{
  "id": "real-interest-rate",
  "version": "70164980772d",
  "status": "published",
  "name": "Real Interest Rate Calculator",
  "question": "What’s the real interest rate?",
  "summary": "Computes the real interest rate from the nominal rate and inflation with the exact Fisher equation and the quick approximation, or the nominal rate or inflation from the other two.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/real-interest-rate-calculator",
  "markdown": "https://www.acalculator.org/finance/real-interest-rate-calculator.md",
  "kind": "formulas",
  "method": "(1 + i) = (1 + r) × (1 + π), so r = (1 + i) ÷ (1 + π) − 1, where i is the nominal rate, π the inflation rate and r the real rate; the quick approximation is r ≈ i − π.",
  "assumptions": [
    "All three rates are for the same period, usually a year, and compound once in that period.",
    "Use expected inflation for a rate agreed today, or measured inflation to see what a past rate really earned.",
    "Arithmetic is exact on the typed decimals; rates round once to 2 decimals for display."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "nominal": {
        "title": "Nominal interest rate",
        "description": "The stated yearly rate, before taking inflation into account.",
        "type": "number",
        "x-unit": "percent",
        "exclusiveMinimum": -100,
        "maximum": 1000000
      },
      "inflation": {
        "title": "Inflation rate",
        "description": "The yearly rise in prices, expected or measured.",
        "type": "number",
        "x-unit": "percent",
        "exclusiveMinimum": -100,
        "maximum": 1000000
      },
      "real": {
        "title": "Real interest rate",
        "description": "The yearly rate after inflation: how fast buying power grows.",
        "type": "number",
        "x-unit": "percent",
        "exclusiveMinimum": -100,
        "maximum": 1000
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "nominal",
      "inflation",
      "real"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "nominal": {
      "label": "Nominal interest rate",
      "description": "(1 + real) × (1 + inflation) − 1, as a percent, to 2 decimals.",
      "format": "percent"
    },
    "inflation": {
      "label": "Inflation rate",
      "description": "(1 + nominal) ÷ (1 + real) − 1, as a percent, to 2 decimals.",
      "format": "percent"
    },
    "real": {
      "label": "Real interest rate",
      "description": "(1 + nominal) ÷ (1 + inflation) − 1, as a percent, to 2 decimals.",
      "format": "percent"
    },
    "approx": {
      "label": "Quick approximation (nominal − inflation)",
      "description": "The nominal rate minus the inflation rate: close to the real rate when both are small.",
      "format": "percent"
    },
    "gap": {
      "label": "Approximation minus the exact real rate",
      "description": "How many percentage points the quick approximation is above the exact real rate: real × inflation ÷ 100.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "nominal": 5,
      "inflation": 3
    },
    "outputs": {
      "real": 1.941747572815534,
      "approx": 2,
      "gap": 0.058252427184466
    },
    "text": "A 5% nominal rate with 3% inflation is a real interest rate of 1.94%."
  },
  "examples": [
    {
      "given": {
        "nominal": 15,
        "inflation": 10
      },
      "expect": {
        "real": 4.545454545454546,
        "approx": 5,
        "gap": 0.45454545454545453
      },
      "source": "Irving Fisher, The Theory of Interest (1930), chapter II, §2 and §4: the money rate and the real rate differ by the rate of change in prices, exactly only for rates reckoned continuously; a 15% money rate with prices rising 10% a year is a real rate of about 5%. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html; hand calculation in content.mdx: 1.15 ÷ 1.10 − 1 = 4.5455% exactly, against the quick 15 − 10 = 5%"
    },
    {
      "given": {
        "nominal": 9,
        "inflation": 3
      },
      "expect": {
        "real": 5.825242718446602,
        "approx": 6
      },
      "source": "OpenStax, Principles of Economics 3e, 22.4 The Confusion Over Inflation (a 9% loan with 3% inflation is a 6% real rate; 4% interest with 5% inflation loses in real terms). https://openstax.org/books/principles-economics-3e/pages/22-4-the-confusion-over-inflation (6% by the quick rule); hand calculation in content.mdx: 1.09 ÷ 1.03 − 1 = 5.8252%"
    },
    {
      "given": {
        "nominal": 4,
        "inflation": 5
      },
      "expect": {
        "real": -0.9523809523809523,
        "approx": -1
      },
      "source": "OpenStax, Principles of Economics 3e, 22.4 The Confusion Over Inflation (a 9% loan with 3% inflation is a 6% real rate; 4% interest with 5% inflation loses in real terms). https://openstax.org/books/principles-economics-3e/pages/22-4-the-confusion-over-inflation; hand calculation in content.mdx: 1.04 ÷ 1.05 − 1 = −0.9524%"
    },
    {
      "given": {
        "real": 3,
        "inflation": 4
      },
      "expect": {
        "nominal": 7.12
      },
      "source": "Irving Fisher, The Theory of Interest (1930), chapter II, §2 and §4: the money rate and the real rate differ by the rate of change in prices, exactly only for rates reckoned continuously; a 15% money rate with prices rising 10% a year is a real rate of about 5%. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html; hand calculation in content.mdx: 1.03 × 1.04 − 1 = 7.12%"
    },
    {
      "given": {
        "nominal": 7.12,
        "real": 3
      },
      "expect": {
        "inflation": 4
      },
      "source": "Irving Fisher, The Theory of Interest (1930), chapter II, §2 and §4: the money rate and the real rate differ by the rate of change in prices, exactly only for rates reckoned continuously; a 15% money rate with prices rising 10% a year is a real rate of about 5%. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html; hand calculation in content.mdx: 1.0712 ÷ 1.03 − 1 = 4%"
    }
  ],
  "sources": [
    "Irving Fisher, The Theory of Interest (Macmillan, 1930), Part I, chapter II, \"Money Interest and Real Interest\", §2 Assuming Foresight (the two rates differ by the rate of divergence between the money and goods standards, strictly true only when reckoned continuously, footnote 19) and §4 (a 15% money rate with prices rising 10% a year is a real rate of about 5%). Library of Economics and Liberty edition. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html (retrieved 2026-10-18)",
    "OpenStax, Principles of Economics 3e, 22.4 The Confusion Over Inflation: a 9% loan made when inflation is 3% has a 6% real interest rate; money earning 4% while inflation is 5% loses value. https://openstax.org/books/principles-economics-3e/pages/22-4-the-confusion-over-inflation (retrieved 2026-10-18)"
  ],
  "related": [
    "interest-rate",
    "effective-interest-rate",
    "apy",
    "rate-of-return"
  ],
  "changelog": []
}