Dot notation (ẋ)
A dot over a letter, ẋ, is a derivative with respect to time: ẋ is the rate at which x changes, dx/dt. Two dots, ẍ, are the second derivative. It is Newton’s notation.
Easily confused with
- Vector arrow and hat (v⃗, x̂)An arrow over a letter, v⃗, marks a vector: a quantity with a direction as well as a size. A hat, x̂, marks a unit vector, which has length one and gives only a direction; î, ĵ and k̂ point along the x, y and z axes.
- Sample mean (x̄)A dot over a letter is a time derivative; a bar is a mean.
How to read it
The IUPAC Green Book lists ẋ beside dx/dt as the first derivative of x with respect to time, and writes velocity as the time derivative of position, ṙ = dr/dt. Unicode’s chart describes its combining dot above (U+0307) as the derivative in Newtonian notation and the combining diaeresis, two dots (U+0308), as the double derivative.
Also searched as: dot above a variable, dot notation symbol, dot over a letter, Newton’s notation, time derivative, ẍ, ẋ, x dot.
Dots, primes and d’s
Three notations for a derivative are still in use. Leibniz wrote dx and dy in a manuscript of 11 November 1675, the d of dy/dx; Lagrange introduced the prime, f′(x) for the first derivative and f″(x) for the second, and used it in 1797 (Miller, Earliest Uses of Symbols of Calculus); and Newton’s dot survives for derivatives in time.
Look-alikes
A bar over a letter is a mean in statistics (x̄), and a hat is a unit vector or an estimate (x̂).
Read next
- Next in Physics and chemistry symbolsProportional to sign (∝)∝ means “is proportional to”. y ∝ x says that y equals x multiplied by a constant, y = kx.
- The same shape in Video game ratingsPEGI 3, 7, 12, 16 and 18PEGI 3, 7, 12, 16 and 18 are the age ratings of PEGI (Pan European Game Information), the video game rating system used in most of Europe. The number is the minimum age PEGI considers the game’s content suitable for.
More physics and chemistry symbols
The same shape elsewhere
Browse symbols drawn with letters and numbers.
Sources
- Combining Diacritical Marks: Range 0300–036F (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Combining Diacritical Marks, 0307–0308
- Quantities, Units and Symbols in Physical Chemistry (the Green Book), IUPAC Green Book, 3rd edition, 2nd printing (2008), International Union of Pure and Applied Chemistry (IUPAC), Sec. 4.2; Sec. 2.1
- Earliest Known Uses of Some of the Words of Mathematics (F), Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics, MacTutor History of Mathematics, University of St Andrews, FLUXION and FLUENT
- Earliest Uses of Symbols of Calculus, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Derivative
Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research
Added .