Projectile Motion Calculator
Enter the launch speed and angle to calculate flight time, maximum height, and horizontal range, ignoring air resistance.
Last updated: September 5, 2026
Frequently asked questions
What angle gives the maximum range?
45° - for a given launch speed on flat ground with no air resistance, 45° splits the velocity evenly between horizontal and vertical components in a way that maximizes horizontal distance. Any other angle (holding speed and ground level fixed) produces a shorter range.
What is the range of a projectile launched at 20 m/s at 45°?
About 40.77 m - vₓ = vy = 20×cos(45°) = 20×sin(45°) ≈ 14.14 m/s, flight time = 2×14.14÷9.81 ≈ 2.88 s, range = 14.14×2.88 ≈ 40.77 m.
Why do 30° and 60° give the same range?
Complementary launch angles (angles that add up to 90°) always produce the same range on flat ground, because the range formula depends on sin(2×angle), and sin(2×30°) = sin(60°) equals sin(2×60°) = sin(120°) - both are the same value.
Does this account for air resistance?
No - this uses ideal projectile motion (only gravity acting on the object), which is accurate for dense, compact objects moving at moderate speeds over short distances, but increasingly diverges from reality for light or fast-moving objects where air drag matters.
How do I calculate the maximum height of a projectile?
Max height = (v × sin(angle))² / (2 × g). For a launch at 20 m/s and 45° with g = 9.81: (20×sin45°)² / (2×9.81) = (14.14)² / 19.62 ≈ 10.19 m.
What happens to the range if I double the launch velocity?
The range quadruples - since range is proportional to velocity squared (range = v²×sin(2×angle)/g), doubling v multiplies the range by 2² = 4, holding angle and gravity constant.
Can I use this for a projectile launched from a height, like off a cliff?
No - this calculator assumes launch and landing occur at the same height (ground level), which simplifies the flight-time formula. A projectile launched from an elevated point needs an additional term accounting for the extra fall distance, which this tool doesn't include.