Projectile Motion Calculator

Calculate range, maximum height, flight time, and velocity components for any projectile. Visualize the trajectory in real time.

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Projectile Motion Calculator

Enter initial velocity and launch angle to instantly calculate range, maximum height, flight time, and velocity components. Visualize the trajectory in real time.

Horizontal Range

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Settings & Actions

Decimal Precision

Enter Values

Initial Velocityⓘ

Velocity Unit

Launch Angleⓘ45°

0°45°90°

💡 45° gives maximum horizontal range in ideal projectile motion.

Gravity (m/s²)ⓘ

Launch Height (m)ⓘ

Trajectory Visualization

Launch Peak Trajectory

Quick Presets

What is a Projectile Motion Calculator?

A Projectile Motion Calculator is a physics tool that computes the trajectory of an object launched into the air under the influence of gravity. Given an initial velocity and launch angle, it calculates the horizontal range, maximum height, time of flight, and velocity components.

Projectile motion follows classical Newtonian mechanics. The horizontal and vertical components of motion are independent — horizontal velocity remains constant (no air resistance), while vertical velocity changes due to gravitational acceleration.

This calculator supports multiple velocity units (m/s, km/h, ft/s, mph), gravity presets for different planets, elevated launch heights, and real-time trajectory visualization on a canvas graph.

How to Use the Projectile Motion Calculator

Step-by-Step Guide

1Enter the initial velocity (e.g. 50 m/s)
2Select the velocity unit — m/s, km/h, ft/s, or mph
3Set the launch angle using the slider or number input (0°–90°)
4Choose a gravity preset (Earth, Moon, Mars, Jupiter) or enter a custom value
5Optionally set a launch height above ground
6View range, height, flight time, and velocity components instantly
7Click Animate to watch the projectile travel along the trajectory

Key Features

✓Real-time calculation as you type or slide
✓Animated trajectory visualization with canvas
✓Gravity presets for Earth, Moon, Mars, Jupiter
✓Multi-unit velocity support (m/s, km/h, ft/s, mph)
✓Elevated launch height support
✓Full results breakdown table
✓Calculation history with localStorage
✓Export results as TXT or chart as PNG
✓Step-by-step formula panel
✓Quick presets for common scenarios

Projectile Motion Formulas Explained

Velocity Components

vx = v · cos(θ)

vy = v · sin(θ)

The initial velocity is split into horizontal (vx) and vertical (vy) components using trigonometry. vx stays constant throughout the flight; vy decreases due to gravity.

Range & Height

R = v²·sin(2θ) / g

H = vy² / (2g)

Range is maximized at 45°. Maximum height depends only on the vertical component and gravity. Complementary angles (30° and 60°) produce equal ranges.

Time of Flight

T = 2·vy / g

Total flight time is twice the time to reach peak height. With an elevated launch, the quadratic formula is used: T = (vy + √(vy² + 2g·h₀)) / g.

Position at Time t

x(t) = vx · t

y(t) = vy·t − ½g·t²

These parametric equations define the parabolic trajectory. The calculator samples 200 points along the path to render the smooth curve on the graph.

Key insight: On the Moon (g = 1.62 m/s²), a projectile travels about 6× farther than on Earth for the same launch conditions — which is why astronauts could hit golf balls enormous distances on the lunar surface.

Example Calculations

Velocity	Angle	Gravity	Range	Max Height	Flight Time
50 m/s	45°	9.81 m/s²	254.8 m	63.7 m	7.2 s
50 m/s	30°	9.81 m/s²	220.6 m	31.9 m	5.1 s
50 m/s	75°	9.81 m/s²	130.5 m	119.0 m	9.8 s
20 m/s	45°	9.81 m/s²	40.8 m	10.2 m	2.9 s
100 m/s	45°	9.81 m/s²	1019.4 m	254.8 m	14.4 s
50 m/s	45°	1.62 m/s²	1543.2 m	385.8 m	43.5 s

Real-World Applications

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Physics Education

Core kinematics concept taught in high school and university physics. Demonstrates independence of horizontal and vertical motion.

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Sports Science

Analyzing ball trajectories in soccer, basketball, baseball, and golf. Optimal launch angles for maximum distance or accuracy.

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Aerospace & Rocketry

Ballistic trajectory calculations for rockets, missiles, and spacecraft re-entry paths under gravitational influence.

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Game Development

Physics engines in video games use projectile equations for realistic bullet, grenade, and ball trajectories.

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Robotics

Calculating throwing trajectories for robotic arms and autonomous systems that need to launch or catch objects.

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Engineering

Structural engineers analyze debris trajectories, water jet paths, and material ejection in manufacturing processes.

Frequently Asked Questions

What is projectile motion?

Projectile motion is the motion of an object thrown or projected into the air, subject only to gravity. The horizontal and vertical components of motion are independent — horizontal velocity is constant, while vertical velocity changes due to gravitational acceleration.

What angle gives maximum range?

In ideal conditions (no air resistance, flat ground), a launch angle of 45° gives the maximum horizontal range. Complementary angles like 30° and 60° produce the same range but different heights and flight times.

How does launch height affect the trajectory?

Launching from an elevated position increases both the range and flight time. The calculator uses the quadratic formula T = (vy + √(vy² + 2g·h₀)) / g to account for the initial height h₀.

Why is gravity different on other planets?

Gravitational acceleration depends on a planet's mass and radius. Earth's gravity is 9.81 m/s², the Moon's is 1.62 m/s² (about 1/6th), Mars is 3.71 m/s², and Jupiter is 24.79 m/s². Lower gravity means longer flight times and greater ranges.

Does this calculator account for air resistance?

No — this calculator uses ideal projectile motion equations without air resistance. In real-world scenarios, drag significantly reduces range and alters the trajectory shape. The ideal model is accurate for dense, slow-moving objects over short distances.

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