Projectile Motion Calculator

Projectile Motion Physics

Calculate trajectory parameters for objects launched at an angle under constant gravity.

Key Formulas

• Range: R = v₀²sin(2θ) / g
• Maximum Height: H = v₀²sin²(θ) / (2g)
• Time of Flight: T = 2v₀sin(θ) / g
• Horizontal Component: vₓ = v₀cos(θ)
• Vertical Component: vᵧ = v₀sin(θ)

How It Works

• Enter initial conditions: Initial velocity, launch angle, and gravity
• Choose calculation type: Range, height, time, or velocity components
• Calculate: Get comprehensive trajectory analysis
• View all parameters: See complete motion characteristics

Important Notes

• Assumptions: No air resistance, constant gravity, level ground
• Optimal angle: 45° gives maximum range on level ground
• Symmetrical path: Time up = time down for level launches
• Units: Ensure consistent units (meters, seconds, m/s, m/s²)

Applications

• Sports ballistics (basketball, soccer, golf)
• Military and defense calculations
• Engineering design (fountains, sprinklers)
• Physics education and research
• Game development and simulations

Try Sample Calculations

Click "Load Sample" to see typical calculations for each parameter type.