Projectile Motion Calculator
Calculate projectile trajectory, range, time of flight
About the Projectile Motion Calculator
Projectile motion describes the curved path of an object launched into the air under the influence of gravity alone. The Projectile Motion Calculator calculates trajectory parameters including maximum height, time of flight, horizontal range, and velocity components from initial velocity and launch angle, assuming no air resistance and standard gravity (9.81 m/s²).
Students solve physics homework problems, ballistics analysts estimate projectile paths, and sports scientists optimize athletic performance. The calculator also provides the trajectory equation, allowing you to predict the projectile's position at any time during flight.
The physics runs as JavaScript on your own machine, so trajectory analysis never sends anything over the network. The tool handles initial height calculations for projectiles launched from elevated positions.
How to Use the Projectile Motion Calculator
- Enter the initial velocity of the projectile in the input field.
- Enter the launch angle in degrees (0° is horizontal, 90° is vertical).
- Optionally enter the initial height if the projectile starts above ground level (default is 0).
- Click Calculate to compute trajectory parameters.
- View maximum height, time of flight, horizontal range, and velocity components (Vx, Vy).
- See the trajectory equation for predicting the projectile's path at any time.
Why Use ToolForge’s Projectile Motion Calculator
- All calculations happen locally in your browser—no data is sent to any server, and the tool works offline once the page has loaded.
- Calculates all trajectory parameters from just two inputs (velocity and angle), saving time compared to manual calculations.
- Supports initial height for projectiles launched from elevated positions, not just ground-level launches.
- Provides the trajectory equation, allowing you to predict the projectile's position at any point during flight.
Frequently Asked Questions
What is projectile motion?
Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration due to gravity. The horizontal motion is constant velocity, while vertical motion is constant acceleration downward. The path followed is a parabola when air resistance is neglected.
What formulas does this calculator use?
The calculator uses standard projectile motion formulas: Vx = V₀·cos(θ) for horizontal velocity, Vy = V₀·sin(θ) for initial vertical velocity, time of flight equations, maximum height H = (Vy²)/(2g), and horizontal range R = Vx·time of flight. It assumes no air resistance and standard gravity (9.81 m/s²).
What velocity units can I enter?
The calculator supports meters per second, kilometers per hour, and miles per hour for initial velocity. Results are displayed in metric units (meters, seconds) by default, with the option to convert to imperial units.
Can I calculate from an initial height?
Yes, you can specify an initial height for the projectile. The calculator will adjust the trajectory calculations accordingly, accounting for the starting elevation. This is useful for projectiles launched from cliffs, towers, or elevated platforms.
What angle gives maximum range?
For a projectile launched from ground level with no air resistance, the launch angle of 45° gives maximum horizontal range. If launched from an elevated position, the optimal angle is slightly less than 45°. The calculator can help you find the optimal angle for your specific situation.
