# Difference between Centre of Curvature and Radius of Curvature

The terms “center of curvature” and “radius of curvature” are often used in relation to curves. These terms describe different aspects of a curved line, and understanding their differences can help us analyze and describe curved shapes.

The main difference is that the center of curvature is the center of the circle that best approximates the curve at a specific point while the radius of curvature is the radius of that circle.

Before we move to the differences, let’s understand what are Centre of Curvature and Radius of Curvature:

• Centre of Curvature: The center of curvature is the center of the circle that best approximates a curve at a specific point. This circle is called the osculating circle, and it touches the curve at that point. In other words, the center of curvature is the point around which the curve is bending the most at that specific point.
• Radius of Curvature: The radius of curvature is the radius of the osculating circle at a specific point on the curve. It is the distance from the point on the curve to the center of curvature.

Now, let’s move to Centre of Curvature vs Radius of Curvature:

## Major differences between Centre of Curvature and Radius of Curvature

Centre of Curvature Radius of Curvature
The center of curvature is a point on the curve. The radius of curvature is a distance.
The center of curvature can be inside, outside, or on the curve. The radius of curvature is always positive.
The center of curvature determines the direction of curvature of the curve at that specific point. The radius of curvature determines the magnitude of that curvature.
The center of curvature is the reciprocal of the curvature at that point. The radius of curvature is the inverse of the curvature.
Center of curvature is the center of the circle that best approximates the curve at a specific point. The radius of curvature is the radius of that circle.

That’s it.

Note that sometimes, the question might also be asked as “distinguish between Centre of Curvature and Radius of Curvature”.

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## Final words

Center of curvature and radius of curvature are two important concepts used in geometry to describe curved lines. These concepts have different characteristics and uses, such as determining the direction and magnitude of curvature of a curve.

Knowing the differences between center of curvature and radius of curvature can help us analyze and understand curved shapes better.

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