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_factor

Effective f-Ratio

eff_fratio = native_fratio * reduction_factor

Speed Gain Factor

speed_gain = 1 / pow(reduction_factor, 2)

Variables

VariableDescriptionDefault
focal_lengthNative Focal Length(mm)1000
native_fratioNative f-Ratio10
reduction_factorReduction Factor0.63

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
  1. 01f_eff = 1000 * 0.63 = 630 mm
  2. 02N_eff = 10 * 0.63 = f/6.3
  3. 03Speed gain = 1 / 0.63^2 = 2.52x faster

Ready to run the numbers?

Open Focal Reducer Effect Calculator