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Projectile Motion Calculator — Range, Height & Flight Time
Calculate projectile range, maximum height, and time of flight from initial velocity and launch angle.
Assumes level ground, no air resistance, and constant gravity. Results are ideal-model estimates.
Projectile Motion Calculator
Enter launch speed and angle — results update as you type.
Results
Projectile Trajectory Graph
Parabolic flight path from launch to landing (ideal conditions).
Range vs Launch Angle
How angle affects range at your current speed. Click a row to apply that angle.
| Angle | Range (m) | Max height (m) | Flight time (s) |
|---|
Real-World Projectile Examples
Approximate launch conditions for sports and demos (ideal physics model).
| Example | Speed | Angle | Est. range |
|---|
Projectile Motion Formulas
Standard kinematic equations (level launch, no drag).
How to Calculate Projectile Motion
A projectile launched at speed v₀ and angle θ (from horizontal) follows a parabolic path under constant gravity g. The horizontal range is R = v₀² sin(2θ) / g, maximum height is h = (v₀ sin θ)² / (2g), and total flight time is T = 2 v₀ sin θ / g when launch and landing heights are equal.
Example: 50 m/s at 45° with g = 9.81 m/s² → range ≈ 255 m, height ≈ 63.9 m, time ≈ 7.2 s. Maximum range is achieved at a 45° launch angle (excluding air resistance). . Complementary launch angles (such as 30° and 60°) result in the exact same horizontal range.
Projectile motion results at 50 m/s (g = 9.81)
| Angle | Range | Max height | Flight time |
|---|---|---|---|
| 30° | 221 m | 31.9 m | 5.1 s |
| 45° | 255 m | 63.9 m | 7.2 s |
| 60° | 221 m | 95.9 m | 8.8 s |
When to use this calculator
- Physics homework — verify range, height, and flight time problems.
- Engineering — rough estimates for water jets, ballistics models without drag.
- Sports science — compare launch angles for golf, soccer, baseball (idealized).
Related calculators
Projectile Motion FAQ
What angle gives maximum range?
45° maximizes horizontal range on level ground with no air resistance and equal launch/landing height.
What is the range formula for projectile motion?
R = v₀² sin(2θ) / g, where v₀ is initial speed, θ is launch angle, and g is gravitational acceleration.
How do I find maximum height?
h = (v₀ sin θ)² / (2g). Only the vertical component of velocity affects peak height.
Does air resistance affect real projectiles?
Yes. This calculator uses the ideal vacuum model. Real balls, bullets, and rockets experience drag that reduces range and alters the path.
Why do 30° and 60° give the same range?
Because sin(2×30°) = sin(60°) and sin(2×60°) = sin(120°) = sin(60°). Complementary launch angles share the same horizontal range.
Analyze projectile motion by calculating range, height, and time of flight for any projectile. Useful in physics, engineering, and sports for understanding motion trajectories.