Projectile Motion Calculator

Projectile motion is one of the most essential concepts in physics and engineering. It describes the motion of an object launched into the air, moving only under the influence of gravity. This type of motion is observed everywhere, from sports (such as football and javelin throwing) to real-world engineering applications and physics experiments.

The Projectile Motion Calculator helps you quickly determine important parameters such as trajectory, maximum height, time of flight, horizontal range, and velocity components. It’s a perfect tool for students, engineers, and physics enthusiasts who want to understand projectile motion accurately and interactively.

Why Use the Projectile Motion Calculator?

Manually calculating projectile motion can be time-consuming, especially when an object is launched from an elevated position. This calculator allows you to:

• Instantly compute time of flight, maximum height, horizontal range, and distance at maximum height.
• Visualize the trajectory graph for better conceptual understanding.
• Adjust input values (velocity, angle, and height) to see real-time effects on the motion.
• Reinforce your physics concepts — applicable in sports, engineering design, and academic learning.

How It Works

Enter the following values:

1. Initial velocity (m/s) – the speed at which the object is launched.
2. Angle of projection (°) – the launch angle with respect to the ground.
3. Initial height (m) – the vertical height from which the object is projected.

Then click Calculate to instantly view:

• Maximum height (H)
• Time of flight (T)
• Horizontal range (R)
• Distance at maximum height (xₘₐₓH)
• Projectile trajectory graph

Key Definitions & Formulas

Projectile

An object thrown, fired, or launched into the air that moves only under the influence of gravity.
Examples: a football, cannonball, bullet, or javelin.

Initial Velocity (V)

The speed at which the projectile is launched, measured in m/s.
It has two components:

• Horizontal velocity (Vₓ) = V × cos(θ)
• Vertical velocity (Vᵧ) = V × sin(θ)

Angle of Projection (θ)

The angle between the horizontal axis and the launch direction, measured in degrees (°).

Initial Height (h₀)

The height from which the projectile is launched, measured in meters (m).

Time of Flight (T)

The total time the projectile remains in the air.

T = 2*Vy/g (h_o=0)

T =-V_y ± (Vy² +2*g*h_o) / ( -g)(h_o≠0)

Maximum Height (H_max)

The highest vertical position reached by the projectile.

H = h₀ +(Vy² /2*g)

Horizontal Range (R)

The total horizontal distance traveled by the projectile.

R = Vx​ * T

Distance at Maximum Height (x @Hmax)

The horizontal distance covered when the projectile reaches its highest point.

X =Vx​ * t_maxH

if ho =0 ;t_maxH= T/2, otherwise t_maxH = V Sin(θ)/ g

Summary

The Projectile Motion Calculator simplifies complex physics equations into an intuitive, interactive tool. Whether you’re solving classroom problems or designing engineering projects, it provides both accuracy and insight — helping you understand the science behind every motion.