{
  "id": "prostate-volume",
  "version": "6fdb3b868f44",
  "status": "published",
  "name": "Prostate Volume Calculator",
  "question": "What is my prostate volume?",
  "summary": "Calculates prostate volume from three ultrasound or MRI measurements with the ellipsoid formula (π/6 × length × width × height), and the PSA density when a PSA value is given.",
  "category": "health",
  "subcategory": "clinical",
  "url": "https://www.acalculator.org/health/prostate-volume-calculator",
  "markdown": "https://www.acalculator.org/health/prostate-volume-calculator.md",
  "kind": "function",
  "method": "Volume (mL) = π/6 × length × width × height, in cm. PSA density = PSA (ng/mL) ÷ volume (mL).",
  "assumptions": [
    "Measurements in centimeters (millimeters are divided by 10); 1 cm³ = 1 mL.",
    "The volume is rounded to 1 decimal and the PSA density to 3 decimals, halves up; the density uses the unrounded volume.",
    "The ellipsoid formula is an estimate. It is closest for glands under about 80 mL (Terris and Stamey 1991)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "l": {
        "title": "Length",
        "description": "The longest dimension of the gland, head to foot (craniocaudal).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.005,
        "maximum": 0.15
      },
      "w": {
        "title": "Width",
        "description": "The widest side-to-side dimension (transverse).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.005,
        "maximum": 0.15
      },
      "h": {
        "title": "Height",
        "description": "The front-to-back dimension (anteroposterior).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.005,
        "maximum": 0.15
      },
      "psa": {
        "title": "PSA (ng/mL)",
        "description": "Optional: the serum prostate-specific antigen, in ng/mL, for the PSA density.",
        "type": "number",
        "minimum": 0,
        "maximum": 10000
      }
    }
  },
  "outputs": {
    "volume": {
      "label": "Prostate volume",
      "description": "The ellipsoid volume in mL (cubic centimeters), to 1 decimal.",
      "format": "number"
    },
    "psad": {
      "label": "PSA density (ng/mL per mL)",
      "description": "PSA divided by the prostate volume, to 3 decimals. Shown when a PSA is given.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "l": 0.045,
      "w": 0.035,
      "h": 0.04
    },
    "outputs": {
      "volume": 33
    },
    "text": "The prostate volume is 33 mL."
  },
  "examples": [
    {
      "given": {
        "l": 0.045,
        "w": 0.035,
        "h": 0.04,
        "psa": 5
      },
      "expect": {
        "volume": 33,
        "psad": 0.152
      },
      "source": "π/6 × 4.5 × 3.5 × 4.0 = 32.987 mL (Terris and Stamey 1991, ellipsoid); 5 ÷ 32.987 = 0.1516 (Benson 1992) (hand calculation in content.mdx)"
    },
    {
      "given": {
        "l": 0.05,
        "w": 0.04,
        "h": 0.045,
        "psa": 3.2
      },
      "expect": {
        "volume": 47.1,
        "psad": 0.068
      },
      "source": "π/6 × 5 × 4 × 4.5 = 47.124 mL; 3.2 ÷ 47.124 = 0.0679 (hand calculation in content.mdx)"
    },
    {
      "given": {
        "l": 0.06,
        "w": 0.055,
        "h": 0.05
      },
      "expect": {
        "volume": 86.4
      },
      "source": "π/6 × 6 × 5.5 × 5 = 86.394 mL (hand calculation in content.mdx)"
    },
    {
      "given": {
        "l": 0.03,
        "w": 0.025,
        "h": 0.028,
        "psa": 1.1
      },
      "expect": {
        "volume": 11,
        "psad": 0.1
      },
      "source": "π/6 × 3.0 × 2.5 × 2.8 = 10.996 mL; 1.1 ÷ 10.996 = 0.1000 (hand calculation in content.mdx)"
    }
  ],
  "sources": [
    "Terris MK, Stamey TA. Determination of prostate volume by transrectal ultrasound. J Urol. 1991;145(5):984-987. https://doi.org/10.1016/S0022-5347(17)38508-7",
    "Benson MC, et al. Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer. J Urol. 1992;147(3 Pt 2):815-816. https://doi.org/10.1016/S0022-5347(17)37393-7"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-30",
      "note": "Published after this site's editorial review against the cited sources (no clinician review); the page notices say so."
    }
  ]
}