Optical Fiber Numerical Aperture Calculator
Calculate the numerical aperture and acceptance angle of an optical fiber from core and cladding refractive indices.
Also calculates the V-number.
The numerical aperture (NA) of an optical fiber defines the maximum acceptance angle of light that can propagate by total internal reflection:
NA = √(n_core² − n_clad²) = sin(θ_max)
The V-number (or normalized frequency) determines how many modes can propagate: V = (2πr/λ) × NA
Where:
- NA = Numerical aperture
- n_core = Refractive index of the fiber core
- n_clad = Refractive index of the cladding
- θ_max = Half-angle of the acceptance cone (in air)
- r = Core radius
- λ = Wavelength of light
V-number interpretation:
- V < 2.405: Single-mode fiber (one light path only: best for long-distance communications)
- V > 2.405: Multi-mode fiber (many light paths: simpler but more dispersion)
Typical fiber parameters:
| Fiber type | n_core | n_clad | NA | θ_max |
|---|---|---|---|---|
| Single-mode (SMF-28) | 1.4677 | 1.4625 | 0.12 | 6.9° |
| Multi-mode (50μm) | 1.480 | 1.460 | 0.24 | 13.9° |
| Plastic optical fiber | 1.490 | 1.400 | 0.51 | 30.7° |
Why NA matters:
- Higher NA = wider acceptance cone = easier to couple light in
- But higher NA also means more modes and more dispersion (pulse spreading)
- Single-mode fiber has low NA but negligible dispersion: used for trans-oceanic cables
- Multi-mode fiber has higher NA: used for short-distance data centers and buildings
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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