  ],
  "last_updated": "2026-08-08",
  "price": {
    "value": 0,
    "currency": "USD"
  },
  "runs_in_browser": true,
  "disclaimer": "Educational estimate produced from a published formula. Not medical, nutritional, or training advice. Calculations are deterministic — apply the formula to the inputs to reproduce the result."
}