{
  "id": "percentage-decrease",
  "version": "c6cdb3fa3a13",
  "status": "published",
  "name": "Percentage Decrease Calculator",
  "question": "What is the percentage decrease?",
  "summary": "Finds the percentage decrease from an original value to a new value, P = (V₁ − V₂) ÷ V₁ × 100, or the new or original value from the percent.",
  "category": "math",
  "subcategory": "percentages",
  "url": "https://www.acalculator.org/math/percentage-decrease-calculator",
  "markdown": "https://www.acalculator.org/math/percentage-decrease-calculator.md",
  "kind": "formulas",
  "method": "P = (V₁ − V₂) ÷ V₁ × 100, where V₁ is the original value and V₂ the new value.",
  "assumptions": [
    "The percent is taken of the original value, not of the new value.",
    "The original value is greater than 0 and the new value is 0 or more, so the decrease is at most 100%.",
    "A new value larger than the original gives a negative decrease, and the answer calls it an increase.",
    "The original value cannot be found from a 100% decrease, because every original value falls to 0."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Original value",
        "description": "The value before the decrease. It must be greater than 0.",
        "type": "number",
        "exclusiveMinimum": 0
      },
      "to": {
        "title": "New value",
        "description": "The value after the decrease. It cannot be negative.",
        "type": "number",
        "minimum": 0
      },
      "percent": {
        "title": "Percentage decrease",
        "description": "How much smaller the new value is, as a percent of the original value. A negative percent is an increase.",
        "type": "number",
        "x-unit": "percent",
        "maximum": 100
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "from",
      "to",
      "percent"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "from": {
      "label": "Original value",
      "description": "The value before the decrease. It must be greater than 0.",
      "format": "number"
    },
    "to": {
      "label": "New value",
      "description": "The value after the decrease. It cannot be negative.",
      "format": "number"
    },
    "percent": {
      "label": "Percentage decrease",
      "description": "How much smaller the new value is, as a percent of the original value. A negative percent is an increase.",
      "format": "percent"
    },
    "change": {
      "label": "Amount of decrease",
      "description": "The original value minus the new value: V₁ − V₂. Negative when the value went up.",
      "format": "number"
    },
    "verdict": {
      "label": "In words",
      "description": "The change in words: a decrease, or an increase when the new value is larger than the original.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": 50,
      "to": 40
    },
    "outputs": {
      "percent": 20,
      "change": 10,
      "verdict": "a 20% decrease"
    },
    "text": "From 50 to 40 is a 20% decrease."
  },
  "examples": [
    {
      "given": {
        "from": 50,
        "to": 40
      },
      "expect": {
        "percent": 20,
        "change": 10,
        "verdict": "a 20% decrease"
      },
      "source": "hand calculation in content.mdx: (50 − 40) ÷ 50 × 100 = 20%"
    },
    {
      "given": {
        "from": 3.71,
        "to": 3.64
      },
      "expect": {
        "percent": 1.8867924528301845
      },
      "source": "OpenStax Prealgebra 2e, Example 6.24: a gas price from $3.71 to $3.64 is a 1.9% decrease (rounded there); (3.71 − 3.64) ÷ 3.71 × 100 = 1.8868%"
    },
    {
      "given": {
        "from": 80,
        "percent": 25
      },
      "expect": {
        "to": 60,
        "change": 20
      },
      "source": "hand calculation in content.mdx: 80 × (1 − 0.25) = 60"
    },
    {
      "given": {
        "to": 60,
        "percent": 25
      },
      "expect": {
        "from": 80
      },
      "source": "hand calculation in content.mdx: 60 ÷ (1 − 0.25) = 80"
    },
    {
      "given": {
        "from": 40,
        "to": 50
      },
      "expect": {
        "percent": -25,
        "change": -10,
        "verdict": "a 25% increase, not a decrease"
      },
      "source": "hand calculation in content.mdx: (40 − 50) ÷ 40 × 100 = −25%, an increase of 25%"
    }
  ],
  "sources": [
    "OpenStax, Prealgebra 2e, §6.2 Solve General Applications of Percent (percent decrease: decrease = original amount − new amount, as a percent of the original; Example 6.24). https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent"
  ],
  "related": [
    "percentage"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "A new value above the original reads as an increase, not a negative decrease."
    }
  ]
}