Last updated: November 19, 2025
Projectile range calculator explained
For projectiles launched and landing at the same elevation (no air drag), horizontal range depends on initial speed , launch angle , and gravity . This calculator uses the closed-form solution to compute range, solve for speed, or determine the needed launch angle.
How the conversion works
The standard formula is:
with measured from the horizontal and generally 9.81 m/s². The calculator converts degrees to radians internally and can back-solve for any variable. Maximum range occurs at when launch and landing heights match.
Units and conversions
| Quantity | Units | Notes |
|---|---|---|
| Velocity | m/s, km/h, mph, ft/s | Converted to m/s. |
| Angle | degrees, radians | Degrees convert to radians for sine. |
| Gravity | m/s² | Modify for other planets or lab experiments. |
| Range | m, km, ft, mi | Uses the same base unit as velocity. |
Worked examples
- Optimal 45 deg launch
m/s, .
- Required launch speed
Need 100 m range at on Earth.
Tips and pitfalls
- The formula assumes launch and landing heights are equal; adjust with full projectile equations if they're different.
- Air drag shortens real-world range; use this tool for idealized physics or quick estimates.
- Doubling speed doubles range because .
- Keep angles between 0 and 90 degrees; beyond that the sine function mirrors and yields redundant results.