{
  "address": "ad1695f6ce19edea9cbc1a28523fc66f",
  "category": "other",
  "question": "What are the percent grade and the angle from horizontal for a rise of 1 over a run of 4?",
  "answer": "grade 25.00%, angle 14.04 degrees",
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  "madeAt": "2026-09-30T22:39:30.722Z",
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  "sources": [
    {
      "label": "Grade percent and slope angle from rise over run",
      "url": null
    }
  ],
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  "source": {
    "kind": "edition_page",
    "value": "Standard geometry/surveying reference (e.g. Coxeter, H.S.M. Introduction to Geometry, 2nd ed., Wiley, 1969, right-triangle trigonometry).",
    "retrieved_utc": "2026-09-30T19:51:00Z"
  },
  "qsha256": "19ea7a514701346e38d6b6118233373b9fc1a18014cc846809db90ef9fa8908f",
  "runOne": null,
  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
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  "method": {
    "name": "Slope grade percent and angle from rise and run",
    "version": "1",
    "source_url_or_file": "methods/slope-grade-and-angle.cjs",
    "sha256_of_method_file": "8176c2a06bfa036223425fd110d865436fedb40d1539db71e9482dbb5b37ea74"
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  "method_deck": {
    "inputs": [
      {
        "name": "rise",
        "type": "number",
        "unit": "length units",
        "required": true,
        "description": "Vertical change.",
        "min": 0
      },
      {
        "name": "run",
        "type": "number",
        "unit": "length units",
        "required": true,
        "description": "Horizontal change.",
        "min": 0
      }
    ],
    "outputs": [
      {
        "name": "grade_percent",
        "unit": "%",
        "description": "Slope expressed as percent grade."
      },
      {
        "name": "angle_degrees",
        "unit": "degrees",
        "description": "Slope expressed as an angle from horizontal."
      }
    ],
    "steps": [
      "Percent grade = (rise / run) * 100.",
      "Angle in degrees = atan(rise / run) converted from radians to degrees.",
      "Round both to 2 decimals."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "rise": 1,
          "run": 4
        },
        "expected": {
          "answer": "grade 25.00%, angle 14.04 degrees"
        },
        "check": "By hand: grade=100*(1/4)=25.00%, a well known road-grade reference value; angle=atan(0.25)=14.0362 degrees rounds to 14.04, cross-checked against a tangent table (tan(14 degrees)=0.2493, close to 0.25)."
      },
      {
        "name": "test vector: 45-degree slope",
        "inputs": {
          "rise": 3,
          "run": 3
        },
        "expected": {
          "answer": "grade 100.00%, angle 45.00 degrees"
        },
        "check": "Equal rise and run is the well known definition of a 45-degree slope (100% grade), since tan(45 degrees)=1 exactly."
      }
    ],
    "disclaimer": null,
    "deck_category": "geometry"
  },
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  "kind": "method",
  "provenanceClass": "own_question",
  "provenance": {
    "schema": "card_provenance/2.0.0",
    "chain": [
      {
        "source": {
          "kind": "edition_page",
          "value": "Standard geometry/surveying reference (e.g. Coxeter, H.S.M. Introduction to Geometry, 2nd ed., Wiley, 1969, right-triangle trigonometry).",
          "retrieved_utc": "2026-09-30T19:51:00Z"
        },
        "sha256": "6ae160f1d3249712bbd5ecb85bac967dd17e07ed788a2ec8ad6741d00b98e768",
        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Slope grade percent and angle from rise and run",
        "why": "the method that computed this answer",
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  }
}