# Formulas of Curvature and Radius of Curvature

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

**1. **Curvature and radius of curvature for a 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 the center of curvature of the curve at then

and