HVAC duct sizing calculator: any two of duct size (round or rectangular), airflow, velo…

{
  "airflow": 1000,
  "friction_rate": 0.08
}

{
  "airflow": 1000,
  "checks": {
    "aspect_ratio": null,
    "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)."
  },
  "friction_factor": 0.01885,
  "friction_rate": 0.08,
  "inputs_used": {
    "airflow": 1000,
    "friction_rate": 0.08
  },
  "next_calls": [
    {
      "arguments": {
        "airflow": 1000,
        "entering": {
          "dry_bulb": 80,
          "wet_bulb": 67
        },
        "leaving": {
          "dry_bulb": 55,
          "wet_bulb": 54
        },
        "units": "IP"
      },
      "price": "$0.002",
      "tool": "hvac_coil_load",
      "why": "What cooling load does 1000 CFM carry from 80/67 to 55/54 °F?"
    }
  ],
  "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."
  ],
  "primary_shape": "round",
  "rectangular": {
    "area": 1.184,
    "aspect_ratio": 1,
    "basis": "equal_friction",
    "equivalent_diameter": 14.27,
    "friction_rate": 0.08,
    "height": 13.06,
    "standard_sizes": [
      {
        "aspect_ratio": 1,
        "best_fit": false,
        "equivalent_diameter": 15.3,
        "friction_rate": 0.0568,
        "height": 14,
        "velocity": 735,
        "width": 14
      },
      {
        "aspect_ratio": 1.33,
        "best_fit": false,
        "equivalent_diameter": 15.11,
        "friction_rate": 0.0605,
        "height": 12,
        "velocity": 750,
        "width": 16
      }
    ],
    "velocity": 845,
    "width": 13.06
  },
  "references": [
    "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design",
    "SMACNA HVAC Duct Design Manual (standard sizes, aspect ratio guidance)"
  ],
  "reynolds_number": 114361,
  "round": {
    "area": 1.1112,
    "diameter": 14.27,
    "friction_rate": 0.08,
    "standard_sizes": [
      {
        "best_fit": true,
        "diameter": 14,
        "friction_rate": 0.088,
        "velocity": 935
      },
      {
        "best_fit": false,
        "diameter": 16,
        "friction_rate": 0.0457,
        "velocity": 716
      }
    ],
    "velocity": 900
  },
  "solved_for": "size",
  "steps": [
    {
      "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",
      "reference": "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design",
      "step": "Round diameter at the friction rate (equal friction)"
    },
    {
      "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",
      "reference": "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design (Huebscher equivalent diameter)",
      "step": "Square equivalent"
    },
    {
      "calculation": "Re = D·V / ν = 1.1895 ft × 14.998 ft/s / 1.56×10⁻⁴ ft²/s = 114,361",
      "reference": null,
      "step": "Round duct: Reynolds number"
    }
  ],
  "unit_labels": {
    "airflow": "CFM",
    "area": "ft²",
    "condensate": "gal / h",
    "density": "lb / ft³",
    "elevation": "ft",
    "enthalpy": "BTU / lb dry air",
    "friction_rate": "in. w.g. / 100 ft",
    "grains": "gr / lb dry air",
    "humidity_ratio": "lb water / lb dry air",
    "length": "in",
    "load": "MBH (1,000 BTU/h)",
    "pressure": "psia",
    "relative_humidity": "%",
    "specific_volume": "ft³ / lb dry air",
    "temperature": "°F",
    "velocity": "FPM",
    "velocity_pressure": "in. w.g."
  },
  "units": "IP",
  "velocity": 900,
  "velocity_pressure": 0.0505
}