Projectile Motion Calculator
Calculate projectile trajectory, range, time of flight
Projectile Motion Calculator tool
Default is 0 for ground level
Gravity (g): 9.81 m/s² (assumes no air resistance)
Results
Max Height (m)
0.00
Time of Flight (s)
0.00
Horizontal Range (m)
0.00
Velocity X (m/s)
0.00
Velocity Y (m/s)
0.00
Projectile Motion Calculator: key facts
- What it does
- Calculate projectile trajectory, range, time of flight
- Category
- Science Calculators
- Cost
- Free, with no account, sign-up, or install.
- Your data
- Runs entirely in your browser — the files and text you enter are never uploaded to a server.
- Last reviewed
- . Report an incorrect result.
About the Projectile Motion Calculator
Projectile motion describes the curved path of an object launched into the air under the influence of gravity alone. The Projectile Motion Calculator calculates trajectory parameters including maximum height, time of flight, horizontal range, and velocity components from initial velocity and launch angle, assuming no air resistance and standard gravity (9.81 m/s²).
Students solve physics homework problems, ballistics analysts estimate projectile paths, and sports scientists optimize athletic performance. The calculator also provides the trajectory equation, allowing you to predict the projectile's position at any time during flight.
The physics runs as JavaScript on your own machine, so trajectory analysis never sends anything over the network. The tool handles initial height calculations for projectiles launched from elevated positions.
How to use it
- Enter the initial velocity of the projectile in the input field.
- Enter the launch angle in degrees (0° is horizontal, 90° is vertical).
- Optionally enter the initial height if the projectile starts above ground level (default is 0).
- Click Calculate to compute trajectory parameters.
- View maximum height, time of flight, horizontal range, and velocity components (Vx, Vy).
- See the trajectory equation for predicting the projectile's path at any time.
Resolving the launch into components
Projectile motion is solved by splitting the initial velocity into horizontal and vertical components with trigonometry, then treating the two independently. Horizontally there is no acceleration, so that component stays constant for the whole flight. Vertically, gravity acts at 9.81 m/s² throughout, decelerating the ascent and then accelerating the descent.
That independence is the key insight and it is genuinely counterintuitive: a ball dropped and a ball fired horizontally from the same height hit the ground simultaneously, because their vertical motions are identical and the horizontal velocity does not affect them.
Time of flight is found by solving for when the projectile returns to ground level, which is why the initial height field changes it. Launching from elevation gives the vertical component extra time to play out, so range increases even though nothing about the launch itself changed.
- The defaults — 50 m/s at 45° from ground level — give components of 35.36 m/s each, a maximum height of 63.71 m, 7.21 s of flight, and a range of 254.84 m.
- The same launch from a 20 m elevation stretches the flight to 7.74 s and the range to 273.48 m.
- From ground level, 45° maximises range, and complementary angles such as 30° and 60° produce identical ranges by different trajectories.
Why use this version
- All calculations happen locally in your browser—no data is sent to any server, and the tool works offline once the page has loaded.
- Calculates all trajectory parameters from just two inputs (velocity and angle), saving time compared to manual calculations.
- Supports initial height for projectiles launched from elevated positions, not just ground-level launches.
- Provides the trajectory equation, allowing you to predict the projectile's position at any point during flight.
No air, and a flat Earth
This is the vacuum solution, and air resistance is the largest thing it omits. Drag scales roughly with the square of speed, so for anything fast or light the real trajectory falls well short of these figures — an actual ball thrown at 50 m/s travels nowhere near 255 metres. Drag also breaks the symmetry of the parabola, making the descent steeper than the ascent, and it lowers the range-maximising angle below 45°.
Several smaller idealisations are also present: gravity is treated as constant and perfectly vertical, the projectile is a point mass, and spin is ignored — though spin is exactly what makes a golf ball or a swerving football behave in ways no parabola predicts. Wind, air density, and the Coriolis effect over long distances are all absent too.
As a result these numbers are a solid model of the underlying physics and a good match for dense, slow, compact objects over short distances. Treat them as an upper bound on range rather than a prediction of where something will land.
Frequently Asked Questions
What is projectile motion?
Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration due to gravity. The horizontal motion is constant velocity, while vertical motion is constant acceleration downward. The path followed is a parabola when air resistance is neglected.
What formulas does this calculator use?
The calculator uses standard projectile motion formulas: Vx = V₀·cos(θ) for horizontal velocity, Vy = V₀·sin(θ) for initial vertical velocity, time of flight equations, maximum height H = (Vy²)/(2g), and horizontal range R = Vx·time of flight. It assumes no air resistance and standard gravity (9.81 m/s²).
What velocity units can I enter?
The calculator supports meters per second, kilometers per hour, and miles per hour for initial velocity. Results are displayed in metric units (meters, seconds) by default, with the option to convert to imperial units.
Can I calculate from an initial height?
Yes, you can specify an initial height for the projectile. The calculator will adjust the trajectory calculations accordingly, accounting for the starting elevation. This is useful for projectiles launched from cliffs, towers, or elevated platforms.
What angle gives maximum range?
For a projectile launched from ground level with no air resistance, the launch angle of 45° gives maximum horizontal range. If launched from an elevated position, the optimal angle is slightly less than 45°. The calculator can help you find the optimal angle for your specific situation.
