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Source: Roblox Creator Hub · CC BY 4.0 · View source · Code samples: MIT Imported 2026-10-03. Formatting adapted for this site.

Vector2

The Vector2 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 data type:

Constructors

Vector2.new

Returns a Vector2 from the given x and y components. Both parameters default to 0 if not provided.

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

Properties

Vector2.X

The x-coordinate of the Vector2, corresponding to the first argument passed to Vector2.new(). This property is read-only.

local v = Vector2.new(3, 4)
print(v.X)  --> 3

Vector2.Y

The y-coordinate of the Vector2, corresponding to the second argument passed to Vector2.new(). This property is read-only.

local v = Vector2.new(3, 4)
print(v.Y)  --> 4

Vector2.Magnitude

The length (magnitude) of the Vector2, computed as math.sqrt(X^2 + Y^2). This property is read-only.

local v = Vector2.new(3, 4)
print(v.Magnitude)  --> 5

Vector2.Unit

A normalized copy of the Vector2 — 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.

local v = Vector2.new(3, 4)
print(v.Unit)             --> 0.6, 0.8
print(v.Unit.Magnitude)   --> 1

Methods

Vector2:Cross

Returns the 2D cross product of this vector with other, computed as self.X * other.Y - self.Y * other.X. Unlike Vector3:Cross() 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.

local a = Vector2.new(1, 0)
local b = Vector2.new(0, 1)
print(a:Cross(b))  -->  1
print(b:Cross(a))  --> -1

Parameters

Returns

Vector2:Abs

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:Ceil

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:Floor

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:Sign

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:Angle

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

Returns

Vector2:Dot

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.

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

Returns

Vector2:Lerp

Returns a Vector2 linearly interpolated between this Vector2 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.

local a = Vector2.new(0, 0)
local b = Vector2.new(4, 8)
print(a:Lerp(b, 0.5))  --> 2, 4

Parameters

Returns

Vector2:Max

Returns a Vector2 with each component as the highest among the respective components of the provided Vector2 objects.

local a = Vector2.new(1, 2)
local b = Vector2.new(2, 1)

print(a:Max(b)) -- Vector2.new(2, 2)

Parameters

Returns

Vector2:Min

Returns a Vector2 with each component as the lowest among the respective components of the provided Vector2 objects.

local a = Vector2.new(1, 2)
local b = Vector2.new(2, 1)

print(a:Min(b)) -- Vector2.new(1, 1)

Parameters

Returns

Vector2:FuzzyEq

Returns true if the X and Y components of the other Vector2 are within epsilon units of each corresponding component of this Vector2. 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.

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

Returns

Constants

Vector2.zero

A Vector2 with a magnitude of zero.

This API member is a constant, and must be accessed through the Vector2 global as opposed to an individual Vector2 object.

print(Vector2.zero)  --> 0, 0

Vector2.one

A Vector2 with a value of 1 on every axis.

This API member is a constant, and must be accessed through the Vector2 global as opposed to an individual Vector2 object.

print(Vector2.one)  --> 1, 1

Vector2.xAxis

A Vector2 with a value of 1 on the X axis.

This API member is a constant, and must be accessed through the Vector2 global as opposed to an individual Vector2 object.

print(Vector2.xAxis)  --> 1, 0

Vector2.yAxis

A Vector2 with a value of 1 on the Y axis.

This API member is a constant, and must be accessed through the Vector2 global as opposed to an individual Vector2 object.

print(Vector2.yAxis)  --> 0, 1

Operators

Vector2 + Vector2 (addition)

Produces a Vector2 with each component of the second added to the corresponding component of the first.

print(Vector2.new(1, 2) + Vector2.new(3, 4))  --> 4, 6

Vector2 - Vector2 (subtraction)

Produces a Vector2 with each component of the second subtracted from the corresponding component of the first.

print(Vector2.new(3, 4) - Vector2.new(1, 2))  --> 2, 2

Vector2 * Vector2 (multiplication)

Produces a Vector2 with each component of the second multiplied by the corresponding component of the first (component-wise multiplication, not a dot or cross product).

print(Vector2.new(2, 3) * Vector2.new(4, 5))  --> 8, 15

Vector2 / Vector2 (division)

Produces a Vector2 with each component of the first divided by the corresponding component of the second (component-wise division).

print(Vector2.new(8, 15) / Vector2.new(4, 5))  --> 2, 3

Vector2 * number (multiplication)

Produces a Vector2 with each component multiplied by the number (scalar multiplication).

print(Vector2.new(2, 3) * 4)  --> 8, 12

Vector2 / number (division)

Produces a Vector2 with each component divided by the number (scalar division).

print(Vector2.new(8, 12) / 4)  --> 2, 3