Every Toolkit

Projectile Motion Calculator

Calculate trajectory, range, maximum height, and time of flight

Input Parameters

Enter launch conditions

Launch speed of the projectile

Angle above horizontal (0° to 90°)

Height above ground at launch

Acceleration due to gravity

Common Examples

Key Concepts

45° Angle:
Maximum range on level ground (when h₀ = 0)
Parabolic Path:
Projectiles follow a parabolic trajectory
Independent Motion:
Horizontal and vertical motions are independent
Symmetry:
Time up equals time down (when h₀ = 0)

Trajectory Results

Calculated motion parameters

Range (Horizontal Distance)
40.77 m
Max Height
10.19 m
Flight Time
2.88 s
Time to Max
1.44 s
Final Velocity
20.00 m/s

Velocity Components

Horizontal (v₀ₓ)14.14 m/s
Constant throughout flight
Vertical (v₀ᵧ)14.14 m/s
Initial upward velocity

Projectile Motion Formulas

Range:
R = v₀ₓ × t = v₀cos(θ) × t
Maximum Height:
h_max = h₀ + v₀ᵧ² / (2g)
Time of Flight:
t = (v₀ᵧ + √(v₀ᵧ² + 2gh₀)) / g
Velocity Components:
v₀ₓ = v₀cos(θ)
v₀ᵧ = v₀sin(θ)

Assumptions

  • No air resistance (vacuum conditions)
  • Constant gravitational acceleration
  • Flat, level ground at landing point
  • Point mass projectile (no rotation)
  • No wind or other external forces

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About Projectile Motion Calculator

Projectile Motion Physics

This calculator analyzes the motion of projectiles launched at an angle, calculating range, maximum height, flight time, and other parameters. It uses kinematic equations to model the parabolic trajectory of objects under constant gravitational acceleration.

Features

  • Calculate range, height, and time of flight
  • Support for elevated launch positions
  • Velocity component breakdown
  • Quick angle presets (15°, 30°, 45°, 60°, 75°)
  • Multiple gravity settings (Earth, Moon, Mars)
  • Real-world examples from sports and ballistics
  • Comprehensive formula reference

Understanding Projectile Motion

Projectile motion is a form of motion where an object moves in a curved path under the influence of gravity. The motion can be analyzed by separating it into horizontal (constant velocity) and vertical (constant acceleration) components. The optimal angle for maximum range on level ground is 45°, but this changes with elevation.

Applications

  • Sports analysis (basketball, golf, soccer)
  • Military ballistics and artillery
  • Aerospace engineering and rocket trajectories
  • Video game physics engines
  • Water fountain and sprinkler design
  • Safety calculations for falling objects
  • Physics education and demonstrations

Important Notes

  • Real projectiles experience air resistance (drag)
  • Spin affects trajectory (Magnus effect)
  • Earth's rotation affects long-range projectiles
  • Maximum range angle < 45° when launched from height
  • Complementary angles (e.g., 30° and 60°) give same range on level ground