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A projectile launched at an angle follows a predictable parabolic path, and its full trajectory — how long it stays airborne, how high it goes, and how far it travels — can be found directly from its initial velocity and angle.
This calculator finds the time of flight, maximum height, and range of a projectile.
How it works
Enter the initial velocity, launch angle, and optional starting height. The calculator splits the velocity into horizontal and vertical components, then applies standard kinematics formulas (using Earth gravity, 9.81 m/s²) to find time of flight, maximum height, and range.
- Enter initial velocity (m/s).
- Enter launch angle (degrees).
- Enter initial height (m, default 0).
- Click Calculate to see your results.
Examples
20 m/s at 45°
A projectile launched at 20 m/s at a 45° angle (from ground level) stays airborne for about 2.88 seconds, reaches a maximum height of about 10.19 m, and travels a range of about 40.77 m.
Who should use it
- Checking physics coursework involving projectile motion and kinematics.
- Estimating the trajectory of a thrown or launched object for a design or game project.
Industry applications
- Physics education
- Game development and ballistics simulation (as a simplified baseline model)
Advantages
- Supports a non-zero starting height for elevated launches, not just ground-level ones.
- Calculates time of flight, maximum height, and range together in one step.
Limitations
- Assumes no air resistance, which is a significant simplification for light or irregular objects.
Common mistakes to avoid
- Forgetting that maximum range occurs at a 45° launch angle (for level ground), not at the steepest or flattest possible angle.
- Ignoring the initial height field when the projectile actually launches from an elevated position.
Best practices
- Remember these results assume no air resistance — real-world objects (especially light or irregularly-shaped ones) will differ, sometimes significantly, from this ideal calculation.
Tips
- Launch angles of 45°+x and 45°-x (for the same speed) always produce the same range — a useful symmetry for checking your understanding of the physics.