Dish gain
A parabolic dish's gain is G = η × (πD/λ)², where D is the diameter, λ the wavelength and η the efficiency, usually 55 to 65% with a well-matched feed. Doubling the diameter, or the frequency, adds 6 dB. That's why a small TV dish is fine for the QO-100 downlink at 10.5 GHz, but the 2.4 GHz uplink needs a bigger dish or more power for the same gain.
Beamwidth and pointing
The half-power beamwidth is about 70λ/D degrees. An 80 cm dish at 10.5 GHz has a beam under 3° wide, so it has to be pointed carefully, while the same dish at 2.4 GHz has a beam of about 11°. The QO-100 calculator and dish alignment calculator give the pointing angles.
Offset dishes
Most satellite TV dishes are offset dishes, a slice of a larger parabola, so the feed doesn't block the beam. Use the dish's width as the diameter. Their focal point is at the end of the feed arm. The focal length from the depth only applies to round prime-focus dishes, where the feed sits on the centre line: f = D² ÷ 16d.
Questions
What is the gain of an 80 cm dish at 10 GHz?
About 36 dBi, with a beamwidth of roughly 2.6°.
What size dish do I need for QO-100?
60 to 80 cm is typical for the downlink with an LNB. For the 2.4 GHz uplink, 80 cm to 1.2 m with a few watts works well.
How do I find a dish's focal point?
For a round prime-focus dish, focal length = diameter² ÷ (16 × depth). Offset dishes have the focus at the end of the feed arm.
Why is my dish's gain lower than calculated?
Feed spill-over, surface errors, blockage and pointing all reduce efficiency. 50 to 60% is realistic for home setups.