Telescope Light Gathering Calculator Formula
Understand the math behind the telescope light gathering calculator. Each variable explained with a worked example.
Formulas Used
Light Gathering Power
lgp = pow(aperture / eye_pupil, 2)Collecting Area
area_cm2 = pi * pow(aperture / 20, 2)Variables
| Variable | Description | Default |
|---|---|---|
aperture | Telescope Aperture(mm) | 200 |
eye_pupil | Eye Pupil Diameter(mm) | 7 |
How It Works
Light Gathering Power
LGP = (D_telescope / D_eye)²
Light collection scales with the area of the aperture. A 200 mm scope collects (200/7)² ≈ 816 times more light than the dark-adapted eye (7 mm pupil).
This is why larger telescopes see fainter objects.
Worked Example
A 200 mm telescope vs 7 mm pupil.
- 01LGP = (200/7)² = 28.57² = 816×
- 02The scope gathers 816 times as much light.
- 03Area = π × (200/20)² = π × 100 = 314 cm²
Frequently Asked Questions
Why is aperture the most important telescope spec?
More light means fainter objects, better resolution, and more detail. Aperture is the single most important factor for astronomical performance.
What pupil size should I assume?
Young adults: about 7 mm in darkness. Over 50: about 5-6 mm. This affects the comparison.
Does a larger scope always show more?
In dark skies, yes. Under light pollution, benefits diminish for extended objects but still help for point sources (stars).
Ready to run the numbers?
Open Telescope Light Gathering Calculator