Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

Core Refractive Index

Required number input.

Cladding Refractive Index

Required number input.

Step-index fiber numerical aperture in air from core and cladding refractive indices: √(ncore²−nclad²). The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Numerical Aperture

The resulting numerical aperture returned as a number.

• A compact formula cannot establish code compliance, safety, durability, manufacturability, or fitness for service. Boundary conditions, material variability, tolerances, dynamic and fatigue effects, environmental exposure, uncertainty, and failure modes may require a fuller model and governing standard.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Aircraft Stall Speed

  Level-flight stall speed from aircraft weight, air density, wing area and maximum lift coefficient: Vs=√[2W/(ρSClmax)].

• Beam Stress Combined Axial Bending

  Combined elastic normal stress N/A+My/I at a chosen signed fiber coordinate; excludes buckling and local effects.

• Bending Stress

  Extreme-fiber bending stress magnitude in an elastic beam section from bending moment, neutral-axis distance and second moment.