# What is the symbol for radius?

## GD&T SYMBOLS

Dimensioning symbols replace text and are used to minimize language barriers. Many companies produce parts all over the world. A print made in the U.S.A. may be read in several different countries. The goal of using dimensioning symbols it to eliminate the need for language translation.

GD&T uses internationally accepted symbols that for the most part cross all language barriers. This enables the correct interpretation of drawing specifications without language translation. The following tables show the symbols that are used in GD&T. The symbols will be illustrated and explained as the learning material unfolds.

__DIMENSIONING SYMBOLS__

Term | Symbol |
---|---|

Diameter | n |

Spherical Diameter | S n |

Radius | R |

Spherical Radius | SR |

Reference Dimension | (8) |

Counterbore / Spotface | v |

Countersink | w |

Number of Places | 4X |

Depth / Deep | x |

Dimension not to scale | 10 |

Square (shape) | o |

Arc Length | |

Conical Taper | y |

Slope | z |

Symmetry | i |

__GD&T GEOMETRIC CHARACTERISTIC SYMBOLS__

Tolerance Type | Characteristic | Symbol | |
---|---|---|---|

For individual features | Form | Straightness | u |

Flatness | c | ||

Circularity | e | ||

Cylindricity | g | ||

For individual or related features | Profile | Profile of a Line | k |

Profile of a Surface | d | ||

For related features | Orientation | Angularity | a |

Perpendicularity | b | ||

Parallelism | f | ||

Location | Position | j | |

Concentricity | r | ||

Symmetry | i | ||

Runout | Circular Runout | h | |

Total Runout | t |

__GD&T MATERIAL CONDITIONS__

Term | Symbol |
---|---|

Maximum Material Condition | m |

Least Material Condition | l |

Regardless of Feature Size | None |

__ADDITIONAL GD&T SYMBOLS__

Term | Symbol |
---|---|

Basic Dimension | |

Between | |

Dimension Origin | |

All Around | |

Controlled Radius | CR |

Statistical Tolerance | |

Projected Tolerance Zone | p |

Regardless of feature size | s or None |

Tangent Plane | |

Free State | |

Datum Feature | |

Datum Target | |

Target Point |

## Circle Math

In circle math the terms related to the circle are discussed here.

We have learned to draw a circle, by tracing the outlines of objects like a bangle or a bottle cap.

We shall learn now how to draw a circle using a compass.

Compass is a handy drawing tool available in the geometry box. A compass has two arms which can be pulled apart easily to adjust to the size of the circle we want to draw.

Fix a sharp pencil into the holder on the compass.

Fix the needle of the compass on the point where the center of the circle would be.

Open and adjust the other arm which is holding the pencil and rotate the compass to draw a circle.

The point O where the needle of the compass is placed in the centre of the circle. The distance of any point on the circle from the centre O is the radius of the circle. In the given figure OX is the radius.

A line segment which joins any two points on the circle is called a chord. MN is a chord in the given figure.

The line passing through the centre which joins two points on the circle is the diameter. Diameter of the circle is twice its radius. YZ is the diameter of the circle in the given figure.

The length of the circle is called its circumference.

A circle is such a closed curve whose every point is equidistant from a fixed point called its center.

**The symbol of circle is O** .

What are the terms related to the circle?

The terms related to the circle math are:

The *center* of a circle is a fixed point within the circle from which all the points of the closing curve are equidistant.

**O** is the centre.

**(ii) Circumference:**

The curve which closes a circle is called its circumference. The length of the *circumference* is called the length of the circle.

The distance from the centre to any point on the circumference of a circle is called the *radius* of the circle. The symbol of the radius is ** r** .

**(iv) Diameter:**

The line-segment passing through the centre and meeting the points on the circumference is called the diameter of the circle. Diameter is denoted by ‘ ** D** ‘.

** AB** is a diameter of the circle.

** Diameter is twice the length of the radius concerned**.

Thus, **D = 2r** [ **Diameter = 2radius** ]

**r =** **D/2** [ **Radius =** **Diameter/2** ]

Any part of the circumference is called an arc of the circle.

The line-segment joining the two ends of an arc is known as a chord. A diameter is the longest chord of a circle.

**O** is the *centre.*

**OP** is one *radius.*

**AB** is a *diameter.*

**MN** is a *chord.* (**line-segment**)

**OA** and OB are also *radii.*

**Related Concepts on** **Geometry — Simple Shapes & Circle**

## Pi ( π )

The circumference divided by the diameter of a circle is always π , no matter how large or small the circle is!

To help you remember what π is . just draw this diagram.

## Finding Pi Yourself

Draw a circle, or use something circular like a plate.

Measure around the edge (the **circumference**):

I got **82 cm**

Measure across the circle (the **diameter**):

I got **26 cm**

82 cm / 26 cm = 3.1538.

That is pretty close to π . Maybe if I measured more accurately?

## Using Pi

We can use π to find a Circumference when we know the Diameter

Circumference = π × Diameter

### Example: You walk around a circle which has a diameter of 100 m, how far have you walked?

Distance walked = Circumference

= π × 100 m

= 314.159. m

= **314 m** (to the nearest m)

Also we can use π to find a Diameter when we know the Circumference

Diameter = Circumference / π

### Example: Sam measured 94 mm around the outside of a pipe . what is its Diameter?

Diameter = Circumference / π

= 94 mm / π

= 29.92. mm

= **30 mm** (to the nearest mm)

## Radius

The radius is half of the diameter, so we can also say:

For a circle with a **radius** of **1**

The distance *half way around* the circle is **π = 3.14159265.**

## Digits

π is approximately equal to:

**3.14159265358979323846…**

The digits go on and on with no pattern.

π has been calculated to over 100 trillion decimal places and still there is **no pattern** to the digits, see Pi Normal.

## Approximation

A quick and easy approximation for π is 22/7

22/7 = **3.1428571.**

But as you can see, 22/7 is **not exactly right**. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.

A really good approximation, better than 1 part in 10 million, is:

355/113 = **3.1415929.** *(think «113355», slash the middle «113/355», then flip «355/113»)*

22/7 | = | 3.1428571. |

355/113 | = | 3.1415929. |

π | = | 3.14159265. |

## Remembering The Digits

I usually just remember «3.14159», but you can also count the letters of:

*«May I have a large container of butter today» 3 1 4 1 5 9 2 6 5*

## To 100 Decimal Places

Here is π with the first 100 decimal places:

3.14159265358979323846264338327950288 4197169399375105820974944592307816 4062862089986280348253421170679. |

### Calculating Pi Yourself

There are many special methods used to calculate π and here is one you can try yourself: it is called the **Nilakantha series** (after an Indian mathematician who lived in the years 1444–1544).

It goes on for ever and has this pattern:

3 + *4* **2×3×4** − *4* **4×5×6** + *4* **6×7×8** − *4* **8×9×10** + .

(Notice the + and − pattern, and also the pattern of numbers below the lines.)

It gives these results:

Term | Result (to 12 decimals) |
---|---|

1 | 3 |

2 | 3.166666666667 |

3 | 3.133333333333 |

4 | 3.145238095238 |

. | . etc! . |

Get a calculator (or use a spreadsheet) and see if you can get better results.

### Pi Day

Pi Day is celebrated on March 14. March is the 3rd month, so it looks like 3/14