Fiber V Number Calculator

Core radius (a)

Radius unit µmmmcmm

Wavelength (λ)

Wavelength unit nmµmmmm

NA source Compute NA from indices Enter NA directly

Core index (n₁)

Cladding index (n₂)

Numerical aperture (NA)

Submit Reset

Tip: Typical single-mode silica fibers at 1550 nm have V near the cutoff.

The fiber V number (normalized frequency) describes how many guided modes a step-index fiber can support.

• V = (2π a / λ) × NA
• NA = √(n₁² − n₂²) when using indices
• Single-mode cutoff reference for step-index fibers: V < 2.405
• Approximate mode count (step-index, large V): M ≈ V² / 2

1. Enter the core radius and select its unit.
2. Enter the wavelength and select its unit.
3. Choose how to provide NA: indices or direct NA.
4. Press Submit to see results above the form.
5. Use Download CSV or Download PDF for reporting.

1) What the V number represents

The fiber V number, also called normalized frequency, combines core size, wavelength, and numerical aperture into one dimensionless value. For step-index fibers it predicts how strongly light is guided and how many spatial modes can propagate. Designers use V to check single-mode cutoffs and compare fibers across wavelengths. It is a fast screening metric before deeper dispersion and bend-loss analyses.

2) Core radius and wavelength effects

V scales linearly with core radius a and inversely with wavelength λ. Doubling the radius doubles V. Doubling the wavelength halves V. This is why a fiber that is multimode at 850 nm can become closer to single-mode at 1310 nm or 1550 nm, using the same glass. Because V ∝ (a·NA/λ), any change in size, NA, or wavelength shifts guidance. Example: a = 4.1 µm, λ = 1550 nm, and NA ≈ 0.131 gives V ≈ 2.2. In compact form, V is proportional to a×NA/λ.

3) Numerical aperture and index contrast

Numerical aperture (NA) measures the acceptance cone and is linked to refractive indices by NA = √(n₁² − n₂²). Small changes in n₁ or n₂ can shift NA and therefore V. For silica fibers, NA values around 0.10–0.15 are common. In air, NA is close to sin(θmax), so a larger NA accepts steeper rays.

4) Single-mode cutoff and practical meaning

A key reference is the step-index single-mode cutoff near V = 2.405. If V is below this value, higher-order modes are typically suppressed. Real links may still show weak higher-order content from bends or launches.

5) Mode count estimate for multimode fibers

A common approximation for guided modes is M ≈ V²/2 for step-index fibers. Use it for trends rather than tight specifications. At high V, small changes in a, NA, or λ can add many modes.

6) Step-index versus graded-index considerations

This calculator uses step-index guidance for clean analytic cutoffs. Graded-index fibers reshape modal delays, so detailed performance may need profile-specific models.

7) Units, tolerances, and measurement inputs

Accurate units matter because V depends on a/λ. Small radius tolerances can shift V near cutoff. Use index or NA values specified at your operating wavelength.

8) Using V for design decisions

Use V to screen designs: smaller core, longer wavelength, or lower NA moves toward single-mode. The opposite improves multimode coupling tolerance. Confirm bend-loss and bandwidth limits. Engineers often evaluate results at 1310 nm and 1550 nm.

1) What is a typical cutoff value for single-mode?

For an ideal step-index fiber, single-mode guidance is expected when V is below about 2.405. Close to cutoff, launch conditions and bending can influence whether weak higher-order content appears.

2) Can I use diameter instead of radius?

Yes. Enter radius as half of the core diameter. For example, a 9 µm core diameter corresponds to a 4.5 µm radius.

3) Why does V change with wavelength?

V is proportional to 1/λ. Longer wavelengths reduce V, which can suppress higher-order modes. Shorter wavelengths increase V and typically increase the number of guided modes.

4) Should I enter NA or refractive indices?

Use indices when you have reliable n₁ and n₂ at the operating wavelength. Use NA directly when the datasheet provides NA or when you are comparing designs with the same NA.

5) Does this account for bend loss?

No. V indicates modal guidance in an idealized straight fiber. Tight bends can increase loss and can preferentially strip higher-order modes, altering real behavior even when V suggests multimode guidance.

6) Is the mode count M ≈ V²/2 always accurate?

It is an approximation for step-index fibers at larger V. Real mode counts depend on profile, polarization effects, and wavelength-dependent indices. Use it to compare trends, not to certify specifications.

7) What if my NA seems greater than 1?

NA should be below 1 in typical fibers because it represents a sine of an acceptance angle in air. If you see NA ≥ 1, check units, index values, or whether the number refers to a different medium.