{
  "id": "acceleration",
  "version": "fc40e31cdd01",
  "status": "published",
  "name": "Acceleration Calculator",
  "question": "What is the acceleration?",
  "summary": "Computes average acceleration from the starting speed, the final speed and the time, or any one of the four from the other three, with the distance covered and the acceleration in g.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/acceleration-calculator",
  "markdown": "https://www.acalculator.org/physics/acceleration-calculator.md",
  "kind": "formulas",
  "method": "a = (v − u) ÷ t; v = u + a × t; u = v − a × t; t = (v − u) ÷ a; distance = (u + v) ÷ 2 × t.",
  "assumptions": [
    "Motion is along a straight line, and the speeds are in the direction of travel (0 or more).",
    "The acceleration is the average over the time; the distance assumes it is constant.",
    "Units are converted exactly: 1 mph = 0.44704 m/s, 1 ft = 0.3048 m, standard gravity g = 9.80665 m/s² (NIST SP 811)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "u": {
        "title": "Starting speed",
        "description": "The speed at the start, along the direction of travel.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0,
        "maximum": 10000000
      },
      "v": {
        "title": "Final speed",
        "description": "The speed at the end, along the same direction.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0,
        "maximum": 10000000
      },
      "t": {
        "title": "Time",
        "description": "The time taken to change from the starting speed to the final speed.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "exclusiveMinimum": 0,
        "maximum": 10000
      },
      "a": {
        "title": "Acceleration (m/s²)",
        "description": "The average acceleration in metres per second squared; negative when the object slows down.",
        "type": "number",
        "minimum": -10000,
        "maximum": 10000
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "u",
      "v",
      "t",
      "a"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "u": {
      "label": "Starting speed",
      "description": "The speed at the start, along the direction of travel.",
      "format": "quantity"
    },
    "v": {
      "label": "Final speed",
      "description": "The speed at the end, along the same direction.",
      "format": "quantity"
    },
    "t": {
      "label": "Time",
      "description": "The time taken to change from the starting speed to the final speed.",
      "format": "quantity"
    },
    "a": {
      "label": "Acceleration",
      "description": "The average acceleration: the change in speed divided by the time, in m/s².",
      "format": "number"
    },
    "g": {
      "label": "Acceleration in g",
      "description": "The acceleration divided by standard gravity, 9.80665 m/s².",
      "format": "number"
    },
    "fts2": {
      "label": "Acceleration in ft/s²",
      "description": "The acceleration in feet per second squared: m/s² ÷ 0.3048.",
      "format": "number"
    },
    "distance": {
      "label": "Distance covered",
      "description": "The distance covered at constant acceleration: (u + v) ÷ 2 × t.",
      "format": "quantity",
      "unit": "ft"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "u": 0,
      "v": 26.8224,
      "t": 8
    },
    "outputs": {
      "a": 3.3528,
      "g": 0.34189045188723977,
      "fts2": 10.999999999999998,
      "distance": 107.2896
    },
    "text": "Going from 0 mph to 60 mph in 8 s is an average acceleration of 3.3528 m/s²."
  },
  "examples": [
    {
      "given": {
        "u": 0,
        "v": 26.8224,
        "t": 8
      },
      "expect": {
        "a": 3.3528,
        "g": 0.34189045188723977,
        "distance": 107.2896
      },
      "source": "OpenStax University Physics Volume 1, section 3.4, Motion with Constant Acceleration (https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration, retrieved 2026-10-01); NIST SP 811: 1 mph = 0.44704 m/s; hand calculation in content.mdx: 26.8224 ÷ 8 = 3.3528",
      "tolerance": 1e-12
    },
    {
      "given": {
        "u": 70,
        "v": 0,
        "a": -5
      },
      "expect": {
        "t": 14,
        "distance": 490
      },
      "source": "OpenStax University Physics Volume 1, section 3.4, Motion with Constant Acceleration, equation v = v₀ + at (https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration); hand calculation in content.mdx: t = (0 − 70) ÷ −5 = 14 s",
      "tolerance": 1e-12
    },
    {
      "given": {
        "u": 10,
        "a": 2,
        "t": 5
      },
      "expect": {
        "v": 20,
        "distance": 75,
        "fts2": 6.561679790026247
      },
      "source": "OpenStax University Physics Volume 1, section 3.4, Motion with Constant Acceleration (https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration); hand calculation in content.mdx: v = 10 + 2 × 5 = 20 m/s",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, section 3.3, Average and Instantaneous Acceleration (a = Δv ÷ Δt), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/university-physics-volume-1/pages/3-3-average-and-instantaneous-acceleration",
    "OpenStax, University Physics Volume 1, section 3.4, Motion with Constant Acceleration (v = v₀ + at, average velocity (v₀ + v) ÷ 2), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (mile per hour = 0.44704 m/s, foot = 0.3048 m, standard acceleration of gravity = 9.80665 m/s²). https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "speed",
    "power"
  ],
  "changelog": []
}