Projectile Motion Calculator
Enter initial velocity and launch angle to instantly get maximum height, time of flight and horizontal range, with a live trajectory graph and velocity breakdown. Built for Class 11, JEE and NEET.
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What is projectile motion?
Projectile motion is the curved path an object follows when launched into the air and moving under gravity alone (ignoring air resistance). It is a core topic in Class 11 Physics under kinematics, and a high-weightage chapter for JEE Main, JEE Advanced and NEET.
A projectile has two independent motions: horizontal (constant velocity, no acceleration) and vertical (uniformly accelerated by gravity). We analyse them separately, then combine. This calculator does it instantly, and unlike most tools it also draws the live trajectory, shows velocity components, and supports a raised launch height plus Moon and Mars gravity.
Key projectile motion formulas
| Quantity | Formula | Unit |
|---|---|---|
| Maximum height (H) | H = (u² × sin²θ) / (2g) | m |
| Time of flight (T) | T = (2 × u × sinθ) / g | s |
| Horizontal range (R) | R = (u² × sin 2θ) / g | m |
| Horizontal velocity (uₓ) | uₓ = u × cosθ | m/s |
| Vertical velocity (u_y) | u_y = u × sinθ | m/s |
The launch angle in degrees is converted to radians with θ_rad = θ × (π / 180) before applying trig functions, exactly as physics requires.
What makes this calculator different
- Live trajectory graph: see the exact parabolic path, apex and landing point drawn to scale.
- Raised launch height: launch from a cliff or table and get the true, longer time of flight and range (most tools assume ground level only).
- Other worlds: switch gravity to Moon or Mars to compare how far the same throw would travel.
- Full velocity breakdown: horizontal and vertical components, impact velocity and impact angle, plus kinetic energy per kilogram.
How to use it
- Enter initial velocity (u) in m/s.
- Enter launch angle (θ) in degrees (0 to 90). Use 45° for maximum range.
- Pick gravity (g): 9.8 for accuracy, 10 for quick exam math, or Moon/Mars to experiment.
- Optionally add a launch height if the projectile starts above the ground.
- Tap Calculate to see results, the trajectory graph and the full breakdown.
Real-world applications
- Sports: a cricket ball, football, basketball shot or javelin all follow projectile paths.
- Defense: artillery shells and ballistic trajectories use these equations.
- Engineering: designing ramps, fountains and water jets.
- Games: physics engines in PUBG, FIFA and Angry Birds simulate projectiles.