Projectile Motion Calculator
Calculate projectile range, maximum height, and time of flight. Enter initial velocity, launch angle, and height. Includes horizontal launch, impact velocity, and optimal angle.
Maximum Height (m)
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Horizontal Range (m) —
Time of Flight (s) —
Extended More scenarios, charts & detailed breakdown ▾
Max Height (m)
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Range (m) —
Time of Flight (s) —
Impact Velocity (m/s) —
Professional Full parameters & maximum detail ▾
Velocity Components
Horizontal Velocity Vx (m/s) —
Vertical Velocity at t (m/s) —
Impact & Optimization
Impact Angle (°) —
Optimal Angle for Max Range (°) —
Artillery Note —
How to Use This Calculator
- Enter Initial Velocity (m/s), Launch Angle (°), and Initial Height (m, default 0).
- Click Calculate to see max height, range, and time of flight.
- Use the Horizontal Launch tab for angle=0 launches from a height.
- Use the Find Angle tab to find the required launch angle for a desired range.
- The Professional tab shows velocity components, impact angle, and trajectory notes.
Formula
Range: R = v·cos(θ)·t | Max Height: H = h₀ + v²sin²(θ)/(2g)
Time of Flight: t = [v·sin(θ) + √(v²sin²(θ)+2g·h₀)] / g
Example
v=20 m/s, θ=45°, h₀=0 → Max H ≈ 10.19 m, Range ≈ 40.77 m, t ≈ 2.88 s.
Frequently Asked Questions
- Projectile motion is the motion of an object thrown or projected into the air under gravity alone (ignoring air resistance). Horizontal velocity stays constant; vertical velocity changes at 9.81 m/s².
- R = v²sin(2θ)/g for level ground. For launch from height h: R = vcos(θ) × [vsin(θ) + √(v²sin²(θ)+2gh)] / g.
- On flat ground, 45° always gives maximum range. When launched from a height, the optimal angle is slightly less than 45°.
- H = h₀ + v²sin²(θ)/(2g). The vertical component decelerates at g=9.81 m/s² until vertical velocity reaches zero.
- Impact velocity = √(vx² + vy_impact²) where vy_impact = √(vy₀² + 2g×max_height) at ground level. The impact angle is arctan(|vy_impact|/vx).