Uncover the fascinating world of cycloid curves! Our Cycloid Calculator helps you determine key properties like parametric equations, arc length, and the area under the curve. Ideal for students, engineers, and anyone exploring advanced geometry and kinematics. Simply input the radius of the rolling circle to instantly visualize and compute this unique mathematical path.
Formula:
The standard parametric equations for a cycloid generated by a circle of radius r are:
- x = r(t - sin(t))
- y = r(1 - cos(t))
Where:
- r = Radius of the rolling circle
- t = Parameter (angle of rotation in radians)
For one arch (t from 0 to 2π):
- Arc Length (L) = 8r
- Area (A) = 3πr²