What is a Beam Field Angle?
The Beam Field Angle (BFA) is the angular spread of a light beam or electromagnetic radiation as it propagates through space. It represents the angle subtended by the illuminated area at the source and is commonly used in optics, lighting design, and antenna engineering.
How to Use This Calculator
- Enter the Diameter of the Object (in meters) - this is the width of the illuminated area or beam spot
- Enter the Distance to the Object (in meters) - this is the distance from the source to the target
- Click Calculate to get the beam field angle in degrees
The Formula
The beam field angle is calculated using:
$$\text{BFA} = 2 \times \arctan\left(\frac{D}{2d}\right) \times \frac{180}{\pi}$$
Where:
- D = Diameter of the illuminated area (meters)
- d = Distance to the object (meters)
- The result is converted from radians to degrees (multiplying by 57.2958)
Calculation Example
Given:
- Diameter = 2.7 meters
- Distance = 40 meters
Solution:
$$\arctan\left(\frac{2.7}{2 \times 40}\right) = \arctan\left(\frac{2.7}{80}\right) = \arctan(0.03375) \approx 0.03374 \text{ radians}$$
$$\text{BFA} = 2 \times 0.03374 \times 57.2958 \approx 3.87 \text{ degrees}$$
Applications
- Lighting Design: Determining the spread angle of spotlights and floodlights
- Optics: Calculating beam divergence in laser systems
- Antenna Engineering: Measuring radiation pattern beam width
- Photography: Understanding lens coverage angles
- Projection Systems: Designing projector throw distances and screen sizes