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Projectile Motion Calculator
Enter launch speed and angle — range, apex and flight time update instantly.
Formula
Range = v²·sin(2θ)/g | Hmax = v²·sin²θ/2g | T = 2v·sinθ/g
Key facts
Maximum range at 45° (flat ground). Complementary angles (30°/60°) give the same range but different apex heights.
FAQ
Why is 45° the optimal angle?
Range carries sin(2θ), which peaks at 2θ = 90°. With air drag the optimum drops to ~30–40° depending on the projectile.
Does launch height matter?
Yes — launching from a height extends both range and time. This calculator assumes launch and landing at the same level.