🎯 Projectile Motion Calculator
Enter launch speed, angle and height, and get the range, maximum height, time of flight and landing speed — plotted as a trajectory.
Range
40.789 m
Max height
10.197 m
Time of flight
2.8842 s
vₓ (horizontal)
14.142 m/s
v_y (vertical)
14.142 m/s
Landing speed
20 m/s
Landing angle 45° below horizontal. Time to apex 1.4421 s.
Ideal projectile motion (no air resistance). R = u²·sin2θ/g and H = u²·sin²θ/(2g) for level ground; height offset handled for h₀ ≠ 0. 🔒 In your browser.
How the projectile motion calculator works
Projectile motion splits into independent horizontal (constant velocity) and vertical (constant acceleration g) components. From launch speed u and angle θ: horizontal velocity is u·cos θ and vertical is u·sin θ. The tool computes range, maximum height H = u²·sin²θ/(2g), time of flight, and landing speed/angle, and draws the parabolic path with the apex and range marked. Air resistance is neglected.
The trajectory graph plus every output at once is the differentiator over a bare formula — and projectile-plus-gravity problems are a documented weak spot for AI. Initial height h₀ ≠ 0 (launching off a cliff or table) is handled.
Frequently asked questions
How do I calculate the range of a projectile?
For level ground, range R = u²·sin(2θ)/g, where u is launch speed, θ the angle and g gravity. Maximum range is at 45°. Enter your values and the tool computes it (and adjusts for a non-zero launch height).
What launch angle gives the maximum range?
45° on level ground. Complementary angles (e.g. 30° and 60°) give the same range. Launching from a height shifts the optimum slightly below 45°.
How is maximum height found?
H = u²·sin²θ/(2g) above the launch point — it depends only on the vertical velocity component. The tool adds any initial height.
Does this include air resistance?
No — it models ideal projectile motion (no drag), the standard classroom assumption. Real projectiles fall a bit shorter, especially at high speed.
What is the time of flight?
How long the projectile is airborne. For level ground it is 2u·sinθ/g; with a launch height it is longer, and the tool solves the full quadratic.
What is the landing speed?
By energy conservation (no drag), an object landing at the launch height returns at the launch speed; from a height it lands faster. The tool reports the landing speed and angle.