Projectile Range Calculator Formula
Understand the math behind the projectile range calculator. Each variable explained with a worked example.
Formulas Used
Horizontal Range
range = pow(velocity, 2) * sin(2 * angle_rad) / gravityVariables
| Variable | Description | Default |
|---|---|---|
velocity | Launch Velocity(m/s) | 30 |
angle | Launch Angle(degrees) | 45 |
gravity | Gravitational Acceleration(m/s²) | 9.81 |
angle_rad | Derived value= angle * pi / 180 | calculated |
How It Works
Projectile Range
For a projectile launched from and landing at the same elevation:
Formula
R = v² * sin(2*theta) / g
Maximum range occurs at a 45-degree launch angle. The range is symmetric about 45 degrees (e.g., 30 and 60 degrees give the same range).
Worked Example
A ball is launched at 30 m/s at 45 degrees.
velocity = 30angle = 45gravity = 9.81
- 01R = v² * sin(2 * theta) / g
- 02R = 900 * sin(90°) / 9.81
- 03R = 900 * 1 / 9.81
- 04R = 91.74 m
Ready to run the numbers?
Open Projectile Range Calculator