Projectile motion calculator API

Compute drag-free projectile range (R = v²·sin2θ/g), max height (H = (v·sinθ)²/2g), time of flight, and velocity components from launch speed and angle. Answers 'how far does a projectile go at 20 m/s 45°','max height of this launch','time of flight of a projectile'.

Price$0.01per request

MethodPOST

Route/v1/calc/eng-projectile

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcengineeringphysicsprojectileballisticsmechanicstrajectorykinematics

API URLhttps://x402.hexl.dev/v1/calc/eng-projectile

Integration docs

Example request

{
  "speedMs": 20,
  "angleDeg": 45
}

Example response

{
  "speedMs": 20,
  "angleDeg": 45,
  "gravityMs2": 9.80665,
  "rangeM": 40.788649,
  "maxHeightM": 10.197162,
  "timeOfFlightS": 2.884193,
  "vxMs": 14.142136,
  "vyMs": 14.142136,
  "formula": "R = v^2*sin(2θ)/g, H = (v*sinθ)^2/(2g), T = 2*v*sinθ/g"
}

Input schema

{
  "type": "object",
  "required": [
    "speedMs",
    "angleDeg"
  ],
  "properties": {
    "speedMs": {
      "type": "number",
      "description": "launch speed m/s",
      "examples": [
        20
      ]
    },
    "angleDeg": {
      "type": "number",
      "description": "launch angle degrees",
      "examples": [
        45
      ]
    },
    "gravity": {
      "type": "number",
      "description": "m/s² (default 9.80665)",
      "examples": [
        9.80665
      ]
    }
  }
}

Output schema

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