By Zencalcy Editorial TeamLast reviewed About us
For a launch and landing at the same height, range depends on speed squared and twice the launch angle. That makes the range symmetric about 45°, so 30° and 60° give the same distance when air resistance is ignored.
Flat-ground range from launch speed and angle.
R = v² · sin(2θ) / g
The result is symmetric about 45°: complementary angles give the same range in a vacuum.
| Symbol | Meaning |
|---|---|
| v | Launch speed, in metres per second. |
| θ | Launch angle above the horizontal. |
| R | Horizontal range, in metres. |
sin(90°) = 1, so the range is 400 / 9.80665 = 40.77 m. The same speed at 30° or 60° gives 35.31 m.
Continue with the Quarter Mile Calculator, Resultant Velocity Calculator, or the Rolling Resistance Calculator — or browse more kinematics tools and all physics calculators.
45° on level ground without air resistance. With drag, the optimum drops to roughly 35° to 40° for many projectiles.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026