Projectile Motion Calculator
Enter speed, angle and gravity, then watch the parabola fly. Range, peak height and flight time are computed instantly.
Inputs
Air resistance is ignored (ideal projectile motion).
Results
Trajectory
About this tool
This calculator models ideal projectile motion: an object launched at a speed and angle, moving freely under gravity with no air resistance. Give it the launch speed, angle, initial height and the gravitational acceleration (Earth, Moon, Mars, Jupiter or a custom value) and it instantly returns the range, maximum height, total flight time, time to the peak, the velocity components and the impact speed. An animated SVG draws the parabolic path with the apex and landing point marked. Everything runs in your browser.
How to use
- 1 Enter the launch speed v₀ in metres per second.
- 2 Set the launch angle θ between 0° and 90° with the slider or field.
- 3 Optionally set an initial height h₀ and choose the gravity (Earth, Moon, Mars, Jupiter or custom).
- 4 Read the range, height and time, then press Play to watch the projectile fly along its parabola.
How it works
The launch velocity is split into a horizontal component v₀ₓ = v₀·cos θ and a vertical component v₀ᵧ = v₀·sin θ. Horizontal motion is constant, while vertical motion is uniformly accelerated by gravity g. For a launch from the ground (h₀ = 0): maximum height H = v₀²·sin²θ / (2g), range R = v₀²·sin(2θ) / g, and flight time T = 2·v₀·sin θ / g. When the initial height h₀ is positive, the landing time is found from the positive root of h₀ + v₀ᵧ·t − ½g·t² = 0, giving T = (v₀ᵧ + √(v₀ᵧ² + 2g·h₀)) / g, and the range is v₀ₓ·T. Air resistance is neglected, so the path is a perfect parabola.
Frequently asked questions
Which angle gives the longest range?
When the launch and landing heights are equal (h₀ = 0), 45° gives the maximum range because sin(2θ) peaks at 90°. If you launch from a height above the ground, the optimal angle is slightly below 45°.
Does this include air resistance?
No. This is ideal projectile motion with no drag, so the trajectory is an exact parabola. Real projectiles travel a bit less far because of air resistance, but the ideal model is what most physics courses use.
Can I use a different gravity?
Yes. Pick Earth (9.81), Moon (1.62), Mars (3.72) or Jupiter (24.79) m/s², or enter any custom value to explore how gravity changes the flight.
What is the impact speed?
It is the magnitude of the velocity when the object hits the ground, combining the constant horizontal component and the vertical component v₀ᵧ − g·T. With h₀ = 0 it equals the launch speed; with a starting height it is larger.
Related tools
Plot the parabola as a function with the Graph Plotter, explore physics formulas in the Formula Solver, and browse the tools page for more science calculators.