{
  "id": "stopping-distance",
  "version": "9860bcc7df2a",
  "status": "published",
  "name": "Stopping Distance Calculator",
  "question": "How long is the stopping distance?",
  "summary": "Stopping distance calculator: the reaction distance plus the braking distance of a vehicle from its speed, the reaction time and the braking deceleration or road friction, on a level road or a grade.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/stopping-distance-calculator",
  "markdown": "https://www.acalculator.org/physics/stopping-distance-calculator.md",
  "kind": "function",
  "method": "Stopping distance = v × t + v² ÷ (2 × (a + g × G)), with v the speed, t the reaction time, a the braking deceleration (or μ × g), G the grade as a decimal (uphill positive) and g = 9.80665 m/s²; time to stop = t + v ÷ (a + g × G).",
  "assumptions": [
    "Constant speed during the reaction time and constant deceleration while braking (OpenStax §3.4).",
    "The grade adds g × G to the deceleration, as in AASHTO’s braking distance on a grade (which uses g = 32.2 ft/s²)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "v": {
        "title": "Speed",
        "description": "The speed when the driver sees the hazard.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0.01,
        "maximum": 150
      },
      "t": {
        "title": "Reaction time (s)",
        "description": "The seconds from seeing the hazard to braking: 2.5 s in AASHTO road design.",
        "type": "number",
        "minimum": 0,
        "maximum": 10
      },
      "by": {
        "title": "Braking by",
        "description": "Give the braking as a deceleration rate or as a tire-road friction coefficient.",
        "type": "string",
        "enum": [
          "rate",
          "friction"
        ]
      },
      "a": {
        "title": "Deceleration",
        "description": "How fast the vehicle slows while braking: 11.2 ft/s² (3.4 m/s²) in AASHTO road design.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 400
      },
      "au": {
        "title": "Deceleration unit",
        "description": "The unit of the deceleration you type.",
        "type": "string",
        "enum": [
          "fts2",
          "ms2",
          "g"
        ]
      },
      "mu": {
        "title": "Friction coefficient (μ)",
        "description": "Kinetic friction of rubber on the road: about 0.7 on dry concrete and 0.5 on wet concrete.",
        "type": "number",
        "minimum": 0.01,
        "maximum": 2
      },
      "g": {
        "title": "Grade",
        "description": "The slope of the road: positive uphill, negative downhill.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -30,
        "maximum": 30
      }
    }
  },
  "outputs": {
    "total": {
      "label": "Stopping distance",
      "description": "Reaction distance plus braking distance.",
      "format": "quantity",
      "unit": "ft"
    },
    "reactionDistance": {
      "label": "Reaction distance",
      "description": "v × t: the distance covered before the brakes go on.",
      "format": "quantity",
      "unit": "ft"
    },
    "brakingDistance": {
      "label": "Braking distance",
      "description": "v² ÷ (2 × (a + g × grade)): the distance while braking.",
      "format": "quantity",
      "unit": "ft"
    },
    "totalM": {
      "label": "Stopping distance (m)",
      "description": "The stopping distance in metres.",
      "format": "number"
    },
    "totalFt": {
      "label": "Stopping distance (ft)",
      "description": "The stopping distance in feet.",
      "format": "number"
    },
    "time": {
      "label": "Time to stop (s)",
      "description": "t + v ÷ (a + g × grade).",
      "format": "number"
    },
    "decelUsed": {
      "label": "Deceleration used (m/s²)",
      "description": "The braking deceleration plus g × grade, in metres per second squared.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "v": "60 mph",
      "t": 2.5,
      "by": "rate",
      "a": 11.2,
      "au": "fts2",
      "mu": 0.7,
      "g": 0
    },
    "outputs": {
      "total": 172.42971428571428,
      "reactionDistance": 67.056,
      "brakingDistance": 105.37371428571429,
      "totalM": 172.42971428571428,
      "totalFt": 565.7142857142857,
      "time": 10.357142857142858,
      "decelUsed": 3.41376
    },
    "text": "At 60 mph, the stopping distance is 565.7 ft: 220 ft of reaction and 345.7 ft of braking."
  },
  "examples": [
    {
      "given": {
        "v": 13.4112,
        "t": 2.5,
        "by": "rate",
        "a": 11.2,
        "au": "fts2",
        "g": 0
      },
      "expect": {
        "totalFt": 196.42857142857142,
        "reactionDistance": 33.528,
        "brakingDistance": 26.34342857142857
      },
      "source": "TxDOT Roadway Design Manual, 4.11.1 Stopping Sight Distance (2.5 s brake reaction time, 11.2 ft/s² deceleration; Table 4-23: 30 mph 110.3 + 86.4 = 196.7 ft, 60 mph 220.5 + 345.5 = 566.0 ft, from AASHTO’s SSD = 1.47Vt + 1.075V² ÷ a), https://www.txdot.gov/manuals/des/rdw/chapter-4--basic-design-criteria/4-11-sight-distance/4-11-1-stopping-sight-distance.html (retrieved 2026-10-18); FHWA, Self-Enforcing Roadways: A Guidance Report (FHWA-HRT-17-098), Chapter 3 (AASHTO 2011: SSD = 1.47Vt + 1.075V² ÷ a, t = 2.5 s; on a grade d = V² ÷ (30((a ÷ 32.2) ± G))), https://www.fhwa.dot.gov/publications/research/safety/17098/004.cfm (retrieved 2026-10-18); hand calculation in content.mdx: 44 ft/s × 2.5 s = 110 ft, 44² ÷ (2 × 11.2) = 86.43 ft, 196.43 ft (AASHTO’s rounded 1.47 gives 196.7 ft)",
      "tolerance": 1e-12
    },
    {
      "given": {
        "v": 26.8224,
        "t": 2.5,
        "by": "rate",
        "a": 11.2,
        "au": "fts2",
        "g": 0
      },
      "expect": {
        "totalFt": 565.7142857142857,
        "time": 10.357142857142858
      },
      "source": "TxDOT Roadway Design Manual, 4.11.1 Stopping Sight Distance (2.5 s brake reaction time, 11.2 ft/s² deceleration; Table 4-23: 30 mph 110.3 + 86.4 = 196.7 ft, 60 mph 220.5 + 345.5 = 566.0 ft, from AASHTO’s SSD = 1.47Vt + 1.075V² ÷ a), https://www.txdot.gov/manuals/des/rdw/chapter-4--basic-design-criteria/4-11-sight-distance/4-11-1-stopping-sight-distance.html (retrieved 2026-10-18); hand calculation in content.mdx: 88 × 2.5 = 220 ft, 88² ÷ 22.4 = 345.71 ft, 565.71 ft (Table 4-23: 566.0 ft calculated, 570 ft design)",
      "tolerance": 1e-12
    },
    {
      "given": {
        "v": 30,
        "t": 0.5,
        "by": "rate",
        "a": 7,
        "au": "ms2",
        "g": 0
      },
      "expect": {
        "total": 79.28571428571429,
        "reactionDistance": 15,
        "brakingDistance": 64.28571428571429
      },
      "source": "OpenStax, University Physics Volume 1, §3.4 Motion with Constant Acceleration (Equation 3.14, v² = v₀² + 2a(x − x₀); Example 3.10: 30.0 m/s, 0.500 s, 7.00 m/s² dry or 5.00 m/s² wet: 79.3 m or 105 m), https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration (retrieved 2026-10-18): 15.0 m + 64.3 m = 79.3 m",
      "tolerance": 1e-12
    },
    {
      "given": {
        "v": 30,
        "t": 0.5,
        "by": "rate",
        "a": 5,
        "au": "ms2",
        "g": 0
      },
      "expect": {
        "total": 105,
        "brakingDistance": 90
      },
      "source": "OpenStax, University Physics Volume 1, §3.4 Motion with Constant Acceleration (Equation 3.14, v² = v₀² + 2a(x − x₀); Example 3.10: 30.0 m/s, 0.500 s, 7.00 m/s² dry or 5.00 m/s² wet: 79.3 m or 105 m), https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration (retrieved 2026-10-18): 15.0 m + 90.0 m = 105 m",
      "tolerance": 1e-12
    },
    {
      "given": {
        "v": 27.77777777777778,
        "t": 1.5,
        "by": "friction",
        "mu": 0.7,
        "g": 0
      },
      "expect": {
        "total": 97.86795706448017,
        "decelUsed": 6.864655
      },
      "source": "hand calculation in content.mdx: a = 0.7 × 9.80665 = 6.864655 m/s²; (250/9) × 1.5 + (250/9)² ÷ (2 × 6.864655); μ from OpenStax College Physics 2e Table 5.1 (rubber on dry concrete, kinetic 0.7)",
      "tolerance": 1e-12
    },
    {
      "given": {
        "v": 26.8224,
        "t": 2.5,
        "by": "rate",
        "a": 11.2,
        "au": "fts2",
        "g": -3
      },
      "expect": {
        "brakingDistance": 115.3112981395937,
        "decelUsed": 3.1195605
      },
      "source": "FHWA, Self-Enforcing Roadways: A Guidance Report (FHWA-HRT-17-098), Chapter 3 (AASHTO 2011: SSD = 1.47Vt + 1.075V² ÷ a, t = 2.5 s; on a grade d = V² ÷ (30((a ÷ 32.2) ± G))), https://www.fhwa.dot.gov/publications/research/safety/17098/004.cfm (retrieved 2026-10-18); hand calculation in content.mdx: a = 3.41376 − 0.03 × 9.80665 = 3.1195605 m/s², 26.8224² ÷ (2 × 3.1195605) = 115.31 m = 378.3 ft (AASHTO’s grade form with 32.2 ft/s² gives 377.6 ft)",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §3.4 Motion with Constant Acceleration: Equation 3.14, v² = v₀² + 2a(x − x₀); Example 3.10, How Far Does a Car Go? (30.0 m/s, 0.500 s, 7.00 or 5.00 m/s²: 79.3 m or 105 m), retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration",
    "FHWA, Self-Enforcing Roadways: A Guidance Report (FHWA-HRT-17-098), Chapter 3: AASHTO 2011 stopping sight distance SSD = 1.47Vt + 1.075V² ÷ a with t = 2.5 s, and braking distance on a grade V² ÷ (30((a ÷ 32.2) ± G)), retrieved 2026-10-18. https://www.fhwa.dot.gov/publications/research/safety/17098/004.cfm",
    "Texas Department of Transportation, Roadway Design Manual, 4.11.1 Stopping Sight Distance: 2.5 s brake reaction time, 11.2 ft/s² deceleration; Table 4-23, retrieved 2026-10-18. https://www.txdot.gov/manuals/des/rdw/chapter-4--basic-design-criteria/4-11-sight-distance/4-11-1-stopping-sight-distance.html",
    "OpenStax, College Physics 2e, §5.1 Friction: Table 5.1, rubber on dry concrete μk = 0.7, on wet concrete μk = 0.5, retrieved 2026-10-18. https://openstax.org/books/college-physics-2e/pages/5-1-friction",
    "NIST, CODATA 2022: standard acceleration of gravity g = 9.80665 m/s² (exact), retrieved 2026-10-18. https://physics.nist.gov/cgi-bin/cuu/Value?gn",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 mph = 0.44704 m/s, 1 ft = 0.3048 m, retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "speed",
    "acceleration",
    "velocity"
  ],
  "changelog": []
}