Focal Reducer Effect Calculator Formula
Understand the math behind the focal reducer effect calculator. Each variable explained with a worked example.
Formulas Used
Effective Focal Length
eff_focal = focal_length * reduction_factorEffective f-Ratio
eff_fratio = native_fratio * reduction_factorSpeed Gain Factor
speed_gain = 1 / pow(reduction_factor, 2)Variables
| Variable | Description | Default |
|---|---|---|
focal_length | Native Focal Length(mm) | 1000 |
native_fratio | Native f-Ratio | 10 |
reduction_factor | Reduction Factor | 0.63 |
How It Works
Focal Reducer Effect
A focal reducer shortens the effective focal length, widening the FOV and making the system faster.
Formulas
f_eff = f * R N_eff = N * R
where R is the reduction factor (e.g., 0.63).
The speed gain (for extended objects) scales as 1/R squared, because the same light is concentrated into a smaller image.
Worked Example
1000 mm f/10 scope with a 0.63x reducer.
focal_length = 1000native_fratio = 10reduction_factor = 0.63
- 01f_eff = 1000 * 0.63 = 630 mm
- 02N_eff = 10 * 0.63 = f/6.3
- 03Speed gain = 1 / 0.63^2 = 2.52x faster
Ready to run the numbers?
Open Focal Reducer Effect Calculator