Projectile Motion Calculator
Calculate range, maximum height, and time of flight for projectile motion. Enter initial velocity and launch angle.
Enter velocity and angle to calculate projectile motion.
Projectile Motion Formulas
Max Height: H = (v² × sin²(θ)) / (2g)
Time of Flight: T = (2v × sin(θ)) / g
Where:
- v = initial velocity (m/s)
- θ = launch angle (degrees)
- g = gravitational acceleration (9.8 m/s²)
Example
Solution:
R = (20² × sin(90°)) / 9.8 = 400 / 9.8 ≈ 40.82 m
H = (20² × sin²(45°)) / (2 × 9.8) = 200 / 19.6 ≈ 10.2 m
T = (2 × 20 × sin(45°)) / 9.8 ≈ 2.89 s
Key Concepts
Projectile motion is two-dimensional motion under constant gravitational acceleration. The horizontal and vertical components are independent of each other.
- Maximum range is achieved at 45° launch angle
- Complementary angles (e.g., 30° and 60°) give the same range
- Air resistance is ignored in these calculations
FAQ
Why is 45° the optimal angle for maximum range?
At 45°, the product of horizontal and vertical velocity components is maximized, which maximizes the range formula sin(2θ). sin(90°) = 1, giving the maximum value.
Does this account for air resistance?
No. This calculator assumes ideal projectile motion in a vacuum. Real projectiles with air resistance will have shorter range and different optimal angles.
What if I launch from a height?
These formulas assume launch and landing at the same height. For elevated launches, more complex equations involving initial height are needed.
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Last updated: 2026-08-08