Projectile Motion Calculator
Calculate range, max height and flight time for a launched projectile.
Results
Projectile motion describes the path of an object launched at an angle under gravity with no air resistance. The range is maximized at 45 degrees and the trajectory is a symmetric parabola. This calculator uses standard gravitational acceleration (9.80665 m/s²) to compute range, height and flight time for any launch speed and angle.
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Frequently asked questions
45 degrees gives the maximum range for a given speed. At 20 m/s, the range is 40.77 m at 45° but only 35.33 m at 30° or 60°.
Use R = v²sin(2θ)/g. At 20 m/s and 45°, R = 400 × sin(90°) / 9.80665 = 40.77 meters.
Max height = v²sin²(θ)/(2g) = 400 × 0.5 / 19.613 = 10.19 meters. The projectile reaches this height at the midpoint of its flight.
Time of flight = 2v·sin(θ)/g. At 20 m/s and 45°, the flight time is 2 × 20 × 0.707 / 9.807 = 2.88 seconds.
Yes, air resistance can reduce range by 20-50% for high-speed projectiles. A baseball thrown at 40 m/s travels about 30% less than the ideal calculation predicts.