Mu — Μ / μ
Mu (Μ μ) is the twelfth letter of the Greek alphabet. The mu symbol is written Μ in uppercase (identical to the Latin M) and μ in lowercase. Its most common meaning is the prefix micro-, one millionth (10⁻⁶), as in μm (micrometre) and μg (microgram); in statistics μ is the population mean, and in physics it denotes the coefficient of friction and magnetic permeability. Copy it with the buttons below, or see how to type Greek letters on any keyboard.
Μ μ
Copy: Μ μ
Unicode code points: U+039C (uppercase), U+03BC (lowercase).
| Uppercase | Μ |
|---|---|
| Lowercase | μ |
| Transliteration | m |
| Pronunciation | mee |
| Numeric value | 40 |
Etymology and Origin
Mu comes from the Phoenician letter "mem," meaning "water." The uppercase mu (Μ) looks identical to the Latin letter M, and both descended from the same ancient source. Mu is the twelfth letter of the Greek alphabet and represents the "m" sound, unchanged from ancient to modern Greek.
Pronunciation
- Ancient Greek: [m] as in "mother"
- Modern Greek: [m] as in "mother" (unchanged)
- English usage: MYOO [mjuː]
Mu as the Micro- Prefix
The lowercase mu (μ) is used as the symbol for the metric prefix "micro-" (μ), meaning one millionth (10⁻⁶). This is one of the most common uses of mu in everyday science and engineering, appearing in measurements from micrometers to microseconds to micrograms.
- Micrometer: 1 μm = 10⁻⁶ m = 0.000001 meters
- Microsecond: 1 μs = 10⁻⁶ s (one millionth of a second)
- Microgram: 1 μg = 10⁻⁶ g (common in chemistry and medicine)
- Microampere: 1 μA = 10⁻⁶ A (electrical current)
Uses of Mu in Mathematics and Statistics
- Population Mean: μ represents the true mean of a population in statistics
- Expected Value: E[X] = μ for random variable X
- Möbius Function: μ(n) in number theory (values -1, 0, 1)
- Measure Theory: μ for general measure in advanced analysis
- Normal Distribution: N(μ, σ²) with mean μ and variance σ²
Uses in Science and Engineering
- Coefficient of Friction: μ = F_friction/F_normal (μ_s = static, μ_k = kinetic)
- Magnetic Permeability: μ₀ ≈ 4π × 10⁻⁷ H/m (permeability of free space)
- Dynamic Viscosity: μ in fluid mechanics (Pa·s)
- Particle Physics: μ⁻ (muon), an elementary particle like heavy electron
- Reduced Mass: μ = m₁m₂/(m₁+m₂) in two-body problems
- Chemical Potential: μ in thermodynamics
- Amplification Factor: μ in vacuum tube electronics
Coefficient of Friction
- Definition: μ = F_friction/F_normal, dimensionless ratio
- Static Friction: μ_s typically 0.5-1.5 (prevents sliding)
- Kinetic Friction: μ_k typically less than μ_s (during sliding)
- Examples: Ice on ice μ ≈ 0.02, rubber on dry concrete μ ≈ 1.0
Mathematical Examples with Mu
Micrometer: Human hair diameter ≈ 50-100 μm
Population mean: If SAT scores have μ = 1050, that's the true population average
Friction: 10 kg block, μ_s = 0.6: Maximum static friction = 0.6 × 10 × 9.8 = 58.8 N
Magnetic permeability: B = μ₀H relates magnetic field B to H-field
Muon lifetime: μ⁻ has mean lifetime τ ≈ 2.2 μs before decay
Writing Tips
- Uppercase Μ: Identical to Latin M - two vertical strokes connected by V at top
- Lowercase μ: Like "u" with tail extending below baseline on left
- Common mistake: Don't confuse μ with "u" - mu has descender on left side
- Handwriting: Start lowercase μ like "u", then extend left stroke downward
Interesting Facts
- Mu is the ancestor of the Latin letter M
- In ancient Greek numerals, Μ΄ = 40
- The muon (μ⁻) is about 207 times heavier than an electron
- Magnetic permeability μ₀ was exactly 4π × 10⁻⁷ H/m until 2019; the SI redefinition made it a measured quantity (still approximately the same value)
- Human eye can resolve details down to about 100 μm without magnification
- Typical bacteria are 1-10 μm in length
- In Zen Buddhism, "mu" (無) means "nothingness" (different origin)
- The Möbius function μ(n) is multiplicative and crucial in analytic number theory
- Rubber on concrete has one of the highest friction coefficients (μ ≈ 1.0)
- Muons created in upper atmosphere reach Earth's surface due to time dilation
Frequently Asked Questions
How do I type μ?
The easiest way is to use the copy buttons at the top of this page. In Microsoft Word, type 03BC and press Alt + X. In HTML, use μ (μ) or Μ (Μ). In LaTeX, use \mu or \Mu. With a Greek keyboard layout enabled, press M. See how to type Greek letters for every method.
Is μ the same as the micro sign µ?
They look identical but are two different characters: μ (U+03BC) is the Greek letter, and µ (U+00B5) is the "micro sign" kept for compatibility with older character sets. Either is understood in units like µm; use μ in Greek text and math.
How do I type the micro symbol µ?
On a Mac, press Option + M. On Windows, hold Alt and type 0181 on the numeric keypad. Both produce the micro sign µ.
What does μ mean in statistics?
μ is the population mean, the true average of a whole population. The sample mean is written x̄.