Projectile Motion Calculator
Find the range, maximum height, flight time and impact speed of a projectile from its launch speed and angle.
How it works
vₓ = v·cosθ · v_y = v·sinθ · range = vₓ·t · max height = h + v_y²/(2g)
A projectile’s motion splits into an unchanging horizontal velocity and a vertical velocity that gravity steadily slows, stops and reverses. The horizontal component carries it forward while the vertical component sets how high it climbs and how long it stays airborne. For a level launch the range is greatest at 45°, where the horizontal and vertical components are balanced.
Worked example
At 20 m/s and 45° from ground level (g = 9.81): vₓ = v_y = 14.14 m/s, flight time ≈ 2.88 s, and range = 14.14 × 2.88 ≈ 40.8 m, peaking at about 10.2 m.
Sources: Projectile motion — Wikipedia
Frequently asked questions
Why is 45° the best angle for range?
From level ground, 45° divides the launch speed equally between forward motion and height, which maximises the product of horizontal speed and airtime. Launching from a raised height shifts the optimum slightly below 45°.
Does this account for air resistance?
No. This is the ideal, drag-free case. Real projectiles fall short of these figures because air resistance bleeds off speed, more so for light or fast objects.
What is the impact speed?
It is the total speed when the projectile lands, combining the constant horizontal component with the vertical speed gained falling. Launched and landing at the same height, it equals the launch speed.
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Educational estimate. Check the formula and units for your exact case.