Chapter iv · The Symbols
A surface plate is flat to a millionth of an inch. The part you set on it is not. Flatness is the gap between them — and it answers to nothing in the universe but the surface itself.
Most of GD&T is about relationships: this hole relative to that face, this slot square to that edge. But four controls ask nothing of the outside world. They compare a feature to a perfect version of itself — no datum, no reference, no second opinion. These are the form characteristics.
There are exactly four: straightness, flatness, circularity, and cylindricity. Each one controls shape — and shape only. A form tolerance can never govern how big a feature is or where it sits. It governs how true the feature is to its own ideal geometry.
A compressor disk that passed every diameter check once still failed on the test stand — its bore was perfectly sized but subtly out-of-round, and the seal it carried leaked under load. Size was fine; form was the killer.
Straightness
Two parallel lines the tolerance apart — how much a line element may bow.
Flatness
Two parallel planes the tolerance apart — how far a surface departs from a true plane.
Circularity
Two concentric circles per cross-section (their radii differ by the tolerance value) — how out-of-round one slice may be.
Cylindricity
Two coaxial cylinders — the 3-D superset bounding the whole surface at once.
The shape of each zone follows from the geometry it controls. A straight line lives between two parallel lines; a flat surface between two parallel planes. Round a single slice between two concentric circles; and a whole cylindrical surface between two coaxial cylinders. Drag the slider below and watch a feature deviate inside its zone — until it breaks past the boundary.
Watch what the slider never does: it never moves the feature's location and never changes its size. The zone floats with the part. That is the signature of form — it is the only family that compares a feature to nothing but its own ideal, which is exactly why none of the four ever carries a datum letter. Remember our bracket: its mounting face can be the right size and square to the world and still rock on the mating plate, because a high spot in the middle means the face isn't flat — and no datum can fix that.
Before you go on, prove it — drag all twelve symbols home.
Tap a symbol, then tap the family it belongs to. All twelve, no datum hints — just memory.
Cylindricity is the 3-D superset
Circularity checks a single cross-section: is this slice round? Cylindricity is far more demanding. It bounds the entire surface between two coaxial cylinders the tolerance apart — so a part passes only if every slice is round, every surface line is straight, and there is no taper from end to end. One control bounds all surface deviations at once: out-of-roundness, taper, axis bow, and surface-line straightness.
That is why cylindricity is rare and expensive to inspect: it requires a full-surface scan, not a single dial-indicator sweep. When a drawing only needs one of those three things controlled, the lesser control (circularity, or surface straightness) is the right tool.
For the advanced reader → Three myths about form
“Circularity controls diameter.” No. Circularity says nothing about how big the circle is — only how round. A 9.8 mm hole and a 10.2 mm hole can both have perfect circularity; size is the job of the size dimension, not the form control.
“Flatness needs a datum.” No — never. A flatness tolerance compares a surface to a perfect plane derived from that same surface. There is no external reference to point at. If you find yourself wanting one, you actually want a different control (parallelism, profile) — that is orientation or profile, not form.
“Cylindricity is just circularity in 3-D.” Close, but it is strictly more: circularity is blind to taper and to a banana-shaped axis line; cylindricity catches both because its zone is two full coaxial cylinders, not a stack of independent circles.
Form on Trial
A shaft is dimensioned ∅10.00 ±0.02 with a circularity tolerance of 0.005. An inspector finds a slice measuring ∅10.30 but perfectly round. What does circularity say?
A drawing applies flatness 0.05 to the bracket’s mounting face — and points a datum letter -A- at that same face. What’s wrong?
A turned pin must be round in every slice AND free of taper or a bowed axis along its length — all under one callout. Which form control does it?
Form is the most honest control in the language. It makes no demand of any other surface, names no datum, and points at nothing but the feature in front of it.
A flat surface is simply a surface that has nowhere to hide — measured against the one standard it can never argue with: a perfect version of itself.
Form asks nothing of the outside world. But the moment you ask ‘is it square to something?’ you need a second opinion — a datum. That's orientation, chapter v.