Last Updated: October 20, 2025
Calculate maximum height of projectile motion instantly with our advanced physics and ballistics calculator to determine the peak height reached by projectiles and analyze launch trajectories for educational and professional applications.
Enter your projectile motion parameters below to calculate maximum height instantly.
Use the input fields to specify initial velocity, launch angle, and other parameters for accurate calculations.
Leave as 0 for ground level launch
Enter values to see results
The Maximum Height Calculator is a specialized physics tool that calculates the peak height reached by projectiles in motion. This fundamental concept in projectile motion helps understand how launch velocity and angle affect the trajectory and maximum elevation of objects in flight.
For more information about projectile motion and maximum height, visit Wikipedia: Projectile Motion and Wikipedia: Trajectory.
Maximum height represents the highest point in a projectile's trajectory, where the vertical velocity component becomes zero before the object begins to fall back down. This occurs when the upward motion is completely overcome by gravitational acceleration.
h_max = (v₀² sin²θ)/(2g) + h₀
Whether you're analyzing ballistics, studying projectile motion, designing launch systems, or investigating motion in sports and engineering, this calculator provides accurate maximum height calculations with comprehensive trajectory analysis for educational and professional applications. For related calculations, explore our velocity calculator, projectile motion calculator, terminal velocity calculator, trajectory calculator, and muzzle velocity calculator.
h_max = (v₀² sin²θ)/(2g) + h₀
For vertical projection: h_max = v₀²/(2g) + h₀
Time to maximum height: t = v₀ sinθ/g
Where v₀ is initial velocity, θ is launch angle, g is gravitational acceleration, and h₀ is initial height.
Maximum height calculation uses the kinematic equations of projectile motion. The key principle is that at maximum height, the vertical velocity component becomes zero, allowing us to solve for the peak elevation using energy conservation or kinematic equations.
The calculator automatically handles unit conversions and provides step-by-step solutions. It can determine maximum height from launch velocity, angle, and initial height, making it suitable for various projectile motion scenarios in physics and engineering.
Initial Velocity: Higher velocity increases maximum height
Launch Angle: 90° gives maximum height for given velocity
Initial Height: Adds to the calculated maximum height
Gravitational Acceleration: Constant downward acceleration (9.81 m/s²)
The calculator supports various input units and automatically converts to standard units for calculation. It provides comprehensive results including maximum height, time to reach peak, and trajectory analysis for different projectile motion scenarios.
Given:
Step 1: Calculate sin²θ
sin(45°) = 0.707
sin²(45°) = (0.707)² = 0.5
Step 2: Calculate maximum height
h_max = (v₀² sin²θ)/(2g) + h₀
h_max = (20² × 0.5)/(2 × 9.81) + 0
h_max = (400 × 0.5)/19.62 = 200/19.62 = 10.19 m
Final Answer
Maximum Height: 10.19 m
The ball reaches a maximum height of 10.19 meters
Given:
Step 1: For vertical projection
h_max = v₀²/(2g) + h₀
h_max = 15²/(2 × 9.81) + 2
h_max = 225/19.62 + 2 = 11.47 + 2 = 13.47 m
Final Answer
Maximum Height: 13.47 m
The projectile reaches a maximum height of 13.47 meters above ground
🏀 Did you know? For maximum height with a given initial velocity, you should launch the projectile straight up (90° angle). For maximum range, the optimal angle is 45° (assuming no air resistance)!
| Field/Application | Typical Height Range | Importance |
|---|---|---|
| Sports Analysis | 1-50 meters | Critical for performance optimization and training |
| Military Applications | 10-1000 meters | Essential for weapon systems and ballistic analysis |
| Aerospace Engineering | 100-10000 meters | Critical for launch systems and trajectory planning |
| Construction Safety | 5-100 meters | Important for material handling and safety zones |
| Entertainment Industry | 5-200 meters | Essential for stunt coordination and special effects |
| Educational Physics | 1-20 meters | Demonstrates fundamental motion principles |
| Emergency Services | 10-500 meters | Critical for rescue operations and safety planning |
| Industrial Applications | 5-100 meters | Important for material transport and processing |
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