Projectile Motion Calculator

How it works

1. 1Enter the launch speed (v₀) and launch angle (θ). Toggle between metric (m/s) and imperial (ft/s) with the unit tabs.
2. 2The calculator converts your inputs to SI units and applies the standard equations of projectile motion, assuming no air resistance and a flat surface.
3. 3Results — range, maximum height, and total time of flight — are displayed in your chosen unit system. The live diagram reshapes the arc as you change the angle.

Use cases

• Physics students building intuition about how launch angle affects range.
• Sports scientists estimating ball-flight distances for throwing events such as javelin or shot put.
• Engineers and game developers checking simplified ballistic trajectories before applying aerodynamic models.

Frequently asked questions

What formulas does this calculator use?

With launch and landing at the same height and no air resistance: range R = v₀²·sin(2θ) ÷ g, maximum height H = v₀²·sin²θ ÷ (2g), and time of flight T = 2·v₀·sinθ ÷ g, where g ≈ 9.81 m/s². Example at 20 m/s and 45°: R ≈ 40.8 m, H ≈ 10.2 m, T ≈ 2.88 s.

Why is 45° the optimal launch angle for maximum range?

Range is proportional to sin(2θ), which peaks at 1 when 2θ = 90°, i.e. θ = 45°. At any other angle the range is shorter. Note that 30° and 60° give identical ranges because sin(60°) = sin(120°).

Does this account for air resistance or launch height?

No. It assumes a vacuum (no drag) and that the projectile lands at the same elevation it launched from. Real trajectories are shorter due to drag, and launching from a height extends the range.