Projectile Motion Calculator

A thrown ball, a kicked football and a water jet all follow the same curved path. This calculator takes the launch speed, angle and height and works out how far the projectile goes, how long it’s in the air, how high it gets and how fast it lands, ignoring air resistance.

How to Use It

1. Enter the Launch Speed and Launch Angle (0° is flat, 90° straight up).
2. Enter the Launch Height above where it lands, or 0 for ground to ground.
3. Leave Gravity at 9.81 m/s², or change it for another world.
4. Choose the unit for Distances In and press Calculate.

How It Works

The launch speed splits into a horizontal and a vertical part:

The horizontal part stays the same the whole way. Gravity slows the vertical part, so the time in the air solves $h + v_y t - \tfrac{1}{2}gt^2 = 0$:

The range is $v_x t$, the maximum height is $h + \frac{v_y^2}{2g}$, reached after $\frac{v_y}{g}$ seconds, and the landing speed is $\sqrt{v^2 + 2gh}$.

Worked Example

A ball is kicked at 20 m/s at 45° from the ground. Then $v_x = v_y = 20 \cos 45° \approx 14.14$ m/s, and:

It peaks at $\frac{14.14^2}{2 \times 9.81} \approx 10.2$ m after about 1.44 s.

Tips and Common Mistakes

• Use the angle from the horizontal. A 30° launch means 30° above the ground, not from vertical.
• Split the speed first. Only the vertical part is affected by gravity.
• Height matters. A launch from a cliff stays up longer and lands faster than one from the ground.
• 45° is best only for level ground. From a height, a lower angle usually goes farther.
• Real flights are shorter. Air resistance slows real projectiles, especially light ones.