F-number to NA converter

Enter a value in either field to convert instantly.

f/#
⇌
NA
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Standard Approximation

How it works?

F-Number (f/#) and Numerical Aperture (NA) are two ways of describing the same thing: the light-gathering cone of an optical system. Photography typically uses f/#, while Microscopy and Fiber Optics use NA.

For small angles (paraxial approximation) in air, the relationship is a simple inverse function:

$$ NA \approx \frac{1}{2 \times f/\#} $$ Finding NA
$$ f/\# \approx \frac{1}{2 \times NA} $$ Finding F-Number

Note: This approximation assumes the system is in air (\(n=1\)) and holds true for f-numbers greater than f/2.0. For very fast lenses (e.g., f/0.7), the exact trigonometric relationship \(NA = \sin(\theta)\) should be used.

Why convert F-Number to NA?

Why this matters
  • Compatibility: Match camera lenses (f/#) to fiber optics (NA).
  • Resolution: Determine the theoretical limit of your imaging system.
  • Laser Focusing: Accurately calculate the spot size of a focused beam.
  • Light Gathering: Compare brightness between different optical systems.

Optical engineers often find themselves translating between two different worlds. If you buy a lens for a machine vision camera, it is specified in f-numbers (e.g., f/1.4). If you buy a lens for a microscope or fiber coupler, it is specified in Numerical Aperture (e.g., NA 0.5).

While they essentially measure the same thing—the light-gathering cone angle—they use different mathematical conventions. This tool allows you to instantly translate system requirements between these two standards to ensure your optical components will work together.

Quick Conversion Table

Typical values for common optical systems (assuming air medium).

Optic Type F-Number (f/#) Num. Aperture (NA)
Standard Zoom f/4.0 0.125
Prime Lens f/2.8 0.18
Fast Lens f/2.0 0.25
Low-Power Objective f/1.4 0.36
Ultra Fast / Fiber f/1.0 0.50
Theoretical Limit (Air) f/0.5 1.00

The Physics: Angle vs. Ratio

F-Number is defined geometrically as the ratio of focal length to diameter (f/# = f / D). It assumes the lens is "thin" and far from the object.

Numerical Aperture is defined trigonometrically (NA = n · sin θ). It measures the actual angle of the light cone. For "slow" lenses (f/2.0 and above), the two concepts map linearly (NA ≈ 1 / 2 × f/#). However, for very "fast" lenses (f/0.7), the geometry curves, and the linear approximation fails. This calculator uses the precise trigonometric relationship for high-speed optics.

1. Fiber Coupling

To launch a laser into an optical fiber, the focusing lens must have an NA equal to or less than the fiber's NA. If your lens is f/4 (NA 0.125) and your fiber is NA 0.14, you are safe. If your lens is f/2 (NA 0.25), you will lose light.

2. Microscope Resolution

In microscopy, brightness is not the only factor. The resolution is directly tied to NA (δ = λ / 2NA). Converting a camera lens f-number to NA helps you determine if that lens can physically resolve the micron-scale defect you are inspecting.

3. Laser Intensity

For laser cutting, you want the highest intensity possible. This requires the smallest spot size, which in turn requires the highest possible NA (lowest f-number). Engineers swap f-numbers to calculate the trade-off between spot size and depth of field.

4. Camera Sensor Matching

Machine vision sensors have a maximum acceptance angle for their pixels. If you use a lens with an f/# that creates a cone steeper than the pixel can accept (pixel vignetting), you waste light. Matching the NA of the lens to the sensor micro-lenses ensures maximum efficiency.

Deep Dive Article What is Numerical Aperture? Dive deeper into acceptance cones, resolution limits, and the difference between dry and oil-immersion optics.
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