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Free online projectile motion calculator to calculate the projectile trajectory, maximum height reached, maximum horizontal range, angle of projection.

This projectile motion calculator will calculate the maximum height reached, time of flight, horizontal range of a projectile motion.

Projectile motion definition

Projectile definition: When an object is freely projected in air in the direction other than vertical, it follows a curved trajectory along its motion. This motion is called as projectile motion.

  1. Velocity of projection: The velocity with which an object is projected in air is called velocity of projection.
  2. Angle of projection: The angle at which the object is projected in air is called as angle of projection, for a projectile motion this angle should lead to other than vertical direction projection.
  3. Maximum Height: The maximum height reached by an object under projectile motion is called the maximum height.
  4. Horizontal range (R): It is the maximum horizontal distance travelled by the object under projectile motion.
  5. Time of flight: The time taken by the object from the point of projection to the point of landing is called as time of flight.

Understanding projectile motion

In projectile motion the trajectory will reach a maximum height and then start to descend until reaching a final point.

In projectile motion the inclined velocity can be resolved into vertical and horizontal components.

The horizontal component of the velocity is responsible for the horizontal range of the object. 

The vertical velocity of object goes on decreasing as the object ascends upwards and becomes zero when the object reaches maximum height, after reaching maximum height the velocity increases in downward direction under the influence of gravity.

Projectile motion equations

The projectile motion formulas are derived from the general equations of motions and are used for calculations of the various attributes.

The general equation of projectile motion is an equation of parabola and is given as follows:

y=x \tan \alpha-\frac{1}{2} \frac{x^{2}}{u^{2}}\left(1+\tan ^{2} \alpha\right)

The maximum height reached by a projectile is given as follows:

h=\frac{u^{2} \sin ^{2} \alpha}{2 g}

The time required to reach maximum height is given as follows:

t_{h}=\frac{u \sin \alpha}{g}

subsequently the total time of flight is given as:

t=\frac{2u \sin \alpha}{g}


How to use Projectile motion calculator

  1. The initial height is the height from the ground from which the object is fired. If the point of firing and point of landing is on the same level than this value has to be 0.
  2. Velocity (u) is the initial velocity of the firing.
  3. Angle (alpha) is the angle of projection, for maximum horizontal range angle of projection has to be 45 degrees.
  4. This calculator also graphs the trajectory.
  5. This calculator is also capable of finding angles of projection which are required for a user defined horizontal range.
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