Terminal velocity (quadratic drag) API

Computes terminal velocity vt=sqrt(2mg/(ρ·Cd·A)) for a body falling through a fluid, with the weight and drag-force balance check at terminal speed. Answers 'What is the terminal velocity of a falling object?', 'How fast does a skydiver fall?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/terminal-velocity

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringmechanicsphysicsterminal-velocitydragaerodynamicsfluidfalling

API URLhttps://x402.hexl.dev/v1/engineering/terminal-velocity

Integration docs

Example request

{
  "massKg": 80,
  "dragCoefficient": 1,
  "fluidDensityKgM3": 1.225,
  "areaM2": 0.7
}

Example response

{
  "massKg": 80,
  "dragCoefficient": 1,
  "fluidDensityKgM3": 1.225,
  "areaM2": 0.7,
  "gravityMs2": 9.80665,
  "terminalVelocityMs": 42.776305,
  "terminalVelocityKmh": 153.9947,
  "weightN": 784.532,
  "dragForceAtTerminalN": 784.532,
  "formula": "vt = sqrt(2*m*g / (ρ*Cd*A))",
  "interpretation": "At terminal velocity drag equals weight, so net acceleration is zero."
}

Input schema

{
  "type": "object",
  "required": [
    "massKg",
    "dragCoefficient",
    "fluidDensityKgM3",
    "areaM2"
  ],
  "properties": {
    "massKg": {
      "type": "number",
      "description": "body mass (kg)",
      "examples": [
        80
      ]
    },
    "dragCoefficient": {
      "type": "number",
      "description": "drag coefficient Cd"
    },
    "fluidDensityKgM3": {
      "type": "number",
      "description": "fluid density ρ (kg/m^3)"
    },
    "areaM2": {
      "type": "number",
      "description": "frontal reference area A (m^2)"
    },
    "gravity": {
      "type": "number",
      "description": "gravity (m/s^2), default 9.80665"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}