Projectile Max Height & Flight Time Calculator
From launch speed and angle, find a projectile’s maximum height, total time of flight and horizontal range.
How it works
H = (v·sinθ)² ÷ (2g) · T = 2·v·sinθ ÷ g · Range = v·cosθ · T
For a projectile launched and landing at the same height, splitting the launch speed into vertical (v·sinθ) and horizontal (v·cosθ) components makes the motion easy: gravity only acts vertically. The peak height depends on the vertical component squared, the total flight time on twice the vertical component over g, and the range on the horizontal component times that time. Air resistance is ignored, so real throws fall a bit short.
Worked example
At 20 m/s and 45° with g = 9.807, v·sinθ = v·cosθ = 14.14 m/s. Max height = 14.14² ÷ (2 × 9.807) = 10.2 m; time of flight = 2 × 14.14 ÷ 9.807 = 2.88 s; range = 14.14 × 2.88 = 40.8 m.
Sources: Projectile motion — Wikipedia
Frequently asked questions
What launch angle gives the greatest range?
On level ground and ignoring air resistance, 45° maximises range. Higher angles gain height but sacrifice horizontal distance; lower angles do the reverse.
Does mass affect the trajectory?
Not in this idealised model. Without air resistance every projectile follows the same path for a given speed and angle, because gravity accelerates all masses equally.
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This calculator is for educational purposes. Double-check important results before acting on them.