Kinematics Tool

Projectile Motion Calculator

Instantly calculate the maximum height, time of flight, and horizontal range of any projectile. Enter your initial velocity and angle below.

Enter Values

Initial Velocity (v₀) in m/s Launch Angle (θ) in degrees Gravity (g) in m/s²

Results

Maximum Height (H)

15.94 meters

Time of Flight (T)

3.61 seconds

Horizontal Range (R)

63.78 meters

Projectile Motion Equations & Formulas

Want to solve it by hand? Here are the three fundamental kinematic equations used to calculate the trajectory of a projectile moving under the influence of gravity (ignoring air resistance).

Time of Flight (T)

The total time the projectile remains in the air before hitting the ground.

T = (2 * v₀ * sinθ) / g

Maximum Height (H)

The highest vertical point reached along the parabolic trajectory.

H = (v₀² * sin²θ) / (2g)

Horizontal Range (R)

The total horizontal distance traveled from launch to landing.

R = (v₀² * sin(2θ)) / g

Assumptions & Pro Tips

Air Resistance: This calculator assumes ideal conditions in a vacuum. In the real world, air drag would decrease both the range and the maximum height.
Launch Angle: To achieve the absolute maximum horizontal range on flat ground, you should always set your launch angle to exactly 45 degrees.
Gravity: Earth’s standard gravity is 9.8 m/s². However, you can change this input if you are trying to solve physics problems located on the Moon (1.62 m/s²) or Mars (3.71 m/s²)!