One **radian** is the angle **θ** swept along a circle whose arc length **S** is equal to the radius **R** of the circle.(1)

Remember that **π** is the ratio of the circumference **C** of a circle to its diameter, which is twice its radius **R**, i.e. **π = C / 2R**.

From this we know the circumference **C** of a circle is **2πR**, i.e. **C = 2πR**.

We also know **C/R = 2π** (2)

To find the number of radians in a circle, we divide the circumference **C** by the number of times we can fit the arc of length **R** from (1) around the whole circle, but that is just **C/R**, and that is always **2π** (2). **So, there are 2π radians in a circle.**

**For any angle θ in radians, θ is in terms of the radius R and arc length S: θ = S/R**

**When arc length of S = length of R, then θ = 1 radian.**

**There are always 2π radians in a circle.**

Subject Index for all interactive diagrams

interactagram.com - Math - Trigonometry - Radian

Source Flash: radian.zip

Visits since 5-29-09: 10572

Interactagram.com uses third-party advertising companies to serve ads when you visit our website. These companies may use information (not including your name, address, email address, or telephone number) about your visits to this and other websites in order to provide advertisements about goods and services of interest to you. If you would like more information about this practice and to know your choices about not having this information used by these companies, click here.