UTILS.
100% in-browser
🎯

Projectile Motion Calculator

Compute range, maximum height, time of flight, and impact velocity from launch speed, angle, and height.

Enter launch speed, angle, and height to get the full trajectory.

About this tool

The Projectile Motion Calculator is a free, in-browser physics tool that takes an initial speed, launch angle, launch height, and gravitational acceleration, then computes the range, maximum height, time of flight, the horizontal and vertical velocity components, and the impact speed. A small SVG plot sketches the trajectory so you can see the arc.

The calculation runs entirely locally in your browser with no data leaving your device. It uses the standard drag-free kinematic equations, resolving the launch velocity into components vx = v·cosθ and vy = v·sinθ and accounting for a non-zero launch height in the time-of-flight and impact-speed formulas.

Speed is in metres per second (m/s), angle in degrees measured from the horizontal, height in metres (m), and gravity in m/s² with a default of 9.80665 (standard gravity) that you can edit for other bodies. Air resistance is ignored, so results describe idealised projectile motion in a vacuum.

Frequently asked questions

What assumptions does the model make?
It assumes ideal projectile motion with no air resistance, constant gravity, and a flat launch surface. The launch angle is measured from the horizontal in degrees and speed is in m/s.
How is a non-zero launch height handled?
Time of flight is t = (vy + √(vy² + 2gh)) ÷ g, so a positive launch height extends the flight and range. Maximum height is h + vy²/(2g) measured from the ground.
What is the impact velocity?
It is the speed when the projectile returns to the ground, √(vx² + vy² + 2gh), combining the unchanged horizontal component with the vertical component gained over the fall.
What is the default gravity and can I change it?
The default is standard gravity g = 9.80665 m/s². You can edit it — for example 1.62 for the Moon or 3.71 for Mars — and every result and the trajectory update accordingly.

More tools