Rho
Rho (Ρ, ρ) is the 17th letter of the Greek alphabet, said “roh” and written r in Latin letters. In science ρ is the symbol for density, and in statistics for the population correlation coefficient.
How to read it
Dictionary.com and the Collins English Dictionary give the pronunciation “roh” (/roʊ/, /rəʊ/); Collins describes rho as a consonant transliterated as r or rh. The capital Ρ has the shape of the Latin P, and Dictionary.com prints it with a Latin P, but it stands for the r sound and a separate character (Latin P is U+0050).
Also searched as: rho letter, rho symbol, ρ, Ρ, ρ meaning.
Capital and small forms
| Form | Character | Code point | Unicode name |
|---|---|---|---|
| Capital | Ρ | U+03A1 | GREEK CAPITAL LETTER RHO |
| Small | ρ | U+03C1 | GREEK SMALL LETTER RHO |
| Variant (“tailed rho”) | ϱ | U+03F1 | GREEK RHO SYMBOL |
Unicode describes ϱ as a technical symbol.
Rho in science and statistics
Density is ρ = m / V, mass divided by volume, in kilograms per cubic metre (NIST’s Guide for the Use of the SI; OpenStax). NIST notes that ρ is also used for charge density, ρ = Q / V. In statistics ρ is the population correlation coefficient; OpenStax’s Introductory Statistics writes the sample correlation coefficient, calculated from data, as r.
In AI and machine learning
In PyTorch’s Adadelta optimiser, rho (ρ) is the coefficient used for computing a running average of squared gradients, 0.9 by default.
In quantum physics
ρ is the density matrix, also called the state operator. MIT’s 22.51 notes describe the state operator for a pure state |ψ⟩ as the outer product ρ = |ψ⟩⟨ψ|, written in Bra-ket notation (|ψ⟩); MIT’s 8.06 notes give the same density matrix.
Write in Greek letters
stringmash.comGreek alphabet translatorWrite English in Greek letters by sound, or turn Greek back into Latin letters as Greek passports do.Read next
- Next in Greek lettersSigmaSigma (Σ, σ, ς) is the 18th letter of the Greek alphabet, said “SIG-muh”. In maths the capital Σ means the sum of a series of numbers, and in statistics the small σ is the standard deviation.
- In Statistics symbolsCorrelation coefficient (r)r is the correlation coefficient, a number from −1 to 1 that measures how closely two variables follow a straight-line relationship, and in which direction. The correlation of a whole population is written with the Greek letter ρ (rho).
More greek letters
The same shape elsewhere
Browse symbols drawn with letters and numbers.
Sources
- rho (Dictionary.com entry), Dictionary.com Unabridged; Collins English Dictionary, Dictionary.com, Entry, American and British (Collins) senses
- Greek and Coptic: Range 0370–03FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Greek letters; variant letterforms
- C0 Controls and Basic Latin: Range 0000–007F (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Basic Latin
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 (2008), National Institute of Standards and Technology, Sec. 8.6.7
- University Physics Volume 1, 14.1 Fluids, Density, and Pressure, OpenStax (Rice University), Density
- Introductory Statistics 2e, 12.4 Testing the Significance of the Correlation Coefficient, OpenStax (Rice University), Section 12.4
- Adadelta (torch.optim.Adadelta), PyTorch 2.14 documentation, PyTorch Foundation, Parameters
- 8.06 Lecture Notes 3: Entanglement, density matrices and decoherence (A. W. Harrow), MIT 8.06, Spring 2016, Massachusetts Institute of Technology, Sec. 2.1–2.2
- 22.51 Course Notes, Chapter 7: Mixed states, MIT OpenCourseWare, Fall 2012, Massachusetts Institute of Technology, Sec. 7.1
Researched, edited and approved by Rory Hansen before publishing. Last reviewed September 30, 2026. How we research
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