How to use this calculator
Enter the launch speed, the angle above horizontal and the launch height above the landing point (0 for level ground). Use a negative angle for a downward throw.
Formulas
Componentsvx = v0 cos θ vy0 = v0 sin θ
Maximum heighthmax = h0 + vy0²2g
Time of flight and rangeT = vy0 + √(vy0² + 2gh0)g R = vxT
Worked example
20 m/s at 40° from 1.5 m (the default)
- vx = 20 cos 40° = 15.32 m/s; vy0 = 20 sin 40° = 12.86 m/s.
- hmax = 1.5 + 12.86²/(2 × 9.807) = 9.93 m.
- T = (12.86 + √(12.86² + 2 × 9.807 × 1.5))/9.807 = 2.734 s.
- R = 15.32 × 2.734 = 41.9 m.
Assumptions and limits
- No air resistance and constant gravity.
- Flat ground at the landing height.
Frequently asked questions
What angle gives the longest range?
45° on level ground without air resistance. Launching from a height, the best angle is a little less than 45°.
Why do 30° and 60° give the same range?
On level ground the range is v₀² sin 2θ / g, and sin 60° = sin 120°, so complementary angles land at the same spot. The steeper one flies higher and longer.