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Focal Ratio Calculator

Work out focal ratio instantly with clear inputs, formula shown and shareable results.

About Focal Ratio Calculator

Focal ratio is focal length divided by aperture: 750 mm over 150 mm is f/5. Because image brightness per unit area scales with the inverse square of the ratio, an f/10 system needs four times the exposure of an f/5 for the same extended-object signal. Aperture alone determines total light gathered and resolution; the ratio determines field and image scale.

Formulas

Focal ratio

f/ratio = focal length / aperture

Exposure scaling

time is proportional to (focal ratio)^2 for extended objects

Worked example

With the default values below, Focal Ratio Calculator returns Focal Ratio of 5.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Focal lengthminimum 0 mm
750 mm
Aperture diameterminimum 0 mm
150 mm

Results

Focal Ratio
5.00 f/
Aperture Area
17,671 mm2
Exposure Time Relative To f/4
1.563 x
Speed Classification
Moderate - a good all-round ratio

Step by step

  1. 1Values used
  2. 2Focal ratio
  3. 3Exposure scaling
  4. 4Focal Ratio= 5.00 f/
  5. 5Aperture Area= 17,671 mm2
  6. 6Exposure Time Relative To f/4= 1.563 x
  7. 7Speed Classification= Moderate - a good all-round ratio

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does a faster ratio see fainter stars?

For point sources, no - aperture decides that. Faster ratios help extended objects like nebulae, where signal is spread over area.

Why do planetary imagers use slow ratios?

Because a long focal length gives the image scale needed to sample fine detail across the sensor pixels.

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