{
  "id": "percentage-increase",
  "version": "2c19b9b86a0c",
  "status": "published",
  "name": "Percentage Increase Calculator",
  "question": "What is the percentage increase?",
  "summary": "Increases a number by a percentage, or finds the percentage increase from one number to another, or the original number.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/percentage-increase-calculator",
  "markdown": "https://www.acalculator.org/math/percentage-increase-calculator.md",
  "kind": "formulas",
  "method": "B = A + |A| × p ÷ 100, so p = (B − A) ÷ |A| × 100, where A is the original value and B the new value.",
  "assumptions": [
    "The increase is measured against the size of the original value, |A|; for a positive A, B = A × (1 + p ÷ 100).",
    "A negative percentage increase is a decrease.",
    "There is no percentage increase from 0: the original value must not be 0.",
    "Finding the original value from the new value and the increase can give two answers, one positive and one negative: both are shown."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Original value",
        "description": "The value A before the increase. Not 0.",
        "type": "number"
      },
      "to": {
        "title": "New value",
        "description": "The value B after the increase.",
        "type": "number"
      },
      "change": {
        "title": "Percentage increase",
        "description": "The increase from A to B as a percent of |A|. A negative increase is a decrease.",
        "type": "number",
        "x-unit": "percent"
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "from",
      "to",
      "change"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "from": {
      "label": "Original value",
      "description": "The value A before the increase. Not 0.",
      "format": "number"
    },
    "to": {
      "label": "New value",
      "description": "The value B after the increase.",
      "format": "number"
    },
    "change": {
      "label": "Percentage increase",
      "description": "The increase from A to B as a percent of |A|. A negative increase is a decrease.",
      "format": "percent"
    },
    "direction": {
      "label": "Increase or decrease",
      "description": "Whether the value went up, went down, or stayed the same.",
      "format": "text"
    },
    "increase": {
      "label": "Amount of increase",
      "description": "The new value minus the original value, B − A, when the new value is at least the original.",
      "format": "number"
    },
    "decrease": {
      "label": "Amount of decrease",
      "description": "The original value minus the new value, A − B, when the new value is smaller.",
      "format": "number"
    },
    "verdict": {
      "label": "In words",
      "description": "The change in words: increased by p%, or decreased by the size of a negative p.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": 80,
      "change": 15
    },
    "outputs": {
      "to": 92,
      "direction": "Increase",
      "increase": 12,
      "verdict": "increased by 15%"
    },
    "text": "80 increased by 15% is 92."
  },
  "examples": [
    {
      "given": {
        "from": 80,
        "change": 15
      },
      "expect": {
        "to": 92,
        "increase": 12,
        "direction": "Increase",
        "verdict": "increased by 15%"
      },
      "source": "hand calculation in content.mdx: 15% of 80 is 12, and 80 + 12 = 92"
    },
    {
      "given": {
        "from": 50,
        "to": 65
      },
      "expect": {
        "change": 30,
        "increase": 15
      },
      "source": "hand calculation in content.mdx: (65 − 50) ÷ 50 × 100 = 30%"
    },
    {
      "given": {
        "to": 92,
        "change": 15
      },
      "expect": {
        "from": 80
      },
      "source": "hand calculation in content.mdx: 92 ÷ 1.15 = 80"
    },
    {
      "given": {
        "from": 200,
        "to": 150
      },
      "expect": {
        "change": -25,
        "decrease": 50,
        "direction": "Decrease",
        "verdict": "decreased by 25%"
      },
      "source": "hand calculation in content.mdx: (150 − 200) ÷ 200 × 100 = −25%, a decrease"
    },
    {
      "given": {
        "from": 0.5,
        "change": 300
      },
      "expect": {
        "to": 2
      },
      "source": "hand calculation in content.mdx: 0.5 × (1 + 3) = 2"
    }
  ],
  "sources": [
    "OpenStax, Elementary Algebra 2e, section 3.2 Solve Percent Applications (percent increase and percent decrease): https://openstax.org/books/elementary-algebra-2e/pages/3-2-solve-percent-applications"
  ],
  "related": [
    "percentage-change",
    "percentage",
    "percentage-difference"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "A negative change reads \"decreased by 10%\", with the amount of decrease; the sentence follows."
    },
    {
      "date": "2026-09-28",
      "note": "An original value of 0 names the rule."
    }
  ]
}