HVAC Duct Sizing Calculator

{
  "type": "json",
  "example": {
    "notes": [
      "The rectangular size has the same friction loss and airflow as the round duct (ASHRAE equivalent diameter); its velocity is lower because its area is larger.",
      "Galvanized steel (ε = 0.0003 ft) and standard air (0.075 lb/ft³, 70 °F, sea level). Fittings and transitions are not included.",
      "For design guidance; the engineer of record is responsible for final selections."
    ],
    "round": {
      "area": 1.1112,
      "diameter": 14.27,
      "velocity": 900,
      "friction_rate": 0.08,
      "standard_sizes": [
        {
          "best_fit": true,
          "diameter": 14,
          "velocity": 935,
          "friction_rate": 0.088
        },
        {
          "best_fit": false,
          "diameter": 16,
          "velocity": 716,
          "friction_rate": 0.0457
        }
      ]
    },
    "steps": [
      {
        "step": "Round diameter at the friction rate (equal friction)",
        "reference": "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design",
        "calculation": "Iterated the diameter (bisection) until the Darcy-Weisbach friction loss at 1,000 CFM equals 0.0800 in. w.g./100 ft → D = 14.27 in"
      },
      {
        "step": "Square equivalent",
        "reference": "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design (Huebscher equivalent diameter)",
        "calculation": "For W = H = S: De = 1.30·S^1.25 / (2S)^0.25 = 1.09317·S → S = 14.27 / 1.09317 = 13.06 in"
      },
      {
        "step": "Round duct: Reynolds number",
        "reference": null,
        "calculation": "Re = D·V / ν = 1.1895 ft × 14.998 ft/s / 1.56×10⁻⁴ ft²/s = 114,361"
      }
    ],
    "units": "IP",
    "checks": {
      "friction": "Typical design range (0.04-0.15 in. w.g./100 ft; about 0.3-1.2 Pa/m).",
      "velocity": "Normal design range (400-2,500 FPM; about 2-12.7 m/s).",
      "aspect_ratio": null
    },
    "airflow": 1000,
    "velocity": 900,
    "next_calls": [
      {
        "why": "What cooling load does 1000 CFM carry from 80/67 to 55/54 °F?",
        "tool": "hvac_coil_load",
        "price": "$0.002",
        "arguments": {
          "units": "IP",
          "airflow": 1000,
          "leaving": {
            "dry_bulb": 55,
            "wet_bulb": 54
          },
          "entering": {
            "dry_bulb": 80,
            "wet_bulb": 67
          }
        }
      }
    ],
    "references": [
      "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design",
      "SMACNA HVAC Duct Design Manual (standard sizes, aspect ratio guidance)"
    ],
    "solved_for": "size",
    "inputs_used": {
      "airflow": 1000,
      "friction_rate": 0.08
    },
    "rectangular": {
      "area": 1.184,
      "basis": "equal_friction",
      "width": 13.06,
      "height": 13.06,
      "velocity": 845,
      "aspect_ratio": 1,
      "friction_rate": 0.08,
      "standard_sizes": [
        {
          "width": 14,
          "height": 14,
          "best_fit": false,
          "velocity": 735,
          "aspect_ratio": 1,
          "friction_rate": 0.0568,
          "equivalent_diameter": 15.3
        },
        {
          "width": 16,
          "height": 12,
          "best_fit": false,
          "velocity": 750,
          "aspect_ratio": 1.33,
          "friction_rate": 0.0605,
          "equivalent_diameter": 15.11
        }
      ],
      "equivalent_diameter": 14.27
    },
    "unit_labels": {
      "area": "ft²",
      "load": "MBH (1,000 BTU/h)",
      "grains": "gr / lb dry air",
      "length": "in",
      "airflow": "CFM",
      "density": "lb / ft³",
      "enthalpy": "BTU / lb dry air",
      "pressure": "psia",
      "velocity": "FPM",
      "elevation": "ft",
      "condensate": "gal / h",
      "temperature": "°F",
      "friction_rate": "in. w.g. / 100 ft",
      "humidity_ratio": "lb water / lb dry air",
      "specific_volume": "ft³ / lb dry air",
      "relative_humidity": "%",
      "velocity_pressure": "in. w.g."
    },
    "friction_rate": 0.08,
    "primary_shape": "round",
    "friction_factor": 0.01885,
    "reynolds_number": 114361,
    "velocity_pressure": 0.0505
  }
}