How to Find the Square Foot of a Dish Head

A satellite dish focuses electromagnetic beams.

A satellite dish is a parabolic reflector. It reflects linear electromagnetic waves that enter it toward a single point, the reflector's focal point. The photons of energy all travel the same distance to various parts of the dish's surface, ultimately reaching the focal point simultaneously. They then hit the antenna, also known as the "antenna feed," which is placed at the focal point. The dish's surface area depends on its focal length, which describes its depth, and its diameter.

Instructions

1. Multiply the dish's diameter, measured in feet, by 0.3048 to convert it to meters. If the dish has a diameter of 16.4 feet: 16.4 x 0.308 = 5 meters.

2. Multiply the dish's focal length, measured in meters, by 4. If, for instance, the dish has a focal length of 0.70 meters: 4 x 0.7 = 2.8.

3. Divide 1 by your answer: 1 / 2.8 = 0.357.

4. Square your answer: 0.357 ^ 2 = 0.127.

5. Square the dish's diameter: 5 ^ 2 = 25.

6. Multiply the answers to Steps 3 and 4: 0.127 x 25 = 3.175.

7. Ad 1 to your answer: 3.175 + 1 = 4.175.

8. Raise your answer to the power of 1.5: 4.175 ^ 1.5 = 8.53.

9. Subtract 1 from your answer: 8.53 - 1 = 7.53.

10. Multiply the answer to Step 3 by 6: 0.127 x 6 = 0.762.

11. Divide the answer from Step 8 by the answer to Step 9: 7.53 / 0.762 = 9.88.

12. Multiply your answer by pi: 9.88 x 3.142 = approximately 31 square meters.

13. Multiply your answer by 10.8 to convert it to square feet: 31 x 10.8 = 334.8 square feet.

References

• Montgomery College: Parabolic Antennas
• Metropolitan State College of Denver: The Reflection Property of a Parabola

Resources

• "Antenna And Wave Propagation"; K.A.Bakshi; 2008