Projectile Motion Calculator
Range, height, and flight time of a projectile.
Defaults to Earth's 9.81 m/s². Assumes level ground and no air resistance.
Results update as you type.
How it works
Projectile motion describes the curved path of anything thrown, launched, or fired near Earth's surface, and this projectile motion calculator finds its three key measurements: how far it travels, how high it climbs, and how long it stays in the air. Enter the launch speed and angle, and the tool splits the motion into horizontal and vertical parts to solve each. Projectile motion matters across sport, engineering, and defence. It governs the arc of a basketball, the reach of a water fountain, the flight of a golf ball, and the trajectory of a launched rocket in its early phase. Because horizontal and vertical motion are independent, a single set of formulas covers them all, and a projectile motion calculator applies those formulas instantly without tedious trigonometry. The calculator assumes level ground and ignores air resistance, the standard idealisation taught in introductory physics. Under those conditions the path is a perfect parabola, and the maximum range for a given speed occurs at a launch angle of forty-five degrees. The vertical component of velocity determines the time aloft and the peak height, while the constant horizontal component carried over that time sets the range. Students, coaches, and engineers use a projectile motion calculator to predict trajectories, compare launch angles, and understand why steeper or flatter shots behave the way they do.
Range = v²·sin(2θ)/g · Height = v²·sin²θ/(2g) · Time = 2v·sinθ/g
A projectile launched over level ground follows a parabola because gravity accelerates it downward while its horizontal speed stays constant. Splitting the launch velocity into horizontal and vertical components with sine and cosine lets each direction be handled separately. The vertical motion sets how long the projectile stays airborne and how high it climbs, while the constant horizontal component carried over that time sets the range. Combining the two yields the compact formulas above, which is why the maximum range occurs at a launch angle of forty-five degrees.
Source:Standard physics (projectile kinematics, no air resistance)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter launch speed and launch angle.
- 2
Adjust the options
Adjust gravity if they apply — sensible defaults are already set.
- 3
Read your result
Horizontal range updates instantly as you type — no button to press.
Frequently asked questions
Why is 45 degrees the angle for maximum range?
The range depends on sin(2θ), which reaches its largest value of one when 2θ equals 90 degrees, meaning θ is 45 degrees. At that angle the launch speed is shared most effectively between climbing high enough to stay airborne and moving forward fast. Steeper angles gain height but sacrifice horizontal reach, while flatter angles move quickly forward but fall back to the ground too soon.
Does this calculator account for air resistance?
No. This calculator uses the idealised model taught in introductory physics, which assumes no air resistance and level ground, producing a perfectly symmetric parabolic path. Real projectiles experience drag that shortens the range, lowers the peak, and skews the trajectory, especially for light or fast objects. The results here are accurate for dense, slow projectiles and for understanding the underlying principles, but treat them as upper-limit estimates.
What happens at a launch angle of 90 degrees?
At 90 degrees the projectile is fired straight up, so sin(2θ) becomes zero and the horizontal range is zero; it goes up and comes straight back down. Meanwhile the maximum height and flight time reach their largest values because all the launch speed goes into vertical motion. This is a useful check on the formulas and matches the intuition of throwing a ball directly upward.
Are complementary angles giving the same range a coincidence?
No, it follows directly from the mathematics. Because sin(2θ) equals sin(180 − 2θ), two launch angles that add up to 90 degrees, such as 30 and 60 degrees, produce identical ranges at the same speed. The higher angle simply trades a longer, taller flight for the same horizontal distance. This complementary-angle property is a classic result of the projectile range formula.
How do I change the calculator for the Moon or Mars?
Edit the gravity field. Earth's default is 9.81 m/s², but the Moon's surface gravity is about 1.62 m/s² and Mars is about 3.71 m/s². Weaker gravity keeps a projectile aloft far longer and lets it travel much farther for the same launch speed, which is why astronauts could hit golf balls enormous distances on the Moon. Enter the appropriate value to model any world.