Nu Symbol (Ν ν): Meaning, Uses, and How to Type It

Nu is the thirteenth letter of the Greek alphabet. The lowercase ν is the symbol for frequency in physics, most famously in Planck's relation E = hν, and it also stands for the neutrino, kinematic viscosity, Poisson's ratio, and the number of degrees of freedom in statistics. The uppercase Ν is identical to the Latin N and is almost never used as a symbol. The letter's biggest practical problem is that ν looks nearly the same as an italic v, so it is often mistaken for velocity. To type nu, use \nu in LaTeX, the HTML entity ν, or the N key on a Greek keyboard layout.

This guide covers what each form of nu means, where it appears in physics, engineering, statistics, and chemistry, and how to type ν and Ν on Mac, Windows, iPhone, in HTML, and in LaTeX.

The Nu Symbol Explained

Nu has two shapes, both of which you can copy from here:

• Ν — uppercase nu (Unicode U+039D)
• ν — lowercase nu (Unicode U+03BD)

There is no variant glyph, so LaTeX has no \varnu. The name is pronounced "new" in English (some physicists say "noo") and "nee" in modern Greek. In the Greek numeral system nu stood for 50. The letter descends from the Phoenician nun and is the ancestor of the Latin N, which is why it sits on the N key of Greek keyboards.

Nu vs. v: Telling Them Apart

In most fonts the lowercase nu is a narrow letter with a straight right stroke and a curved left stroke that meet at a sharp point at the bottom, while an italic Latin v has a rounded bottom and often a small hook on the right. Physics writers rely on convention more than on the glyph: ν is frequency (or a neutrino), v is velocity. When both appear in the same equation, authors often switch to f for frequency, as in E = hf, precisely to avoid the confusion. In LaTeX the two are unambiguous, \nu versus v, which is one reason to typeset equations rather than hand-write them.

Uppercase Nu (Ν)

Because uppercase nu looks exactly like the Latin N, it has essentially no use as a mathematical symbol. Writing Ν for a variable would be read as N. You will meet the capital letter only in Greek words and in the names of fraternities and honor societies such as Nu Rho Psi (neuroscience) or Sigma Nu.

LaTeX reflects this: there is no \Nu command. If you need an upright capital nu in an equation, type \mathrm{N}.

Lowercase Nu (ν)

Uses of lowercase ν:

• Frequency — ν in E = hν and c = λν
• Neutrino — ν_e, ν_μ, ν_τ, and the antineutrino ν̄
• Kinematic viscosity — ν = μ/ρ in fluid mechanics
• Poisson's ratio — ν in materials science
• Degrees of freedom — ν in the t and χ² distributions
• Stoichiometric coefficient — ν_i in chemical reactions
• Wavenumber — ν̃ (nu with a tilde) in spectroscopy
• Critical exponent — ν for the correlation length in phase transitions

Frequency and Planck's Relation

Frequency is the number of cycles per second, measured in hertz, and physics traditionally writes it as ν. It is the reciprocal of the period, ν = 1/T, and for a wave it is related to wavelength λ and speed by:

c = λν

for light in vacuum. The most famous equation with ν is Max Planck's relation from 1900, which Einstein used in 1905 to explain the photoelectric effect:

E = hν

A photon's energy is its frequency times Planck's constant h ≈ 6.626 × 10⁻³⁴ J·s. Combining the two formulas gives E = hc/λ, the form used in spectroscopy. Engineers and electrical engineers normally write f instead of ν, so E = hf and c = λf mean exactly the same thing.

In spectroscopy the related quantity wavenumber ν̃ = 1/λ, measured in cm⁻¹, is written as nu with a tilde. Infrared spectra are plotted against ν̃, and a peak near 1700 cm⁻¹ is the signature of a carbonyl bond.

Neutrinos

In particle physics ν is the symbol of the neutrino, the nearly massless, electrically neutral particle that interacts only through the weak force and gravity. There are three flavors, ν_e, ν_μ, and ν_τ, matching the electron, muon, and tau, and each has an antiparticle written with a bar, ν̄. Beta decay produces an electron antineutrino:

n → p + e⁻ + ν̄_e

Wolfgang Pauli proposed the particle in 1930 to save energy conservation in beta decay, and Enrico Fermi named it "little neutral one" in Italian. The discovery that neutrinos oscillate between flavors, which proves they have mass, won the 2015 Nobel Prize in Physics.

Kinematic Viscosity

Fluid mechanics has two viscosities. Dynamic viscosity μ measures a fluid's resistance to shear, while kinematic viscosity ν is the dynamic viscosity divided by the density:

ν = μ / ρ

Its SI unit is m²/s; the older unit is the stokes (1 St = 10⁻⁴ m²/s). Water at 20 °C has ν ≈ 1.0 × 10⁻⁶ m²/s, and air has ν ≈ 1.5 × 10⁻⁵ m²/s, which is larger than water's even though air is far less viscous in the everyday sense, because air is so much less dense. Kinematic viscosity is the version that appears in the Reynolds number:

Re = uL / ν

where u is the flow speed and L a characteristic length. Low Re means smooth laminar flow; high Re means turbulence.

Poisson's Ratio

When you stretch a material it usually gets thinner. Poisson's ratio ν is the negative ratio of transverse strain to axial strain:

ν = −ε_trans / ε_axial

For most metals ν is close to 0.3, for rubber it approaches the incompressible limit of 0.5, and for cork it is nearly 0, which is why a cork can be pushed into a bottle without bulging. Materials with negative ν, called auxetics, get fatter when stretched. Poisson's ratio connects the elastic moduli: E = 2G(1 + ν), where E is Young's modulus and G the shear modulus.

Degrees of Freedom in Statistics

Statisticians write ν (or sometimes df) for the number of degrees of freedom of a distribution. Student's t distribution with ν degrees of freedom has heavier tails for small ν and approaches the normal distribution as ν → ∞; the χ² distribution with ν degrees of freedom has mean ν and variance 2ν. A t-test on a sample of n observations uses ν = n − 1.

Nu in Different Fields

Physics

• Photon frequency in E = hν and the photoelectric equation K_max = hν − Φ
• Neutrinos ν_e, ν_μ, ν_τ and antineutrinos
• Collision frequency ν in plasma physics and kinetic theory

Engineering

• Kinematic viscosity ν in the Reynolds number and boundary-layer theory
• Poisson's ratio ν in stress–strain relations and finite-element models

Mathematics and Statistics

• Degrees of freedom ν of the t, χ², and F distributions
• Critical exponent ν, with correlation length ξ ∝ |T − T_c|^(−ν)
• Order of a Bessel function J_ν(x)
• A measure ν in measure theory, often paired with μ

Chemistry

• Stoichiometric coefficients ν_i, negative for reactants and positive for products, so that Σ ν_i A_i = 0
• Wavenumber ν̃ in infrared and Raman spectroscopy

How to Type Nu

Windows: Nu has no classic Alt code, so Alt + 957 works only in Microsoft Word and other apps that accept Unicode Alt codes. In Word, the most reliable method is to type 03BD and press Alt + X. In other programs, open Character Map, search for "nu," and copy the character, or use the emoji panel (Win + .) and its Symbols tab.

Mac: macOS has no Option-key shortcut for nu. Add the Greek keyboard in System Settings > Keyboard > Input Sources, switch to it, and press N for ν or Shift + N for Ν. Alternatively, open the Character Viewer with Control + Command + Space and search for "nu."

iPhone and iPad: Go to Settings > General > Keyboard > Keyboards > Add New Keyboard and choose Greek. Switch keyboards with the globe key; ν sits on the N key. Android users can add Greek in Gboard's language settings.

Word and Google Docs: In Word, use Insert > Symbol > More Symbols with the subset set to Greek and Coptic. In Google Docs, use Insert > Special characters and search for "nu."

HTML: Write ν for ν and Ν for Ν. For wavenumber, combine ν with a tilde using ν̃.

LaTeX: In math mode, \nu gives ν. There is no \Nu; for an upright capital use \mathrm{N}. Wavenumber is \tilde{\nu} and an antineutrino is \bar{\nu}. The following document compiles as written:

1\documentclass{article}
2\usepackage{amsmath}
3\begin{document}
4Frequency is $\nu$, not velocity $v$; wavenumber is $\tilde{\nu}$
5and the antineutrino is $\bar{\nu}_e$.
6\[
7  E = h\nu,
8  \qquad
9  \nu = \frac{\mu}{\rho},
10  \qquad
11  \nu = -\frac{\varepsilon_{\mathrm{trans}}}{\varepsilon_{\mathrm{axial}}},
12  \qquad
13  n \to p + e^{-} + \bar{\nu}_e
14\]
15\end{document}
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For nu in running text, the textgreek package provides \textnu, which gives an upright ν that matches the surrounding font.

Related Greek Letters

Frequency ν pairs with wavelength λ and angular frequency ω = 2πν; kinematic viscosity ν pairs with dynamic viscosity μ and density ρ; and degrees of freedom ν accompany the χ² distribution.

• Lambda symbol (Λ λ) — wavelength in c = λν
• Mu symbol (Μ μ) — dynamic viscosity and the muon that partners ν_μ
• Omega symbol (Ω ω) — angular frequency ω = 2πν
• Pi symbol (Π π) — the 2π in ω = 2πν and ħ = h/2π

The full list of letters is on our Greek alphabet reference, and Greek letters in math and science lists every letter's standard meanings. For a copy-and-paste palette, see the Greek symbol tool.

FAQ

What does ν mean in physics?

In most physics contexts ν is frequency, measured in hertz, as in E = hν. In particle physics it is the neutrino, in fluid mechanics it is kinematic viscosity, and in materials science it is Poisson's ratio. The surrounding equation makes the meaning clear.

Is ν the same as v?

No. ν (nu, U+03BD) is a Greek letter and v (U+0076) is a Latin letter. They look similar in italic type, which is why frequency ν and velocity v are so often confused. If you can, use f for frequency when velocity appears in the same equation, and always use \nu rather than v in LaTeX.

Why is frequency written ν instead of f?

Both are standard. Physicists, especially in optics, quantum mechanics, and spectroscopy, inherited ν from nineteenth-century usage, while engineers prefer f. The ISO 80000 standards list both f and ν as acceptable symbols for frequency.

Writing with Greek Symbols

Papers that mix frequencies, viscosities, and neutrinos need nu typeset cleanly and consistently. In LaTeX that means \nu in math mode rather than a pasted Unicode character or a plain v, which keeps the letter unambiguous throughout the document.

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