Real-Time Projectile Motion Calculator

LIVE STATS UPDATING

Calculate projectile trajectory, flight time, maximum height, and range with our free physics tool. Adjust parameters and see results update instantly.

Input Parameters

v0
5 m/s 50 m/s 100 m/s
θ
0° 45° 90°
45°
h0
Ground 50m 100m

Trajectory Visualization

Real-time

Real-time Statistics

Time of Flight
2.55 s
t = √(2h/g) + √(2(h+H)/g)
Maximum Height
15.94 m
H = h + (v₀²·sin²θ)/(2g)
Range
45.05 m
R = (v₀²·sin(2θ))/g
Impact Velocity
25.00 m/s
v = √(vₓ² + vᵧ²)

Projectile Motion Calculator

Welcome to our free Projectile Motion Calculator - an essential tool for physics students, educators, and professionals. This calculator helps you understand and visualize the motion of projectiles under Earth's gravity with real-time updates.

What is Projectile Motion?

Projectile motion refers to the motion of an object thrown or projected into the air, subject only to acceleration due to gravity. The object is called a projectile, and its path is called its trajectory. The motion involves both horizontal and vertical components.

Real-time Calculation Advantage

Unlike traditional calculators, our tool provides instant feedback as you adjust parameters. See how changes in velocity, angle, or height affect the trajectory and calculated values without pressing any buttons. This immediate feedback helps develop intuition about physics principles.

Practical Applications

Understanding projectile motion has numerous real-world applications including sports (throwing a ball), engineering (designing water fountains), military (calculating artillery trajectories), and space exploration (calculating rocket paths).

Frequently Asked Questions

What is the optimal angle for maximum range?

When launched from ground level (initial height = 0), the optimal angle for maximum range is 45 degrees. For non-zero initial heights, the optimal angle is slightly less than 45 degrees.

How accurate is this calculator?

This calculator provides ideal projectile motion calculations without considering air resistance, wind, or other real-world factors. For classroom and basic applications, it's highly accurate. For advanced simulations, additional factors would need to be considered.

Why do the stats update so quickly?

Our calculator uses optimized JavaScript algorithms and efficient rendering techniques to provide real-time feedback. All calculations happen instantly in your browser without server requests, making it extremely responsive.