Maximum Bullet Range Calculator

Formula

The formula to calculate the maximum bullet range (R) is:

\[ R = \frac{v^2 \sin(2\theta)}{g} \]

Where:

\( R \) is the maximum bullet range
\( v \) is the initial velocity of the bullet in meters per second (m/s)
\( \theta \) is the launch angle in degrees
\( g \) is the acceleration due to gravity in meters per second squared (m/s²)

Definitions

Maximum Bullet Range: The farthest distance a bullet can travel when fired at an optimal angle, typically 45 degrees, in a vacuum or under ideal conditions. This range is influenced by the initial velocity of the bullet, the launch angle, and the acceleration due to gravity. In real-world scenarios, factors such as air resistance, wind, and the bullet’s shape and mass can affect the actual range.

Example

Let's say the initial velocity (v) is 800 m/s, the launch angle (θ) is 45 degrees, and the acceleration due to gravity (g) is 9.81 m/s². Using the formula:

\[ R = \frac{800^2 \sin(2 \times 45)}{9.81} \]

We get:

\[ R = \frac{640000 \times 1}{9.81} \approx 65229.36 \, \text{meters} \]

So, the maximum bullet range is approximately 65229.36 meters.