Try our official app! Developed by Calculatoric Team:
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.
Enter launch speed and angle — results update as you type.
Parabolic flight path from launch to landing (ideal conditions).
How angle affects range at your current speed. Click a row to apply that angle.
| Angle | Range (m) | Max height (m) | Flight time (s) |
|---|
Approximate launch conditions for sports and demos (ideal physics model).
| Example | Speed | Angle | Est. range |
|---|
Standard kinematic equations (level launch, no drag).
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.
| 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 |
45° maximizes horizontal range on level ground with no air resistance and equal launch/landing height.
R = v₀² sin(2θ) / g, where v₀ is initial speed, θ is launch angle, and g is gravitational acceleration.
h = (v₀ sin θ)² / (2g). Only the vertical component of velocity affects peak height.
Yes. This calculator uses the ideal vacuum model. Real balls, bullets, and rockets experience drag that reduces range and alters the path.
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.