Math

Rotation Calculator

Rotate a point about the origin by a given angle.

Calculated Output

x′ 0

y′ 1

Formula: x′ = x·cosθ − y·sinθ ; y′ = x·sinθ + y·cosθ

Step-by-Step Breakdown

1. Values used:

2. x = 1

3. y = 0

4. Angle (counter-clockwise) = 90 °

6. x′ = x x y = 1 x 0 = 0

7. y′ = x + y = 1 + 0 = 1

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The math behind it

Apply the 2D rotation matrix: x′ = x cosθ − y sinθ and y′ = x sinθ + y cosθ.

Rotating (1, 0) by 90° gives (0, 1).

How do I rotate about another point?

Translate so that point is the origin, rotate, then translate back.