Estimate the range, maximum height, and flight time of an object launched at a given velocity and angle. Enter the initial velocity, launch angle, initial height, and gravitational acceleration.
🚀 Projectile Motion v1.0
Calculate range, max height, and time of flight.
📊 Flight Results real‑time
What Is Projectile Motion?
Projectile motion describes the movement of an object launched through the air when gravity is the primary acceleration considered.
Examples include:
- A ball thrown through the air
- A projectile launched at an angle
- A basketball shot
- A model rocket
- Physics classroom experiments
Calculator Inputs
Initial Velocity
The starting speed of the projectile in meters per second.
Launch Angle
The angle at which the projectile is launched.
- 0° = horizontal
- 90° = vertical
Initial Height
The height of the projectile above the landing level at launch.
Gravity
The gravitational acceleration used in the calculation.
Earth is approximately:
9.81 m/s²
How to Use It
- Enter the initial velocity.
- Enter the launch angle.
- Enter the initial height.
- Enter gravitational acceleration.
- Click Calculate.
Main Projectile Equations
Horizontal velocity:
vx = v cos(θ)
Vertical velocity:
vy = v sin(θ)
Vertical position can be modeled as:
y = h + v sin(θ)t − ½gt²
The calculator can use this relationship to determine the time until the projectile reaches the ground.
Maximum height is:
H = h + (v² sin²θ)/(2g)
Horizontal range is based on:
Range = v cos(θ) × flight time
Example
Suppose:
- Initial velocity = 30 m/s
- Launch angle = 45°
- Initial height = 0 m
- Gravity = 10 m/s²
The calculator can use these values to estimate the projectile’s flight time, maximum height, and horizontal range.
Assumptions
This type of basic projectile model generally assumes:
- No air resistance
- Constant gravitational acceleration
- A fixed launch velocity
- A flat landing reference level
Real-world projectiles can behave differently because of air resistance, wind, spin, and changing conditions.