--- name: Vector2 last_updated: 2026-10-29T23:45:56Z type: datatype summary: "Represents a 2D value with direction and magnitude." --- # Vector2 Represents a 2D value with direction and magnitude. **Type:** datatype ## Description The [Vector2](/docs/reference/engine/datatypes/Vector2.md) data type represents a 2D value with direction and magnitude. Some applications include GUI elements and 2D mouse positions. #### Math Operations The following math operations are valid for the [Vector2](/docs/reference/engine/datatypes/Vector2.md) data type: | Operation | Description | | --- | --- | | [Vector2](/docs/reference/engine/datatypes/Vector2.md) `+` [Vector2](/docs/reference/engine/datatypes/Vector2.md) | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the second added to the corresponding component of the first. | | [Vector2](/docs/reference/engine/datatypes/Vector2.md) `-` [Vector2](/docs/reference/engine/datatypes/Vector2.md) | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the second subtracted from the corresponding component of the first. | | [Vector2](/docs/reference/engine/datatypes/Vector2.md) `*` [Vector2](/docs/reference/engine/datatypes/Vector2.md) | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the second multiplied by the corresponding component of the first. | | [Vector2](/docs/reference/engine/datatypes/Vector2.md) `/` [Vector2](/docs/reference/engine/datatypes/Vector2.md) | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the first divided by the corresponding component of the second. | | [Vector2](/docs/reference/engine/datatypes/Vector2.md) `*` `number` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component multiplied by the number. | | [Vector2](/docs/reference/engine/datatypes/Vector2.md) `/` `number` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component divided by the number. | ## Constructors ### Vector2.new **Signature:** `Vector2.new(x: number, y: number)` Returns a [Vector2](/docs/reference/engine/datatypes/Vector2.md) from the given x and y components. Both parameters default to `0` if not provided. ```lua local a = Vector2.new(3, 4) print(a.X, a.Y) --> 3 4 -- Omitted arguments default to 0 local b = Vector2.new() print(b.X, b.Y) --> 0 0 ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `x` | `number` | | The x-coordinate of the new vector (defaults to 0). | | `y` | `number` | | The y-coordinate of the new vector (defaults to 0). | ## Constants | Name | Type | Description | |------|------|-------------| | `Vector2.zero` | `Vector2` | A [Vector2](/docs/reference/engine/datatypes/Vector2.md) with a magnitude of zero. | | `Vector2.one` | `Vector2` | A [Vector2](/docs/reference/engine/datatypes/Vector2.md) with a value of 1 on every axis. | | `Vector2.xAxis` | `Vector2` | A [Vector2](/docs/reference/engine/datatypes/Vector2.md) with a value of 1 on the X axis. | | `Vector2.yAxis` | `Vector2` | A [Vector2](/docs/reference/engine/datatypes/Vector2.md) with a value of 1 on the Y axis. | ## Properties ### Vector2.X **Type:** `number` The x-coordinate of the [Vector2](/docs/reference/engine/datatypes/Vector2.md), corresponding to the first argument passed to [Vector2.new()](/docs/reference/engine/datatypes/Vector2.md). This property is read-only. ```lua local v = Vector2.new(3, 4) print(v.X) --> 3 ``` ### Vector2.Y **Type:** `number` The y-coordinate of the [Vector2](/docs/reference/engine/datatypes/Vector2.md), corresponding to the second argument passed to [Vector2.new()](/docs/reference/engine/datatypes/Vector2.md). This property is read-only. ```lua local v = Vector2.new(3, 4) print(v.Y) --> 4 ``` ### Vector2.Magnitude **Type:** `number` The length (magnitude) of the [Vector2](/docs/reference/engine/datatypes/Vector2.md), computed as `math.sqrt(X^2 + Y^2)`. This property is read-only. ```lua local v = Vector2.new(3, 4) print(v.Magnitude) --> 5 ``` ### Vector2.Unit **Type:** `Vector2` A normalized copy of the [Vector2](/docs/reference/engine/datatypes/Vector2.md) — one that has the same direction as the original but a magnitude of 1. If the vector has zero magnitude the result is undefined (contains `nan` values). This property is read-only. ```lua local v = Vector2.new(3, 4) print(v.Unit) --> 0.6, 0.8 print(v.Unit.Magnitude) --> 1 ``` ## Methods ### Vector2:Cross **Signature:** `Vector2:Cross(other: Vector2): number` Returns the 2D cross product of this vector with `other`, computed as `self.X * other.Y - self.Y * other.X`. Unlike [Vector3:Cross()](/docs/reference/engine/datatypes/Vector3.md) which returns a vector, the 2D cross product returns a scalar representing the signed magnitude of the perpendicular (Z) component. The result is positive when `other` is counter-clockwise from `self`, negative when clockwise, and zero when the vectors are parallel. ```lua local a = Vector2.new(1, 0) local b = Vector2.new(0, 1) print(a:Cross(b)) --> 1 print(b:Cross(a)) --> -1 ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `other` | `Vector2` | | The vector to compute the cross product against. | **Returns:** `number` — The signed scalar magnitude of the perpendicular component, computed as `self.X * other.Y - self.Y * other.X`. ### Vector2:Abs **Signature:** `Vector2:Abs(): Vector2` Returns a new vector from the absolute values of the original's components. For example, a vector of `(-2, 4)` returns a vector of `(2, 4)`. **Returns:** `Vector2` — A new vector whose components are the absolute values of the original's components. ### Vector2:Ceil **Signature:** `Vector2:Ceil(): Vector2` Returns a new vector from the ceiling of the original's components. For example, a vector of `(-2.6, 5.1)` returns a vector of `(-2, 6)`. **Returns:** `Vector2` — A new vector whose components are the ceiling (rounded up) of the original's components. ### Vector2:Floor **Signature:** `Vector2:Floor(): Vector2` Returns a new vector from the floor of the original's components. For example, a vector of `(-2.6, 5.1)` returns a vector of `(-3, 5)`. **Returns:** `Vector2` — A new vector whose components are the floor (rounded down) of the original's components. ### Vector2:Sign **Signature:** `Vector2:Sign(): Vector2` Returns a new vector from the sign (-1, 0, or 1) of the original's components. For example, a vector of `(-2.6, 5.1)` returns a vector of `(-1, 1)`. **Returns:** `Vector2` — A new vector whose components are the sign (-1, 0, or 1) of the original's components. ### Vector2:Angle **Signature:** `Vector2:Angle(other: Vector2, isSigned?: boolean): number` Returns the angle in radians between the two vectors. Specify `true` for the optional `isSigned` boolean if you want a signed angle. By default, the method returns the absolute value. Signed angles are a negative when going clockwise. Values are in the range `[0, pi]` for absolute angles and `[-pi, pi]` for signed angles. **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `other` | `Vector2` | | The vector to measure the angle to. | | `isSigned` | `boolean` | `false` | Whether to return a signed angle (negative when clockwise) instead of the absolute value. | **Returns:** `number` ### Vector2:Dot **Signature:** `Vector2:Dot(v: Vector2): number` Returns the scalar dot product of this vector and `v`, computed as `self.X * v.X + self.Y * v.Y`. The result equals the product of the two magnitudes multiplied by the cosine of the angle between them. A positive value means the vectors point in roughly the same direction; zero means they are perpendicular; negative means they point in roughly opposite directions. ```lua local a = Vector2.new(1, 0) local b = Vector2.new(0, 1) print(a:Dot(b)) --> 0 (perpendicular) print(a:Dot(a)) --> 1 (parallel, equal to Magnitude^2) ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `v` | `Vector2` | | The vector to compute the dot product with. | **Returns:** `number` ### Vector2:Lerp **Signature:** `Vector2:Lerp(v: Vector2, alpha: number): Vector2` Returns a [Vector2](/docs/reference/engine/datatypes/Vector2.md) linearly interpolated between this [Vector2](/docs/reference/engine/datatypes/Vector2.md) and the given goal `v` by the fraction `alpha`, using the formula `self + (v - self) * alpha`. An `alpha` of 0 returns `self`, an `alpha` of 1 returns `v`, and values between 0 and 1 return a point in between. Note that `alpha` is **not** clamped to `[0, 1]` — values outside that range extrapolate beyond the two endpoints. ```lua local a = Vector2.new(0, 0) local b = Vector2.new(4, 8) print(a:Lerp(b, 0.5)) --> 2, 4 ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `v` | `Vector2` | | The goal vector to interpolate toward. | | `alpha` | `number` | | The interpolation fraction, where 0 returns this vector and 1 returns `v`. | **Returns:** `Vector2` ### Vector2:Max **Signature:** `Vector2:Max(others...: Tuple): Vector2` Returns a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component as the highest among the respective components of the provided [Vector2](/docs/reference/engine/datatypes/Vector2.md) objects. ```lua local a = Vector2.new(1, 2) local b = Vector2.new(2, 1) print(a:Max(b)) -- Vector2.new(2, 2) ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `others...` | `Tuple` | | One or more [Vector2](/docs/reference/engine/datatypes/Vector2.md) objects to compare against. | **Returns:** `Vector2` ### Vector2:Min **Signature:** `Vector2:Min(others...: Tuple): Vector2` Returns a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component as the lowest among the respective components of the provided [Vector2](/docs/reference/engine/datatypes/Vector2.md) objects. ```lua local a = Vector2.new(1, 2) local b = Vector2.new(2, 1) print(a:Min(b)) -- Vector2.new(1, 1) ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `others...` | `Tuple` | | One or more [Vector2](/docs/reference/engine/datatypes/Vector2.md) objects to compare against. | **Returns:** `Vector2` ### Vector2:FuzzyEq **Signature:** `Vector2:FuzzyEq(other: Vector2, epsilon?: number): bool` Returns `true` if the X and Y components of the other [Vector2](/docs/reference/engine/datatypes/Vector2.md) are within `epsilon` units of each corresponding component of this [Vector2](/docs/reference/engine/datatypes/Vector2.md). The comparison is per-component: both `math.abs(self.X - other.X)` and `math.abs(self.Y - other.Y)` must be less than or equal to `epsilon`. The optional `epsilon` parameter defaults to `1e-5` (0.00001) and must be a positive value no greater than `0.1`. ```lua local a = Vector2.new(1, 2) local b = Vector2.new(1.000009, 2.000009) print(a:FuzzyEq(b)) --> true (within default 1e-5) print(a:FuzzyEq(b, 0.000001)) --> false (tighter epsilon) ``` **Parameters:** | Name | Type | Default | Description | |------|------|---------|-------------| | `other` | `Vector2` | | The vector to compare against. | | `epsilon` | `number` | `0.00001 (1e-5)` | The maximum difference allowed for each component to still be considered equal. | **Returns:** `bool` ## Math Operations | Operation | Type A | Type B | Returns | Description | |-----------|--------|--------|---------|-------------| | `+` | `Vector2` | `Vector2` | `Vector2` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the second added to the corresponding component of the first. | | `-` | `Vector2` | `Vector2` | `Vector2` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the second subtracted from the corresponding component of the first. | | `*` | `Vector2` | `Vector2` | `Vector2` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the second multiplied by the corresponding component of the first. | | `/` | `Vector2` | `Vector2` | `Vector2` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component of the first divided by the corresponding component of the second. | | `*` | `Vector2` | `number` | `Vector2` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component multiplied by the number. | | `/` | `Vector2` | `number` | `Vector2` | Produces a [Vector2](/docs/reference/engine/datatypes/Vector2.md) with each component divided by the number. |