🎯Projectile Motion Calculator
Enter your launch speed, angle, and starting height to instantly compute the range, maximum height, time of flight, and impact velocity — then watch the trajectory animate on the canvas.
Formulas Used
Time of Flight
t = (v₀sinθ + √(v₀²sin²θ + 2gh₀)) / g
Range
R = v₀ cosθ · t
Maximum Height
H = h₀ + (v₀ sinθ)² / (2g)
Impact Velocity
|v| = √(vₓ² + vᵧ²)
Free Projectile Motion Calculator Online
Want to see projectile motion in action, not just on paper? Our free Projectile Motion Calculator solves the physics and animates the path the moment you enter your values. As a fast and reliable projectile motion calculator, it takes your launch speed, angle, and starting height and instantly works out the range, maximum height, time of flight, and impact velocity — no manual equations required.
But it does more than return numbers. A live canvas animation traces the projectile's arc so you can watch how changing the angle or speed reshapes the trajectory, and a clear results breakdown shows each value alongside the formula behind it. Whether you're a student learning kinematics, checking homework, or teaching the concept, the maths and the motion are right in front of you.
Simply enter your launch values to see the results and animation instantly. No sign-up, no downloads, no limits — just clear physics whenever you need it.
How Does Projectile Motion Work?
A projectile follows a parabolic path under gravity alone (no air resistance). Horizontal and vertical motion are independent. The horizontal velocity v₀ cosθ stays constant throughout the flight. The vertical velocity starts at v₀ sinθ, decreases at rate g, reaches zero at peak height, then increases downward until impact.
- Range — horizontal distance from launch to landing: R = v₀ cosθ · t
- Maximum height — highest point above the ground: H = h₀ + (v₀ sinθ)² / (2g)
- Time of flight — total time in the air, found by solving the vertical displacement equation for t = 0
- Impact velocity — speed at landing: |v| = √(vₓ² + vᵧ²)
For ground-level launches (h₀ = 0), a 45° angle maximises the range. Complementary angles (e.g. 30° and 60°) give equal ranges. A non-zero launch height shifts the optimal angle below 45°.
About the Projectile Motion Calculator
Key features
Four computed quantities
Horizontal range, maximum height, total time of flight, and impact velocity — all four update simultaneously whenever any input changes, with no manual submit required.
Live canvas trajectory
An HTML5 Canvas draws the parabolic arc in real time. Press Play to watch a ball animate along the path from launch to landing; press Replay to watch it again. The arc redraws instantly on any input change.
Optional launch height
Set a starting height above the ground. The calculator uses the full quadratic formula for time of flight so the result is exact even when h₀ > 0, extending range and flight time correctly.
Configurable gravity
Choose from Earth (9.81 m/s²), Moon (1.62 m/s²), Mars (3.72 m/s²), or Jupiter (24.79 m/s²), or enter a fully custom g value to model any gravitational environment.
Formula breakdown
The page shows all four equations used — time of flight, range, maximum height, and impact velocity — so you can follow the maths alongside the numerical results.
Fully responsive
The inputs and canvas stack vertically on mobile so the tool works on any screen size without horizontal overflow. The canvas scales to the available width automatically.
How the calculation works
The horizontal and vertical components of motion are treated independently. The horizontal velocity vₓ = v₀ cosθ is constant throughout the flight (no drag). The vertical velocity starts at vᵧ = v₀ sinθ and decreases at rate g until it reaches zero at peak height, then increases downward until impact.
Time of flight is found by solving the vertical displacement equation for y = 0: h₀ + vᵧ t − ½g t² = 0. Using the quadratic formula gives t = (vᵧ + √(vᵧ² + 2g h₀)) / g, which handles both ground-level and elevated launches exactly. Range is then R = vₓ · t, maximum height is H = h₀ + vᵧ² / (2g) (valid whenever vᵧ > 0), and impact velocity is |v| = √(vₓ² + vᵧ_final²).
The canvas trajectory is pre-computed as 300 evenly-spaced points along the flight time. The animation maps elapsed time to a position in that point array using requestAnimationFrame, so the ball moves at a consistent pace independent of frame rate.
Who it's for
Students
Verify homework answers, explore how angle and speed affect range, or confirm that complementary angles (30° and 60°) give equal ranges from ground level.
Teachers
Build live demonstrations in class — change the angle or gravity setting and watch the arc reshape instantly, making the physics tangible rather than abstract.
Exam candidates
Use it to check answers during practice sessions. The formula breakdown shows the equations alongside the results so you can verify each step of your manual calculation.
Curious minds
See how far a ball would travel on the Moon or Mars with the same throw. Switch gravity from 9.81 to 1.62 and watch the arc extend dramatically — physics made intuitive.
Frequently Asked Questions
How does the projectile motion calculator work?
Enter your initial speed, launch angle, and starting height, and the tool instantly computes the range, maximum height, time of flight, and impact velocity, then animates the trajectory on a canvas — no button refresh needed. The results and animation update live as you change any input.
Is this calculator free to use?
Yes, it's completely free with no sign-up, downloads, or limits. Run as many scenarios as you like — Earth, Moon, Mars, or any custom gravity. Everything runs in your browser and your inputs are never sent to a server.
What values does it calculate?
It computes four key quantities from your inputs: the horizontal range (how far the projectile travels), the maximum height (the apex of the arc), the total time of flight (from launch to landing), and the impact velocity (the speed at the moment of landing). All four are computed simultaneously and update instantly when you change any value.
Can I launch from a height above the ground?
Yes. The Launch Height input lets you set a starting height above the ground in metres. The calculator accounts for it in the time-of-flight equation — a higher starting point means more time in the air, a longer range, and a higher impact velocity. The trajectory on the canvas also shows the dashed drop from launch height down to the ground.
Does it show the trajectory visually?
Yes. The canvas on the right draws the complete parabolic arc every time the inputs change. Press Play to watch a ball animate along the arc from launch to landing. You can press Stop at any point, or Replay once the animation has finished. Changing the inputs redraws the arc immediately so you can see how angle, speed, or gravity reshapes the trajectory in real time.
Does it account for air resistance?
No. Like most introductory physics models, this calculator assumes ideal projectile motion with no air resistance (drag). That means results match the standard kinematic equations taught in physics courses. Real-world trajectories will differ due to drag, spin, and wind, particularly at high speeds or over long distances.
Can I change the value of gravity?
Yes. The Gravity dropdown lets you choose from four presets — Earth (9.81 m/s²), Moon (1.62 m/s²), Mars (3.72 m/s²), and Jupiter (24.79 m/s²) — or enter a fully custom g value. Selecting Moon gravity, for example, produces a much longer range and flatter arc than on Earth for the same launch conditions.
Is my data stored anywhere?
No. Your inputs are processed entirely in your browser using JavaScript. Nothing is sent to a server, stored in a database, or logged. Close the tab and all your inputs are gone — there is no account, no history, and nothing persisted beyond the current session.
Does it work on mobile devices?
Yes, the tool is fully responsive. The inputs and the canvas stack vertically on small screens so everything stays accessible without horizontal scrolling. The canvas scales to the available width, and the Play button is large enough to tap comfortably on touch screens.
How accurate are the results?
The calculator uses the standard kinematic equations for ideal projectile motion. For a ground-level launch (h₀ = 0), the impact speed equals the launch speed (energy is conserved), complementary angles give equal ranges, and 45° gives the maximum range — all of which you can verify with the tool. Results are displayed to two decimal places, which is consistent with the precision of the inputs.