{
  "id": "treadmill-incline",
  "version": "c98512977003",
  "status": "published",
  "name": "Treadmill Incline Calculator",
  "question": "What does treadmill incline add?",
  "summary": "Computes the distance, elevation gain, oxygen cost, METs and calories of a treadmill walk or run at an incline with the ACSM metabolic equations, and the flat speed with the same effort.",
  "category": "sports",
  "subcategory": "fitness",
  "url": "https://www.acalculator.org/sports/treadmill-incline-calculator",
  "markdown": "https://www.acalculator.org/sports/treadmill-incline-calculator.md",
  "kind": "function",
  "method": "S = speed in m/min, G = incline ÷ 100. Walking VO2 = 0.1S + 1.8SG + 3.5; running VO2 = 0.2S + 0.9SG + 3.5. kcal/min = VO2 × kg ÷ 1,000 × 5.",
  "assumptions": [
    "The ACSM equations estimate the oxygen cost of steady treadmill exercise for an average adult; your own cost may differ.",
    "Elevation gain is belt distance × grade, as treadmill grade is defined.",
    "5 kcal per liter of oxygen and 1 MET = 3.5 ml/kg/min."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "units": {
        "title": "Units",
        "description": "US (mph, pounds, miles, feet) or metric (km/h, kilograms, kilometers, meters).",
        "type": "string",
        "enum": [
          "us",
          "metric"
        ]
      },
      "gait": {
        "title": "Walking or running",
        "description": "Which ACSM equation to use: walking (up to about 3.7 mph) or running (above 5 mph).",
        "type": "string",
        "enum": [
          "walk",
          "run"
        ]
      },
      "v": {
        "title": "Speed (mph)",
        "description": "The treadmill speed in miles per hour.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 20
      },
      "vk": {
        "title": "Speed (km/h)",
        "description": "The treadmill speed in kilometers per hour.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 30
      },
      "g": {
        "title": "Incline (%)",
        "description": "The treadmill grade in percent: rise per 100 units of belt travel.",
        "type": "number",
        "minimum": 0,
        "maximum": 40
      },
      "t": {
        "title": "Time (minutes)",
        "description": "How long you walk or run, in minutes.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 1440
      },
      "wt": {
        "title": "Body weight (lb)",
        "description": "Your body weight in pounds, for calories.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 2200
      },
      "wtk": {
        "title": "Body weight (kg)",
        "description": "Your body weight in kilograms, for calories.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "kcal": {
      "label": "Calories",
      "description": "Total energy: kcal per minute × minutes.",
      "format": "number"
    },
    "gain": {
      "label": "Elevation gain",
      "description": "Distance × grade, in feet (US) or meters (metric).",
      "format": "number"
    },
    "distance": {
      "label": "Distance",
      "description": "Speed × time, in miles (US) or kilometers (metric).",
      "format": "number"
    },
    "vo2": {
      "label": "Oxygen cost (ml/kg/min)",
      "description": "The ACSM estimate of oxygen uptake.",
      "format": "number"
    },
    "mets": {
      "label": "METs",
      "description": "Oxygen cost ÷ 3.5.",
      "format": "number"
    },
    "kcalMin": {
      "label": "Calories per minute",
      "description": "Oxygen cost × body weight in kg ÷ 1,000 × 5 kcal per liter.",
      "format": "number"
    },
    "flat": {
      "label": "Same effort on the flat",
      "description": "The speed at 0% incline with the same oxygen cost, in mph or km/h.",
      "format": "number"
    },
    "range": {
      "label": "Equation range",
      "description": "Whether the speed is inside the range the chosen ACSM equation was built for.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "units": "us",
      "gait": "walk",
      "v": 3,
      "vk": 5,
      "g": 10,
      "t": 30,
      "wt": 160,
      "wtk": 70
    },
    "outputs": {
      "kcal": 283.3771085393741,
      "gain": 792,
      "distance": 1.5,
      "vo2": 26.030816,
      "mets": 7.437376,
      "kcalMin": 9.445903617979136,
      "flat": 8.4,
      "range": "Inside the equation’s range"
    },
    "text": "About 283 kcal and 792 of climb over 1.5."
  },
  "examples": [
    {
      "given": {
        "units": "us",
        "gait": "walk",
        "v": 3,
        "g": 10,
        "t": 30,
        "wt": 160
      },
      "expect": {
        "kcal": 283.3771085393741,
        "gain": 792,
        "distance": 1.5,
        "vo2": 26.030816,
        "mets": 7.437376,
        "kcalMin": 9.445903617979136,
        "flat": 8.4,
        "range": "Inside the equation’s range"
      },
      "source": "hand calculation in content.mdx: S = 3 × 1,609.344 ÷ 60 = 80.4672 m/min; VO2 = 8.04672 + 14.484096 + 3.5 = 26.030816; Python 3: Fraction; Moore CC et al., Development of a Cadence-Based Metabolic Equation for Walking, Med Sci Sports Exerc 2021;53(1):165–173 (ACSM walking equation VO2 = 0.1·speed + 1.8·speed·grade + 3.5; speed in m/min, grade as a decimal; most accurate at 1.9–3.7 mph), https://pmc.ncbi.nlm.nih.gov/articles/PMC7896743/; Compendium of Physical Activities, Unit conversions (1 MET = 3.5 ml/kg/min; L/min × 5 = kcal/min), https://pacompendium.com/unite-conversions/"
    },
    {
      "given": {
        "units": "metric",
        "gait": "run",
        "vk": 10,
        "g": 2,
        "t": 20,
        "wtk": 70
      },
      "expect": {
        "vo2": 39.833333333333336,
        "kcalMin": 13.941666666666666,
        "kcal": 278.8333333333333,
        "gain": 66.66666666666667,
        "flat": 10.9
      },
      "source": "hand calculation in content.mdx: S = 10,000 ÷ 60 = 166.67 m/min; VO2 = 33.33 + 3 + 3.5 = 39.83; Python 3: Fraction; Koutlianos N et al., Indirect estimation of VO2max in athletes by ACSM’s equation: valid or not? Hippokratia 2013;17(2):136–140 (VO2 = 0.2·S + 0.9·S·G + 3.5; for speeds above 5.0 mph), https://pmc.ncbi.nlm.nih.gov/articles/PMC3743617/; Compendium of Physical Activities, Unit conversions (1 MET = 3.5 ml/kg/min; L/min × 5 = kcal/min), https://pacompendium.com/unite-conversions/"
    },
    {
      "given": {
        "units": "us",
        "gait": "walk",
        "v": 4.5,
        "g": 0,
        "t": 10,
        "wt": 200
      },
      "expect": {
        "range": "Outside the range: the walking equation is for 1.9 to 3.7 mph (3.06 to 5.95 km/h)",
        "gain": 0
      },
      "source": "Moore CC et al., Development of a Cadence-Based Metabolic Equation for Walking, Med Sci Sports Exerc 2021;53(1):165–173 (ACSM walking equation VO2 = 0.1·speed + 1.8·speed·grade + 3.5; speed in m/min, grade as a decimal; most accurate at 1.9–3.7 mph), https://pmc.ncbi.nlm.nih.gov/articles/PMC7896743/ (most accurate at 1.9 to 3.7 mph)"
    }
  ],
  "sources": [
    "Moore CC, Aguiar EJ, Ducharme SW and others. Development of a Cadence-Based Metabolic Equation for Walking. Med Sci Sports Exerc. 2021;53(1):165–173 (the ACSM walking equation, VO2 = 0.1·speed + 1.8·speed·grade + 3.5, speed in m/min, grade as a decimal, most accurate at 1.9–3.7 mph). https://pmc.ncbi.nlm.nih.gov/articles/PMC7896743/ (retrieved 2026-10-19)",
    "Koutlianos N, Dimitros E, Metaxas T and others. Indirect estimation of VO2max in athletes by ACSM’s equation: valid or not? Hippokratia. 2013;17(2):136–140 (ACSM running equation VO2 = 0.2·S + 0.9·S·G + 3.5, designed for speeds above 5.0 mph). https://pmc.ncbi.nlm.nih.gov/articles/PMC3743617/ (retrieved 2026-10-19)",
    "Compendium of Physical Activities, Unit conversions (1 MET = 3.5 ml/kg/min; liters of oxygen per minute × 5 = kcal per minute). https://pacompendium.com/unite-conversions/ (retrieved 2026-10-19)",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 mi = 1,609.344 m, 1 ft = 0.3048 m and 1 lb = 0.45359237 kg exactly. https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-19)"
  ],
  "related": [
    "pace",
    "vo2-max"
  ],
  "changelog": []
}