Enter Launch Data
Provide the initial velocity, launch angle, starting height, velocity unit, and gravitational acceleration.
Physics and Kinematics Tool
Projectile Motion Calculator
Calculate horizontal range, maximum height, total flight time, velocity components, impact velocity, and the complete projectile trajectory using accurate kinematic equations.
Instant calculations
Visual trajectory graph
No data stored
Launch Parameters
Enter the projectile's initial conditions below.
Please enter valid values.
This ideal model ignores air resistance, wind, spin, and changes
in gravitational acceleration.
Projectile Results
Results update using the selected launch conditions.
Horizontal range
0 m
Maximum height
0 m
Flight time
0 s
Horizontal velocity
0 m/s
Impact speed
0 m/s
Trajectory Preview
Ideal motion| Initial vertical velocity | 0 m/s |
|---|---|
| Time to maximum height | 0 s |
| Vertical impact velocity | 0 m/s |
| Impact angle | 0° |
| Selected gravity | 9.80665 m/s² |
| Trajectory equation | y = 0 |
Simple process
How the Projectile Motion Calculator Works
The calculator separates the initial velocity into horizontal and vertical components before applying standard kinematic equations.
Apply Motion Equations
The tool calculates velocity components and solves the vertical position equation to determine total flight time.
Review the Trajectory
View the range, peak height, flight duration, impact data, and a scaled visual representation of the projectile's path.
What Is Projectile Motion?
Projectile motion describes the path of an object launched into the air and influenced mainly by gravity. Examples include a ball being thrown, a golf shot, a water stream, or an object launched from an elevated platform.
In an ideal projectile model, horizontal velocity remains constant, while vertical velocity changes because gravity continuously accelerates the object downward.
Horizontal and Vertical Velocity Components
An initial velocity is separated into horizontal and vertical components using the launch angle.
Core Projectile Motion Formulas
vₓ = v₀ × cos(θ) vᵧ = v₀ × sin(θ) y(t) = h₀ + vᵧt - ½gt² x(t) = vₓt Maximum height = h₀ + vᵧ² ÷ 2gCalculating Total Flight Time
When the projectile starts above the landing surface, the calculator solves the vertical displacement equation and selects the positive time value:
t = [vᵧ + √(vᵧ² + 2gh₀)] ÷ gThe horizontal range is then calculated by multiplying the horizontal velocity by the total time in the air.
Why Launch Height Matters
A projectile launched from an elevated position normally remains airborne longer than one launched from ground level. This extra flight time can increase its horizontal range even when the initial speed and angle stay unchanged.
Understanding the 45-Degree Rule
When launch and landing heights are equal and air resistance is ignored, a 45-degree angle produces the maximum theoretical range. When the projectile starts above the landing level, the best angle for maximum range can be lower than 45 degrees.
Common questions
Projectile Motion Calculator FAQs
Learn more about projectile range, launch angles, maximum height, gravity, and calculation accuracy.
It calculates horizontal range, maximum height, total flight
time, horizontal and vertical velocity components, impact speed,
impact angle, and the projectile's ideal trajectory.
A 45-degree angle gives the maximum theoretical range when the
projectile launches and lands at the same height, gravity is
constant, and air resistance is ignored.
Mass does not affect the ideal projectile range when air
resistance is ignored. In real conditions, shape, size, drag,
spin, and wind can make objects with different masses behave
differently.
Yes. Select the Moon, Mars, or Jupiter gravity preset. You can
also enter a custom gravitational acceleration for another
planet, moon, or theoretical environment.
No. The calculator uses the standard ideal projectile model.
Air resistance requires additional information such as drag
coefficient, air density, object area, mass, wind, and rotation.
A negative angle represents a projectile launched downward.
It can still travel horizontally before reaching the landing
level, especially when released from an elevated position.
It is mathematically accurate for an ideal projectile under
constant gravity. Real-world results may differ because of air
resistance, wind, spin, changing terrain, measurement errors,
and other environmental factors.