Projectile Motion Calculator
Enter initial velocity and launch angle to instantly calculate Maximum Height, Time of Flight, and Horizontal Range. Step-by-step physics tool for Class 11, JEE & NEET students.
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Angle for maximum range is 45° — try it!
What is Projectile Motion?
Projectile motion is the curved path an object follows when it is thrown or launched into the air and moves under the influence of gravity alone (ignoring air resistance). It is one of the most fundamental topics in Class 11 Physics, covered under Kinematics and Laws of Motion, and is a critical chapter for JEE Main, JEE Advanced, and NEET examinations.
A projectile has two simultaneous motions: horizontal motion (uniform, constant velocity — no acceleration) and vertical motion (uniformly accelerated due to gravity). Because these two motions are independent of each other, we analyze them separately and combine the results.
Our Projectile Motion Calculator does all this instantly for you — just enter your initial velocity (u), launch angle (θ), and your preferred value of gravitational acceleration (g), and get accurate results in a single click.
Key Projectile Motion Formulas
All three outputs of this tool are derived from standard physics equations. Here is the complete formula reference:
| Quantity | Formula | Unit |
|---|---|---|
| Maximum Height (H) | H = (u² × sin²θ) / (2g) | meters (m) |
| Time of Flight (T) | T = (2 × u × sinθ) / g | seconds (s) |
| Horizontal Range (R) | R = (u² × sin 2θ) / g | meters (m) |
| Horizontal Velocity (uₓ) | uₓ = u × cosθ | m/s |
| Vertical Velocity (u_y) | u_y = u × sinθ | m/s |
In our calculator, the launch angle in degrees is first converted to radians using θ_rad = θ × (π / 180) before applying trigonometric functions — exactly as required by JavaScript's Math library.
How to Use This Projectile Motion Calculator
Follow these simple steps to get your results in seconds:
- Enter the Initial Velocity (u) in meters per second (m/s). This is the speed at which the object is launched.
- Enter the Launch Angle (θ) in degrees. Valid range is 0° to 90°. Use 45° for maximum range.
- Select the value of Gravity (g): choose 9.8 m/s² for real-world accuracy, or 10 m/s² for simplified exam calculations (commonly used in JEE/NEET).
- Click Calculate and view your results: Maximum Height, Time of Flight, and Horizontal Range — all rounded to 2 decimal places.
- Use the Reset button to clear all fields and start fresh.
Important Notes
- Angle = 0°: The projectile moves purely horizontally with zero height and zero time of flight from a ground-level launch.
- Angle = 90°: The projectile goes straight up. Maximum height is achieved but horizontal range is zero.
- Angle = 45°: This gives the maximum horizontal range for any given initial velocity.
- This calculator assumes the projectile is launched from and lands at the same horizontal level (symmetric trajectory).
- Air resistance is not considered in these calculations (ideal/theoretical projectile motion).
Real-World Applications of Projectile Motion
Projectile motion is not just a physics concept — it appears everywhere in real life and engineering:
- Sports: The trajectory of a cricket ball, football, basketball shot, or javelin throw all follow projectile motion paths.
- Military & Defense: Artillery shells, missiles, and ballistic calculations are based on projectile motion equations.
- Space Science: Understanding the motion of rockets during their launch phase involves projectile and kinematics concepts.
- Engineering: Civil and mechanical engineers use these concepts to design ramps, arches, fountains, and ballistic systems.
- Video Games: Realistic physics engines in games like FIFA, PUBG, and Angry Birds simulate projectile trajectories.
- Irrigation & Water Jets: The range and height of water sprinkler jets are calculated using projectile motion principles.
Frequently Asked Questions (FAQs)
What is the formula for maximum height of a projectile?
The maximum height is given by H = (u² × sin²θ) / (2g). Here, u is the initial velocity in m/s, θ is the launch angle in degrees, and g is the acceleration due to gravity. At maximum height, the vertical component of velocity becomes zero.
At what angle is the range of a projectile maximum?
The horizontal range is maximum at a launch angle of θ = 45°. At this angle, sin(2θ) = sin(90°) = 1, which maximises the range formula R = u²sin2θ / g. You can verify this by entering 45° in our calculator.
What is the relation between Time of Flight and Maximum Height?
The time to reach maximum height is exactly half the total time of flight (T/2). This is because the projectile's vertical motion is symmetric — it takes the same time to go up as it does to come down (when launched and landed at the same level).
Should I use g = 9.8 or g = 10 m/s² in exams?
For JEE and NEET, questions often specify the value of g. If not specified, use g = 10 m/s² for quick mental calculations. For board exams (CBSE/ICSE) and real-world physics, use g = 9.8 m/s² for higher accuracy.
Why does this calculator ignore air resistance?
Standard physics formulas for projectile motion assume a vacuum (no air resistance). This is the ideal projectile motion model used in all school and competitive exam syllabi. In the real world, air resistance reduces range and height, especially for lightweight objects at high speeds.
What happens if I enter 0° or 90° as the launch angle?
At 0°, sin(0) = 0, so both the maximum height and time of flight are zero — the object doesn't leave the ground (in the ideal model). At 90°, cos(90°) = 0, so the horizontal range is zero — the projectile goes straight up and comes straight back down.