# Quaternion > Quaternions are used to represent rotations. ## Definition * **Type:** Struct * **Namespace:** [UnityEngine](/engine/6000.6/script-reference/unityengine.md) * **Assembly:** UnityEngine.CoreModule * **Implements:** [IEquatable\](https://learn.microsoft.com/dotnet/api/system.iequatable-1), [IFormattable](https://learn.microsoft.com/dotnet/api/system.iformattable) ```csharp public struct Quaternion : IEquatable, IFormattable ``` ## Remarks A quaternion is a four-tuple of real numbers \{x,y,z,w}. A quaternion is a mathematically convenient alternative to the euler angle representation. You can interpolate a quaternion without experiencing gimbal lock. You can also use a quaternion to concatenate a series of rotations into a single representation. Unity internally uses Quaternions to represent all rotations. In most cases, you can use existing rotations from methods such as [Transform.localRotation](/engine/6000.6/script-reference/unityengine/transform/localrotation.md) or [Transform.rotation](/engine/6000.6/script-reference/unityengine/transform/rotation.md) to construct new rotations. For example, use existing rotations to smoothly interpolate between two rotations. The most used Quaternion functions are as follows: [Quaternion.LookRotation](/engine/6000.6/script-reference/unityengine/quaternion/lookrotation.md), [Quaternion.Angle](/engine/6000.6/script-reference/unityengine/quaternion/angle.md), [Quaternion.Euler](/engine/6000.6/script-reference/unityengine/quaternion/euler.md), [Quaternion.Slerp](/engine/6000.6/script-reference/unityengine/quaternion/slerp.md), [Quaternion.FromToRotation](/engine/6000.6/script-reference/unityengine/quaternion/fromtorotation.md), and [Quaternion.identity](/engine/6000.6/script-reference/unityengine/quaternion/identity.md). You can use the Quaternion.operator \* to rotate one rotation by another, or to rotate a vector by a rotation. Note that Unity expects Quaternions to be normalized. ## Fields | Value | Description | | ---------------------------------------------------------------- | ------------------------------------------------------------------------------------------------- | | [w](/engine/6000.6/script-reference/unityengine/quaternion/w.md) | W component of the Quaternion. Do not directly modify quaternions. | | [x](/engine/6000.6/script-reference/unityengine/quaternion/x.md) | X component of the Quaternion. Don't modify this directly unless you know quaternions inside out. | | [y](/engine/6000.6/script-reference/unityengine/quaternion/y.md) | Y component of the Quaternion. Don't modify this directly unless you know quaternions inside out. | | [z](/engine/6000.6/script-reference/unityengine/quaternion/z.md) | Z component of the Quaternion. Don't modify this directly unless you know quaternions inside out. | ## Constructors | Constructor | Description | | ------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------- | | [Quaternion(System.Single,System.Single,System.Single,System.Single)](/engine/6000.6/script-reference/unityengine/quaternion/ctor.md) | Constructs new Quaternion with given x,y,z,w components. | ## Properties | Property | Description | | ------------------------------------------------------------------------------------ | --------------------------------------------------------------------------- | | [eulerAngles](/engine/6000.6/script-reference/unityengine/quaternion/eulerangles.md) | Returns or sets the euler angle representation of the rotation in degrees. | | [this\[\]](/engine/6000.6/script-reference/unityengine/quaternion/item.md) | Access the x, y, z, w components using \[0], \[1], \[2], \[3] respectively. | | [normalized](/engine/6000.6/script-reference/unityengine/quaternion/normalized.md) | Returns this quaternion with a magnitude of 1 (Read Only). | ## Static Properties | Property | Description | | ------------------------------------------------------------------------------ | ---------------------------------- | | [identity](/engine/6000.6/script-reference/unityengine/quaternion/identity.md) | The identity rotation (Read Only). | ## Methods | Method | Description | | ------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------- | | [Equals](/engine/6000.6/script-reference/unityengine/quaternion/equals.md) | Performs exact binary comparison of each Quaternion component (x, y, z, w). | | [Normalize](/engine/6000.6/script-reference/unityengine/quaternion/normalize.md) | Converts this quaternion to a quaternion with the same orientation but with a magnitude of 1.0. | | [Set](/engine/6000.6/script-reference/unityengine/quaternion/set.md) | Set x, y, z and w components of an existing Quaternion. | | [SetFromToRotation](/engine/6000.6/script-reference/unityengine/quaternion/setfromtorotation.md) | Creates a rotation which rotates from `fromDirection` to `toDirection`. | | [SetLookRotation](/engine/6000.6/script-reference/unityengine/quaternion/setlookrotation.md) | Creates a rotation with the specified `forward` and `upwards` directions. | | [ToAngleAxis](/engine/6000.6/script-reference/unityengine/quaternion/toangleaxis.md) | Converts a rotation to angle-axis representation. | | [ToString](/engine/6000.6/script-reference/unityengine/quaternion/tostring.md) | Returns a formatted string for this quaternion. | ## Static Methods | Method | Description | | ------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------- | | [Angle](/engine/6000.6/script-reference/unityengine/quaternion/angle.md) | Returns the angle in degrees between two rotations `a` and `b`. The resulting angle ranges from 0 to 180. | | [AngleAxis](/engine/6000.6/script-reference/unityengine/quaternion/angleaxis.md) | Creates a rotation which rotates `angle` degrees around `axis`. | | [Dot](/engine/6000.6/script-reference/unityengine/quaternion/dot.md) | The dot product between two rotations. | | [Euler](/engine/6000.6/script-reference/unityengine/quaternion/euler.md) | Converts an input Euler angle rotation specified as three floats to a Quaternion. | | [FromToRotation](/engine/6000.6/script-reference/unityengine/quaternion/fromtorotation.md) | Creates a rotation from `fromDirection` to `toDirection`. | | [Inverse](/engine/6000.6/script-reference/unityengine/quaternion/inverse.md) | Returns the Inverse of `rotation`. | | [Lerp](/engine/6000.6/script-reference/unityengine/quaternion/lerp.md) | Interpolates between `a` and `b` by `t` and normalizes the result afterwards. | | [LerpUnclamped](/engine/6000.6/script-reference/unityengine/quaternion/lerpunclamped.md) | Interpolates between `a` and `b` by `t` and normalizes the result afterwards. The parameter `t` is not clamped. | | [LookRotation](/engine/6000.6/script-reference/unityengine/quaternion/lookrotation.md) | Creates a rotation with the specified `forward` and `upwards` directions. | | [Normalize](/engine/6000.6/script-reference/unityengine/quaternion/normalize.md) | Converts this quaternion to a quaternion with the same orientation but with a magnitude of 1.0. | | [RotateTowards](/engine/6000.6/script-reference/unityengine/quaternion/rotatetowards.md) | Rotates a rotation `from` towards `to`. | | [Slerp](/engine/6000.6/script-reference/unityengine/quaternion/slerp.md) | Spherically linear interpolates between unit quaternions `a` and `b` by a ratio of `t`. | | [SlerpUnclamped](/engine/6000.6/script-reference/unityengine/quaternion/slerpunclamped.md) | Spherically linear interpolates between unit quaternions `a` and `b` by t. | ## Operators | Operator | Description | | ------------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | [operator ==](/engine/6000.6/script-reference/unityengine/quaternion/op-equality.md) | Are two quaternions equal to each other? | | [Quaternion](/engine/6000.6/script-reference/unityengine/quaternion/op-implicit.md) | Converts a [quaternion](/engine/6000.6/script-reference/unity/mathematics/quaternion.md) to a [Quaternion](/engine/6000.6/script-reference/unityengine/quaternion.md). | | [quaternion](/engine/6000.6/script-reference/unityengine/quaternion/op-implicit.md) | Converts a [Quaternion](/engine/6000.6/script-reference/unityengine/quaternion.md) to a [quaternion](/engine/6000.6/script-reference/unity/mathematics/quaternion.md). | | [operator \*](/engine/6000.6/script-reference/unityengine/quaternion/op-multiply.md) | Combines rotations `lhs` and `rhs`. |