Projectile Motion Calculator
This projectile motion calculator works out the range, maximum height, flight time, and impact velocity of an object launched into the air at an angle. Enter the initial velocity, launch angle, starting height, and gravity, and every result updates instantly alongside a live trajectory graph. It is built for physics students, teachers, and anyone curious about how a thrown or fired object travels.
Projectile motion is the curved, parabolic path an object follows under gravity alone. This tool splits that motion into its horizontal part (constant velocity) and its vertical part (accelerated by gravity), then plots the full arc with the launch, peak, and landing points clearly marked. You can stack up to three trajectories to compare how angle, speed, or planet changes the path.
How to Use the Projectile Motion Calculator
Enter the launch parameters
Type the Initial Velocity (v₀), set the Launch Angle (θ) with the field or slider, and enter the Initial Height (h₀) — use 0 for ground level. Each input has its own unit selector.
Pick the gravity
Tap a planet preset for Earth, Moon, Mars, or Jupiter, or type a custom value in m/s². The default is Earth's 9.81 m/s².
Read the results
The panel shows Range, Max Height, Flight Time, and Impact Velocity, plus the optimal launch angle for maximum range. Results recalculate the moment any value changes.
Explore and compare
Hover or touch the curve to read the position, time, and velocity at any point. Press the + button to add up to three color-coded trajectories and compare different launches side by side.
Features
Four Key Results
Get range, maximum height, flight time, and impact velocity from a single set of inputs.
Trajectory Visualization
An interactive canvas draws the parabolic path with a grid, axis labels, and marked launch, peak, and landing points.
Compare Up to 3 Trajectories
Overlay up to three launches in blue, amber, and green to compare angles, speeds, or gravity at a glance.
Planetary Gravity Presets
Switch instantly between Earth (9.81), Moon (1.62), Mars (3.72), and Jupiter (24.79) m/s², or set a custom value.
Unit Conversion
Switch velocity (m/s, km/h, ft/s), distance (m, ft), and angle (deg, rad) without losing your values.
Angle Slider
Drag the slider for quick angle changes or type a precise value — the two stay in sync.
Interactive Tooltip
Hover or touch any point on the curve to read its horizontal distance, height, elapsed time, and velocity.
Optimal Angle
See the launch angle that gives the maximum range — 45° on flat ground, and less when launching from a height.
Real-World Quick Presets
Load a football kick, firework, cannon ball, or basketball shot to see projectile motion in everyday scenarios.
Dark Mode & Responsive
A built-in dark theme and a layout that adapts to phones, tablets, and desktops.
Frequently Asked Questions
What launch angle gives the maximum range?
On flat ground (h₀ = 0), the optimal angle is 45° — the perfect balance between horizontal distance and time in the air. When you launch from above ground level, the best angle is slightly less than 45°. The calculator shows the exact optimal angle automatically for any height.
How do you calculate projectile range?
Range is the horizontal distance the projectile covers before landing: range = v₀·cos(θ) × flight time. For a launch from flat ground this simplifies to the classic formula R = v₀²·sin(2θ) / g. This calculator uses the full flight-time method so it also handles launches from a starting height correctly.
How is time of flight and maximum height found?
Flight time is found by solving the vertical equation h₀ + v₀·sin(θ)·t − ½·g·t² = 0 for the moment the object returns to the ground. Maximum height is h₀ + (v₀·sin θ)² / (2g). Both are computed instantly and shown in the results panel along with range and impact velocity.
Does this account for air resistance?
No. It uses the ideal projectile motion model, which assumes no air resistance and constant gravity. Real-world drag reduces both range and maximum height. The ideal model is accurate for dense objects at moderate speeds and is the standard approach used in physics education.
Why does the same velocity give different ranges on different planets?
Range depends on gravity. Under the Moon's weak 1.62 m/s² the projectile stays airborne longer and travels much farther. On Jupiter, with 24.79 m/s², it is pulled down quickly and lands sooner, so the range is far shorter — even with identical speed and angle.
Can I use it for objects launched from a height?
Yes. Set the Initial Height (h₀) to the launch height in meters or feet. The calculator accounts for the extra height when computing flight time, range, and impact velocity — useful for throws from buildings, cliffs, or elevated platforms.
Is my data stored or sent anywhere?
No. All calculations happen entirely in your browser with JavaScript. Nothing you enter is uploaded to any server.
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