Using the Theta Symbol
Theta is the eighth letter of the Greek alphabet, an oval with a horizontal bar, and in mathematics it is the default name for an angle. Trigonometry textbooks write sin θ, cos θ and tan θ, polar coordinates use (r, θ), and the angle between two vectors is θ in the dot-product formula a · b = |a||b| cos θ. ### Other meanings
- Big Theta notation: Θ(n log n) says an algorithm's running time is bounded above and below by the same function; it is the tight-bound cousin of Big O.
- Statistics and machine learning: θ is the generic parameter of a model, the vector of weights that gradient descent adjusts.
- Physics: θ is the polar angle in spherical coordinates, the scattering angle, and the Bragg angle in crystallography.
- Finance: theta is an option's time decay, the daily loss of value as expiry approaches.
θ, ϑ and Θ
Unicode encodes three shapes. θ is the standard small letter. ϑ, the GREEK THETA SYMBOL, is a cursive form with an open top that mathematicians use when a second theta-like variable is needed, and it is the usual letter for the Jacobi theta functions; LaTeX produces it with \vartheta. Capital Θ is the letter used in Big Theta, and ϴ is a separate capital variant with a shorter bar that exists mainly for maths fonts. Choose θ unless you have a specific reason to want one of the others.
Typography and spacing
Like any Greek variable, θ is set italic in typeset maths and upright in prose. Function names stay upright with a thin space before the argument: sin θ, not sinθ. Degrees follow the value with no space (θ = 30°), and when θ multiplies a number the number comes first (2θ). ### Typing it
No Latin-1 Alt code exists for theta on Windows; open the Win + . panel or, in Word, type 03B8 and press Alt + X (0398 gives capital Θ). The Mac offers no Option shortcut either; add the Greek keyboard and press U, which is where theta sits on the Greek layout, or find it in the Character Viewer. iPhone and Android users add the same Greek keyboard, where U types θ and Shift + U types Θ. The HTML entity is θ, and in LaTeX it is \theta.
Lookalikes and culture
Two unrelated letters are visually identical in many fonts: the Cyrillic barred o ө of Kazakh and Mongolian, and the IPA vowel ɵ. Copying a "theta" from a Cyrillic web page will give you one of those, which breaks search and screen-reader output, so take the character from this page instead. Culturally θ is the letter of Theta Chi, Kappa Alpha Theta and other Greek-life chapters, and, thanks to Big Theta and the ML parameter vector, a favourite in computer-science handles beside the lambda symbol and the sigma symbol. Its rounded shape suits the bubble fonts generator, and for the angle sign itself see the degree symbol page.