The commonly used results and formulas of curvature and radius of curvature as shown below:

**1. **Curvature and radius of curvature for Cartesian curve is

and

**2. **If the equation of the curve is given by the implicit relation , then

and

**3. **If the curve is defined by parametric equations and then

and so

**4. **For the curve i.e., the curve in polar coordinates

and thus

**5. **For the pedal curve then,

**6.**If are the coordinates of center of curvature of the curve at then

and