Theta (θ) in HTML
Theta is the eighth Greek letter, written Θ and θ. The capital is at U+0398 and the small letter at U+03B8.
At a glance
- Character
- Θ θ
- Named entity
- Θ θ
- Decimal reference
- Θ θ
- Hex reference
- Θ θ
- Unicode code point
- U+0398, U+03B8
- Unicode name
- GREEK CAPITAL LETTER THETA, GREEK SMALL LETTER THETA
- In the entity reference
- Greek
In detail
The small theta is the default name for an angle. In polar coordinates it is the angular component beside the radius, in trigonometry it is the argument of a sine or cosine, and in a rotation matrix it is the amount of rotation. When you see it in a formula with no definition, an angle is the safe assumption.
The unit is not implied by the letter. Almost every trigonometric function in a programming language takes radians while almost every user interface presents degrees, so a conversion sits between the two and forgetting it produces results that are wrong by a factor of about fifty seven. CSS transform functions are the exception that proves the rule, taking an explicit unit suffix so the ambiguity cannot arise.
The capital theta names a growth rate in complexity analysis. Where big O gives an upper bound only, big theta asserts a tight bound: the algorithm is bounded both above and below by the same function up to constants. Claiming big theta is therefore a stronger statement than claiming big O, and a good deal of casual writing uses the wrong one.
A second glyph for the small letter exists at U+03D1, the theta symbol, which is drawn as a script or cursive form. It is a separate code point rather than a font variant, so choosing it means choosing a character that some fonts do not have.
Examples
<p>x = r cos θ, y = r sin θ</p>
.dial { transform: rotate(45deg); }const toRadians = (deg) => (deg * Math.PI) / 180;
Math.cos(toRadians(60)); // 0.5
Math.cos(60); // not what a user asking for 60 degrees expectsThings that catch people out
- Passing degrees to a trigonometric function that expects radians produces a plausible looking wrong answer rather than an error.
- Big theta and big O are different claims. Big theta says the bound is tight in both directions.
- The theta symbol at U+03D1 is a distinct character, not a stylistic alternate you can reach with a font setting.
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