Projectile Range Calculator
Horizontal range for level-ground launch.
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Formula
R = v² sin(2θ) ÷ g
For launch and landing at the same height, with no air drag, range depends on speed, angle, and gravity. 45° maximizes range on level ground.
Worked example
20 m/s at 45° gives R ≈ 40.8 m on Earth, with matching time-of-flight and apex height computed.
Where this can give the wrong answer
- Ignores air resistance — real baseballs and golf balls fall short.
- Launch and landing heights must match for this closed form.
- Angles near 0° or 90° give very small horizontal range.
FAQ
- sin(2θ) peaks at 90° when θ = 45°. Complementary angles (30° and 60°) give the same range.