About the Projectile Motion Calculator
A free, instant calculator that computes range, maximum height, time of flight, and impact velocity from your launch conditions — with a live canvas animation of the trajectory arc.
What it is
The Projectile Motion Calculator solves the four standard kinematic quantities for any launch scenario. Enter a launch speed, angle, and starting height and results appear instantly — no submit button, no page reload. It handles ground-level launches, elevated starting positions, and a range of gravity settings from the Moon to Jupiter.
A live HTML5 Canvas animation traces the parabolic arc, showing how the trajectory changes as you adjust the inputs. Everything runs in your browser — your values are never sent to a server.
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.
Completely free
No sign-up, no rate limit, no premium tier. Run as many scenarios as you like. If you find it useful, sharing it with a classmate or colleague is all we ask.