The projectile motion calculator computes range, maximum height, and time of flight for any projectile launched at an angle. Enter initial velocity, launch angle, and optional initial height. Supports metric (m, m/s) and imperial (ft, ft/s) units. Assumes no air resistance.
Projectile Motion Calculator
How to Use the Projectile Motion Calculator
This projectile motion calculator uses kinematic equations to find range, maximum height, and time of flight for any launch scenario. The calculation assumes no air resistance and constant gravitational acceleration.
Step 1: Enter Initial Conditions
Enter the initial velocity (m/s or ft/s), launch angle (0-90 degrees), and optional initial height above the landing surface.
Step 2: Understand the Results
Range: Horizontal distance traveled when the projectile returns to launch height (or ground level if height is set). Max Height: Peak height above the launch point. Time of Flight: Total time in the air. Peak Time: Time to reach maximum height.
Formulas Used
Horizontal component: vx = v₀ cos θ. Vertical component: vy = v₀ sin θ. Max height: H = h₀ + vy²/(2g). Time to peak: t_peak = vy/g. Range from ground level: R = vx × t_total.
Example
A ball kicked at 25 m/s at 40°: vx = 19.15 m/s, vy = 16.07 m/s. Max height = 13.17 m. Time of flight = 3.28 s. Range = 62.8 m.
FAQ
What is projectile motion?
Projectile motion is the curved path an object follows when launched with an initial velocity under gravity alone. Horizontally, the object moves at constant velocity. Vertically, it decelerates going up (at 9.81 m/s²) and accelerates going down. The path is a parabola.
What launch angle gives maximum range?
45 degrees gives maximum range on flat ground (ignoring air resistance). For launch heights above the landing point, the optimal angle is slightly less than 45°. For cannon balls and sports balls, drag from air resistance shifts the optimal angle lower, typically 30-38°.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
Does this calculator account for air resistance?
No — this calculator uses the standard kinematic equations assuming no air resistance. In reality, air resistance reduces range significantly, especially at high velocities. For precise ballistic calculations, you'd need to model drag coefficient, cross-sectional area, and air density.