How to Find the Focal Point of a Parabolic Dish

A parabola is a curved mathematical shape.

Measure and Calculate

Satellite dishes are shaped like parabolas in order to focus the somewhat weak signal from the satellite.Satellite dishes are shaped like parabolas in order to focus the somewhat weak signal from the satellite.
It is a useful shape for dishes that collect or distribute light or radio waves, because parallel beams that approach a parabola head-on will all be reflected onto a single point, called the focal point. Conversely, if a source of light or radio waves is placed at the focal point of a parabolic dish, parallel beams will be produced that can be emitted in a specific direction by changing the orientation of the dish. You can find the focal length of a parabolic dish either by measurement and calculation, or with a simple experiment if the dish reflects light well.

Measure the diameter of the dish with the tape measure. If you look down on the dish from above, just measure from one edge of the dish across to the other, right through the center, to get the diameter.

Measure the depth of the dish, which is the height of the dish when viewed from the side. With the dish sitting on a level surface, simply measure with the tape from the outer edge straight downward to the surface it's resting on.

Square the dish's diameter by multiplying the value you measured in Step 1 by itself.

Divide the square of the diameter, the value from the last step, by 16.

Divide the value from the previous step by the depth of the dish you measured in Step 2. This value is the focal length, and it is the distance from the bottom of the dish directly upward to the focal point.

Light Experiment

Take your dish outside on a sunny day. You can also perform this experiment indoors if you have a bright, directed light source like a spotlight. In either case, this experiment will only work for a dish that reflects light to some reasonable degree, though it need not be a mirror.

Set the dish down, facing toward the sun or light source.

Hold a piece of paper or something similar above the surface of the dish, directly above the center. If the dish is reflective enough, you will see a spot of light shining on the paper. Slowly move the paper up and down, watching the spot. When the paper is at the focal distance, the spot of light will be at its smallest and most intense. This is the focal point of the mirror.

Things You Will Need

  • Tape measure (optional)


  • Use caution when testing a very reflective dish in sunlight, because the energy at the focal point can easily burn you.

About the Author

Michael Carroll is a high school mathematics teacher. He has written for various websites since 2010, specializing in programming, web design, electronics and various pieces of software. He holds a bachelor's degree in electrical engineering from the University of Texas, with specialization in embedded system design.