superellipse()

Syntax

css

superellipse(infinity)
superellipse(4)
superellipse(1.7)
superellipse(0)
superellipse(-2.8)
superellipse(-3)
superellipse(-infinity)

Parameters

<number>: A number in the range of -infinity to infinity, inclusive.

The superellipse() function returns a superellipse shape, which is used to specify corner-shape values. A superellipse is a closed curve symmetric shape between a rectangle and an ellipse. It resembles an ellipse that retains the geometric features of its two axes.

The superellipse shape is calculated using a modified version of an ellipse. The following equation defines an ellipse centered at the origin:

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

The a and b variables refer to the radii of the ellipse, while the x and y coordinates are points on the ellipse's circumference.

A circle is an ellipse where the radii, the a and b in the previous equation, are the same length. With a and b both equal to r, the equation for a circle can be written as:

x^{2} + y^{2} = r^{2}

In this equation, the x and y are coordinates of points on the circle's circumference, and the r is the radius of the circle, with the center of the circle being (0, 0). The ellipse is produced by scaling a circle shape along the x and/or y axis.

A superellipse shape is created by replacing the 2 exponent in each case with 2^K, K being the argument passed to the superellipse() function, which modifies the curvature of the ellipse:

x^{2^{K}} + y^{2^{K}} = 1

The following diagram illustrates different superellipse() values for the top right corner of a container: infinity, 1, 0, -1, and -infinity:

Line diagram illustrating the ellipses created using different K values, as described subsequently

A K value of 0 creates a straight line. This value can be used to create bevelled corners and corresponds to the <corner-shape-value> bevel keyword.
A K value of 1 creates an ordinary ellipse, corresponding to the round keyword.
A K value of >1 makes the ellipse shape more square; 2 corresponds to the squircle keyword.
A K value of infinity creates a perfect square (corresponding to the square keyword), although K values of 10 or more are virtually indistinguishable from a square.
Negative K values result in a concave curve, resulting in corner shapes that are curved inward, or "scooped out". A K value of -1 corresponds to the scoop keyword and -infinity corresponds to the notch keyword.

A negative or positive superellipse would appear symmetrical to a superellipse with its inverse value.

Note: For any K parameter value passed, the superellipse() function's return value will always be the same for that K value. When that value is applied to two elements, the appearance of the corner shape may differ if the box size or border-radius values differ.

Formal syntax

<superellipse()> = 
  superellipse( <number [-∞,∞]>  |
  infinity                       |
  -infinity )

Examples

`superellipse()` value comparison

In this example, two <input type="range"> sliders allow you to cycle through many different corner-shape superellipse() values and border-radius values enabling you to compare the effects of each on a container. The code is hidden for brevity, but the full explanation of the superellipse value comparison is provided on the corner-shape reference page.

<form>
  <div>
    <label for="superellipse-slider">Choose a superellipse() value:</label>
    <input
      type="range"
      id="superellipse-slider"
      min="-5"
      value="0"
      max="5"
      step="0.1" />
  </div>
  <div>
    <label for="radius-slider">Choose a border-radius value:</label>
    <input type="range" id="radius-slider" min="0" value="45" max="90" />
  </div>
</form>
<section></section>

html {
  font-family: Arial, Helvetica, sans-serif;
}

body {
  width: fit-content;
  margin: 20px auto;
}

section {
  display: flex;
  justify-content: center;
  align-items: center;
  flex: 100%;
  margin-top: 20px;
}

form div {
  margin-top: 5px;
  display: flex;
}

section {
  width: 100%;
  height: 180px;
  background-color: orange;
  background-image: linear-gradient(
    to bottom,
    rgb(255 255 255 / 0),
    rgb(255 255 255 / 0.5)
  );
}

section {
  box-shadow: 1px 1px 3px gray;
}

const rectangle = document.querySelector("section");
const superEllipseRange = document.getElementById("superellipse-slider");
const borderRadiusRange = document.getElementById("radius-slider");

function setCorners() {
  const seValue = `superellipse(${superEllipseRange.value})`;
  rectangle.style.cornerShape = seValue;
  const brValue = `${borderRadiusRange.value}px`;
  rectangle.style.borderRadius = brValue;
  rectangle.innerHTML = `<div><code>corner-shape: ${seValue};</code><br><code>border-radius: ${brValue};</code></div>`;
}

superEllipseRange.addEventListener("input", setCorners);
borderRadiusRange.addEventListener("input", setCorners);
setCorners();

Note: See also the <corner-shape-value> value comparison example.