Symbol: 
Relative to Datum: No
MMC or LMC applicable: Yes – New in 2009
Drawing Callout:
Description:
GD&T Flatness is very straight forward. It is a common symbol that references how flat a surface is regardless of any other datums or features. It comes in useful if a feature is to be defined on a drawing that needs to be uniformly flat without tightening any other dimensions on the drawing. The flatness tolerance references two parallel planes (parallel to the surface that it is called out on) that define a zone where the entire reference surface must lie. Flatness tolerance is always less than the dimensional tolerance associated with it.
Tolerance Zone:
Two Sets of Parallel Planes where the entire referenced surface must lie.
Gauging / Measurement:
Flatness is can be measured using a height gauge run across the surface of the part if only the reference feature is held parallel. You are trying making sure that any point along the surface does not go above or below the tolerance zone. Modern CMM’s are best for measuring the part as they can create virtual planes that the true surface profile can be compared to. This is a 3D measurement so points must be measured across the length and width of the part to ensure the entire surface is in tolerance. Flatness cannot be measured by simply placing the part on a granite slab and running a height gauge or microheight over it. This would be measuring parallelism instead as you are fixing the bottom of the part as a datum.
Relation to Other Symbols:
Flatness is the 3D version of surface straightness – Instead of the tolerance zone between two lines; the tolerance zone exists between two planes.
When Used:
When you want to constrain the amount of waviness or variation in a surface without tightening the dimensional tolerance of said surface. Usually, flatness is used to give a surface an even amount of wear or for sealing properly with a mating part. Commonly used on a fixture that must mate flush with another part without wobbling, but where orientation is not important.
Example:
If you want to make sure that a tabletop is perfectly flat, if you did not have a flatness callout, you would have to constrain the height of the table very tightly to make sure that the entire surface is straight. With flatness, you can allow the table to be flat without constraining the tabletop thickness very tight. (You would be rejecting tables that were good thicknesses and normally in spec if using GD&T)
Flatness Example 2 Table without GD&T
Table using the GD&T flatness Symbol
Final Notes:
Flatness is not the same as parallelism. Parallelism uses a datum to control a surface while flatness does not. Think of a table with two missing legs at an angle to the floor. The tabletop may be within flatness tolerance but would not be parallel to the floor.
2) Straightness
Special Note:
Straightness actually has two very different functions in GD&T depending on how it is called out. In its normal form or Surface Straightness, is a tolerance that controls the form of a line somewhere on the surface or the feature. Axis Straightness is a tolerance that controls how much curve is allowed in the part’s axis. This is usually called out with an included call to maximum material condition. Both callouts are very different from each other!
GD&T Symbol: 
Relative to Datum: No
MMC or LMC applicable: Yes – Axis Straightness
Drawing Callout:
Surface Straightness
Axis Straightness with Maximum Material Condition
Note: Surface Straightness is called out on the surface of the part. Axis straightness is called out next to the size dimension of the axis.
Description:
Surface Straightness:
The standard form of straightness is a 2-Dimensional tolerance that is used to ensure that a part is uniform across a surface or feature. Straightness can apply to either a flat feature such as the surface of a block, or it can apply to the surface of a cylinder along the axial direction. It is defined as the variance of the surface within a specified line on that surface.
Axis Straightness:
The form of straightness that controls the central axis of a part is sometimes referred to as Axial Straightness. This tolerance callout specifies how straight the axis of a part is (usually a cylinder). By definition, axis straightness is actually a 3D tolerance that constrains the center axis of the part preventing it from bending or twisting too far.
Maximum Material Condition further specifies this by controlling the size of the feature in addition to the allowed “bend” of the axis. Although a control of the axis, when MMC is called out, the entire part is used to determine if the tolerance has been met with a Go-Gauge. (See Gauging Section)
GD&T Tolerance Zone:
Surface:
Two Parallel Lines on either side of a surface line where the surface must lie (2D)
Axis:
A cylindrical boundary around the true central axis of the part, where the derived midpoint axis of the part must fit into.
Gauging / Measurement:
Surface:
A part is constrained and a gauge measures along a straight line. In this example, the height variance is measured to see how flat or straight the line is along this surface.
Axis:
To gauge axis straightness effectively, MMC is commonly called out. To ensure that a part or feature is axially straight, a cylinder gauge is used to determine if the part fits in its total envelope at MMC. This is both a control of the diameter and of the axial straightness. The ID of the cylinder gauge represents the maximum virtual condition of the part.
Gauge Cylinder ID = Max Ø part (MMC) + Straightness Tolerance
See the 2nd Example below for how axis straightness is used with a maximum material callout.
Note on Bonus Tolerance: When a functional gauge is used to measure axis straightness, the straightness tolerance can have bonus tolerance added when the part diameter is smaller than MMC. The goal of a maximum material condition callout is to ensure that when the part is in its worst tolerances, both straightness and dimensionally, that the part will always fit a given size hole. This means that if you make a part smaller in OD, you gain bonus tolerance and can actually have it be less straight! Remember – the goal of this callout is functional: The part must fit in a specific envelope.
Bonus Tolerance = difference between MMC and the actual size of the part.
For more detail, see the sections on Maximum Material Condition.
Relation to Other GD&T Symbols:
Surface:
Straightness can be considered the 2-Dimensional version of Flatness as both are measured without a datum and controls and refine the size of the feature. While flatness measures the variance across a 2D plane, Straightness only measures the variance on a straight line.
Axis:
Axis Straightness is also closely related to axis parallelism and axis perpendicularity since they both are controlling a center axis with a cylindrical tolerance zone. When MMC is applied, all of these callouts constrain the central axis to a specific variance amount ensuring the even at the worst-case tolerances, the part will function properly.
When Used:
Surface:
Commonly used for sealing surfaces or surfaces that mate with another part. For example, hydraulic channel cover in a transmission would need to make steel on steel contact in order to seal off the open hydraulic channels and maintain pressure. With a straightness call out you can specify which lines on the surfaces are most critical to making sure the pressure is maintained.
Axis / Max Material Condition:
Used mainly on pins or cylindrical surfaces which must be installed with clearance into a bore or hole. The straightness callout ensures that even in the Maximum material condition; the part will still fit its mating hole or section. Straightness is commonly used to control the curve of some parts that may be prone to bending during manufacturing.
Surface Straightness Example:
A steel bar is welded in a T pattern to another steel bar. If you want to make sure that the surface of the tube is always uniform, where the weld occurs, you would need to either greatly tighten the dimensional diameter of the tube, (which would be very costly for such a simple part!), or callout straightness along the mating surface.
Ensuring straightness without GD&T
Controlling the surface of the tube in the weld area with GD&T straightness callout.
Axial Straightness with MMC Example:
A boss pin on an engine housing is inserted into the chassis of a car to set the alignment before being bolted in. The pin is always in the correct position, however since it is so critical the dimension of the chassis mating hole is very tight. To ensure that this pin is always a correct fit for the hole, straightness is called out on the axis with maximum material condition.
Ensuring straightness on the drawing
To quickly check for this a gauge was made to check that the pin always fits into the hole in the maximum material condition. Using the calculation below the ID of the cylinder gauge can be determined to check for this during production.
Gauge Cylinder ID = MMC + Straightness
Gauge ID = Maximum Material Condition of Part + Straightness Bonus Tolerance
Gauge ID = 10.100 + 0.050
Gauge ID = 10.150 mm
Gauge control for axis/MMC straightness
If the part is close to MMC, it has to be a tighter straightness tolerance than if it was smaller and closer to the least material condition. As long as the entire part envelope fits within the 10.15 cylinder, the part is in specification. This extra tolerance on the straightness is the bonus tolerance
Final Notes:
Straightness and Perpendicularity with maximum material condition are most commonly used when controlling the form of a pin – while straightness controls the curve or bend of the center axis, perpendicularity controls the angle at which the pin is to a datum. Both constrain the axis of a pin feature and used gauges to control the entire feature’s boundary.
3) Circularity
GD&T Symbol: 
Relative to Datum: No
MMC or LMC applicable: No
Drawing Callout:
Description:
The circularity symbol is used to describe how close an object should be to a true circle. Sometimes called roundness, circularity is a 2-Dimensional tolerance that controls the overall form of a circle ensuring it is not too oblong, square, or out of round. Roundness is independent of any datum feature and only is always less than the diameter dimensional tolerance of the part. Circularity essentially makes a cross-section of a cylindrical or round feature and determines if the circle formed in that cross-section is round.
GD&T Tolerance Zone:
Two concentric circles, one inner and one outer, in which all the points within the circular surface must fall into. The tolerance zone lies on a plane that is perpendicular to the central axis of the circular feature.
Gauging / Measurement:
Circularity is measured by constraining a part, rotating it around the central axis while a height gauge records the variation of the surface. The height gauge must have total variation less than the tolerance amount.
Relation to Other GD&T Symbols:
Circularity is the 2D version of cylindricity. While cylindricity ensures all the points on a cylinder fall into a tolerance, circularity only is concerned with individual measurements around the surface in one circle. If you think of a stack of coins, circularity would be a measurement around one coin while cylindricity would have to measure the entire stack. (cylindricity is actually a combination of circularity and straightness)
When Used:
Circularity is a very common measurement and is uses in all forms of manufacturing. Any time a part needs to be perfectly round such as a rotating shaft, or a bearing, circularity is usually called out. You will see this GD&T symbol very often on mechanical engineering drawings.
Example:
If you had a hole that was around a rotating shaft, Both pieces should be circular and have a tight tolerance. Without circularity, the diameter of the hole and shaft would have to be very tight and more expensive to make.
Example 1: Controlling circularity without GD&T Symbol
Example 2: Controlling both features with circularity allows the diameter tolerances of the part to be opened up much larger.
Why isn’t the circularity 0.08 to replace ±0.08 of size tolerance?
You may be thinking, “well hang on – if it is ± 0.08 and circularity is the radial distance between the two circles, wouldn’t that mean the circularity should be only 0.08 since it would be on both sides? No – and this is because of how the two-point measurement of any feature would work when compared to the smallest size vs the biggest size it could be. In GD&T there is a rule that states you need perfect form at the MMC size – meaning at the largest size for a pin (smallest for a hole), your shape of this round feature cannot let it outside of a size of 10.08 for the first example.
Here is a diagram showing where the surface is allowed to lie without any circularity added for a size tolerance of 20±0.5. As you can see the max size can cause the shape of the part to go to 20.5 – just like you would assume. However due to the rule in the GD&T standard – the LMC size – in this case, the smallest size tolerance, only needs to be inspected with a two-point measurement. For an odd-number lobed part – geometrically this means that the circularity is limited by the TOTAL size tolerance. So for a size tolerance of 1.0 (±0.5), your equivalent circularity control would be 1.0.
To Recap – you need to be within a perfect boundary at MMC (largest pin, smallest hole) but for the LMC (smallest pin, largest hole size) you only need to take a 2-point measurement.
Final Notes:
Roundness:
Circularity in GD&T is sometimes also referred to as Roundness. Since it is a 2-Dimensional tolerance sometimes multiple sections of the same feature must be measured to ensure that the entire length of a feature is within roundness. Usually, two or three measurements are taken to ensure the part meets roundness for each segment of the part.
Statistical Tolerance Stacks:
Because circularity specifies the form of the surface in a specific area it needs to be considered when calculating a statistical tolerance stack. For example, if you have a part with a specified diameter and circularity callout, you must use both in your statistical stack since the geometric tolerance can contribute to a large part envelope than just the diameter tolerance alone. This will skew the statistical tolerance slightly higher and should be considered since parts are rarely perfectly circular.
4) Cylindricity
GD&T Symbol:
Relative to Datum: No
MMC or LMC applicable: No
Drawing Callout:
Description:
The Cylindricity symbol is used to describe how close an object conforms to a true cylinder. Cylindricity is a 3-Dimensional tolerance that controls the overall form of a cylindrical feature to ensure that it is round enough and straight enough along its axis. Cylindricity is independent of any datum feature the tolerance needs to be less than the diameter dimensional tolerance of the part. Cylindricity essentially forms a perfect cylindrical boundary around the object that the entire 3-Dimensional part must lie in.
GD&T Tolerance Zone:
Two concentric cylinders that run the entire length of the feature – one inner and one outer, in which all the points on the entire surface of the cylindrical feature must fall into. The entire length of the called out feature would be controlled.
Gauging / Measurement:
Cylindricity is measured by constraining a part on its axis, and rotating it around while a height gauge records the variation of the surface in several locations along the length. The height gauge must have total variation less than the tolerance amount.
Relation to Other GD&T Symbols:
Cylindricity is a merger of circularity and surface straightness. It is the 3-Dimensional version of circularity along an entire cylinder length. While circularity only is concerned with individual measurements around the surface in one circle, cylindricity takes into account how straight the axial portion of the cylinder is. Thinking of stack of coins, cylindricity would measure to make sure that the entire stack is straight up and that every coin is round. Circularity would only be measurements of the roundness of the individual coins.
When Used:
Cylindricity is a fairly common callout for shafts, pins and any critical cylindrical element. When a part needs to be both round and straight along its axis, such as a sliding shaft, or a dynamic locating pin, cylindricity is usually called out. You will see this GD&T symbol very often in automotive drawings and mechanical systems.
Example:
If you had a bushing that was to be pressed into a housing, the bushing would take the form of the housing bore when inserted. To ensure that the bushing maintains its round shape, and wears evenly along its surface, the housing bore needs to be very cylindrical. To do this without GD&T you would need very tight dimensions on the diameter of the bore, which may be very hard to control when being machined (and expensive)
Cylindricity example 1: Controlling cylindricity without GD&T Symbol
Controlling the circularity and the straightness of the bore with cylindricity.
This GD&T control allows the diameter tolerances of the part to be opened up much larger, and better controls the entire length of the bore. You can now accept a much broader range of hole sizes as long as the cylindricity is met.
Final Notes:
Statistical Tolerances:
Because cylindricity specifies the form of the surface, it must be considered when calculating a statistical tolerance stack. For example, if you have a part with a diameter and cylindricity callout, you must input both into your statistical stack since the cylindricity can contribute to a large part envelope than just the diameter tolerance alone. There are different theories on doing this and how to implement it; however, it can make a slight impact on skewing the results higher. Normal tolerance stacks do not require this since due to the envelope principle; the maximum radial envelop cannot exceed your maximum diameter tolerance due to rule #1 of GD&T.
