GD&T — Geometric Dimensioning & Tolerancing
A complete interactive guide to GD&T per ASME Y14.5-2018 / ISO 1101: all 14 geometric characteristics, the Feature Control Frame, Datum Reference Frame, MMC/LMC/RFS modifiers, True Position, Profile, Runout, and tolerance stack-up — with hands-on interactive widgets for every symbol.
⊕GD&T — Geometric Dimensioning & Tolerancing
ASME Y14.5-2018 / ISO 1101. A universal language for geometric tolerances — 14 characteristics, 5 categories.
⊕ GD&T — 14 Geometric Characteristics | Click for details
📊 GD&T Categories
| Category | Symbols | Datum? | Definition |
|---|---|---|---|
| Form | — □ ○ ⌀ | None! | Deviation from perfect form |
| Orientation | ∥ ⊥ ∠ ⌖ | Required | Orientation relative to a Datum |
| Location | ⊕ ◎ ≡ | Required | Location of a feature relative to a Datum |
| Runout | ↗ ↗↗ | Required | For rotating parts only |
| Profile | ⌢ ⌣ | Optional | Tolerance on a free-form line/surface |
□ FCF — Feature Control Frame
| Field | Content | Example | Explanation |
|---|---|---|---|
| 1 | Geometric symbol | ⊥ | Perpendicularity |
| 2 (prefix) | ⌀ if cylindrical | ⌀0.05 | Zone = Cylinder |
| 2 | Tolerance value | 0.05 | 0.05mm tolerance zone |
| 3 | Datum A | A | Primary — 3 points contact |
| 4 | Datum B | B | Secondary — 2 points contact |
| 5 | Datum C | C | Tertiary — 1 point contact |
| Mode | Ⓜ MMC / Ⓛ LMC / Ⓢ RFS | Ⓜ | Tolerance calculation mode |
► Key rule: Form = no Datum | Orientation/Location/Runout = Datum required
► ⌀ before the tolerance = Cylindrical zone — common for axes!
► No ⌀ = Zone between two planes (Width)
▶ YouTube► ⌀ before the tolerance = Cylindrical zone — common for axes!
► No ⌀ = Zone between two planes (Width)
△ Datum Reference Frame — 3-2-1
| Datum | Min. Contact | DOF Locked | Example |
|---|---|---|---|
| Primary (A) | 3 points | Z + Rx + Ry (3 DOF) | Bottom face |
| Secondary (B) | 2 points | Y + Rz (2 DOF) | Long side |
| Tertiary (C) | 1 point | X (1 DOF) | Short side |
► Order matters! A first, B second, C third. Changing the order = changing the result
► Datum Simulator = the ideal surface (surface plate, granite, V-block)
► Datum Feature = the actual physical surface on the part (not perfect!)
► Unstable Datum? = failure! Use a Customized DRF (ASME Y14.5-2018)▶ YouTube
► Datum Simulator = the ideal surface (surface plate, granite, V-block)
► Datum Feature = the actual physical surface on the part (not perfect!)
► Unstable Datum? = failure! Use a Customized DRF (ASME Y14.5-2018)▶ YouTube
Ⓚ Material Condition Modifiers
| Modifier | Symbol | Definition | Bonus? | Usage |
|---|---|---|---|---|
| MMC | Ⓜ | Maximum Material Condition | Yes | Pin: MMC=Max ⌀. Hole: MMC=Min ⌀ |
| LMC | Ⓛ | Least Material Condition | Yes (reversed) | Protects minimum wall thickness |
| RFS | Ⓢ / none | Regardless of Feature Size | No | Default (ASME 2018). Strictest! |
| Projected | Ⓟ | Projected Tolerance Zone | — | For bolts — zone extends beyond the hole |
► Bonus = MMC − Actual Size (for pins) — grows as the part gets smaller
► Virtual Condition (VC): Pin VC = MMC + GeoTol | Hole VC = MMC − GeoTol
► Fixed Fastener: T₁ + T₂ = H − F (Hole − Fastener MMC)
► ASME 2009 vs 2018: In both 2009 and 2018, RFS is the default. In 2018 the ⓢ symbol was removed — RFS applies automatically with no marking
▶ YouTube► Virtual Condition (VC): Pin VC = MMC + GeoTol | Hole VC = MMC − GeoTol
► Fixed Fastener: T₁ + T₂ = H − F (Hole − Fastener MMC)
► ASME 2009 vs 2018: In both 2009 and 2018, RFS is the default. In 2018 the ⓢ symbol was removed — RFS applies automatically with no marking
📘 Key GD&T Rules (ASME Y14.5)
Rule #1 — Perfect Form at MMC
DefinitionAt MMC, a feature must be in perfect form
ExamplePin ⌀20±0.1 — at ⌀20.1 (MMC) it must be straight!
At LMC⌀19.9 — up to 0.2mm bow is allowed
Rule #1 = Taylor's Principle
Allowed deviation = MMC − Actual Size
⊘ Envelope Principle — ISO 8015 equivalent
▶ YouTubeAllowed deviation = MMC − Actual Size
⊘ Envelope Principle — ISO 8015 equivalent
Rule #2 — RFS Default
DefinitionIn ASME 2018, RFS is the default
MeaningFixed geometric tolerance — no bonus
ExceptionPosition/Runout — can take Ⓜ
Rule #2 = if no modifier is stated = RFS
Most conservative = strictest
▶ YouTubeMost conservative = strictest
ISO vs ASME — Key Differences
Rule #1ASME: Envelope Principle. ISO: not by default! Must specify ⊙
DefaultASME: RFS. ISO: RFS (ISO 2692)
AngularityISO: included under Orientation. ASME: separate symbol ∠
ProfileISO: can include Size. ASME: kept separate
Always state: ASME Y14.5-2018 or ISO 1101 in the title block
Datum Target — Reference Points
PurposeWhen a surface isn't accurate enough for a regular Datum
Datum Target PointA1, A2, A3 — defined contact points
Target LineContact along a defined line
Target Area⌀20 A1 — round ⌀20 contact area
Used for: castings, forgings — rough surfaces
▶ YouTube⊕ True Position — the most central GD&T concept
| Parameter | Definition | Calculation |
|---|---|---|
| True Position | Exact theoretical location (TED — Basic Dim) | Shown on drawing as BASIC (boxed) |
| Actual Position | The measured actual location | CMM: actual X,Y |
| Positional Tolerance | ⌀ of the allowed zone | ⌀T from the FCF |
| Deviation | Deviation from True Position | d = √(ΔX²+ΔY²) |
| Acceptance | d ≤ T/2 | d beyond T/2 = rejected |
► Actual Position = ⌀ 2×√(ΔX²+ΔY²) — double the deviation!
► Basic Dimensions = dimensions defining True Position (boxed on the drawing)
► Pattern Locations: PLTZF (Pattern Loc. Tol. Zone Framework) for a group of holes
► Composite Position: two-row FCF — Location + Feature Relationship
▶ YouTube► Basic Dimensions = dimensions defining True Position (boxed on the drawing)
► Pattern Locations: PLTZF (Pattern Loc. Tol. Zone Framework) for a group of holes
► Composite Position: two-row FCF — Location + Feature Relationship
△ Profile — line and surface profile
| Symbol | Name | What is defined? | Datum? | Usage |
|---|---|---|---|---|
| ⌢ | Profile of a Line | Deviation of a 2D cross-section | Optional | Cross-sections, 2D airfoils |
| ⌣ | Profile of a Surface | Deviation of the entire surface | Optional | 3D printing, free-form design |
| Bilateral Equal | ±t/2 | Equal in both directions | — | Default |
| Bilateral Unequal | +0.8/−0.2 | Not equal | — | Marked with (0.8) in parentheses |
| Unilateral | 0 / +t | One direction only | — | Draft angle, mold |
► The most powerful symbol in GD&T: Profile can replace any other symbol!
► Dynamic Profile (ASME 2018): a Profile that allows scaling — new!
► All Around ○: Profile applied to the entire perimeter
► All Over (sphere): Profile applied to the entire 3D surface
▶ YouTube► Dynamic Profile (ASME 2018): a Profile that allows scaling — new!
► All Around ○: Profile applied to the entire perimeter
► All Over (sphere): Profile applied to the entire 3D surface
↺ Runout
| Characteristic | Symbol | What is measured? | Measurement | Datum? |
|---|---|---|---|---|
| Circular Runout | ↗ | Single cross-section, rotating | Dial indicator × rotation | Axis required |
| Total Runout | ⇈ | Full length/surface, rotating | Traverse × rotation | Axis required |
| Total Runout > Circular | — | TotalRunout ≥ CircularRunout | — | — |
| Face Runout | ↗ on a perpendicular face | Deviation of an end face | Axial DI | Axis |
► Runout ≠ Roundness: Runout = deviation from a Datum axis. Roundness = form only
► Runout includes: Circularity + Coaxiality + Taper
► Total Runout includes: Cylindricity + Coaxiality
► Measurement: Datum on a V-block/centers + dial gauge
▶ YouTube► Runout includes: Circularity + Coaxiality + Taper
► Total Runout includes: Cylindricity + Coaxiality
► Measurement: Datum on a V-block/centers + dial gauge
∑ Tolerance Stack-up
Worst Case — WC
MethodSum of all tolerances (MAX)
FormulaT_total = ΣT_i
Pro100% guarantee — every part will assemble
ConVery tight tolerances = ↑cost
Recommended for: critical parts / small assemblies
Safety/Medical/Aerospace
Safety/Medical/Aerospace
RSS — Root Sum Square
Method√(ΣT_i²) — statistical
FormulaT_total = √(T₁²+T₂²+...+Tₙ²)
ProTolerance ↑ 2-3× vs WC
ConOnly 99.73% coverage (±3σ)
Recommended for: high volume production (SPC)
Less conservative than WC
Less conservative than WC
Example: 3-Part Stack
Part A20.00 ± 0.10
Part B15.00 ± 0.05
Part C10.00 ± 0.08
WC Total±(0.10+0.05+0.08) = ±0.23
RSS Total±√(0.01+0.0025+0.0064) = ±0.131
RSS allows ±0.131 vs WC ±0.23 — a big difference!
▶ YouTubeStack-up Tools
1D Stack-upClosed Loop: ΣT = 0 (Check Loop)
2D Stack-upVector loop in every direction
Software3DCS, CETOL, Sigmetrix, OpenVSP
ExcelPossible! WC+RSS in a simple Excel sheet
Loop: every dimension from A to B is +/−
Loop sum = 0 = validation!
Loop sum = 0 = validation!
📊 Quick Reference Table — All 14 Symbols
| Symbol | Name | Category | Datum? | Zone | Common Use | ISO 1101 |
|---|---|---|---|---|---|---|
| — | Straightness | Form | No | 2 Lines / ⌀ Cyl | Rod axis, panel edge | — |
| □ | Flatness | Form | No | 2 Planes | Mating surfaces, Datums | □ |
| ○ | Circularity | Form | No | 2 Circles | Lathe axis, bearing | ○ |
| ⌀ | Cylindricity | Form | No | 2 Cylinders | Piston, precision shaft | ⌀ |
| ⌢ | Profile of a Line | Profile | Optional | 2D Zone | Airfoil, free-form section | ⌢ |
| ⌣ | Profile of a Surface | Profile | Optional | 3D Zone | Free-form, casting | ⌣ |
| ∠ | Angularity | Orientation | Required | 2 Planes | Angle other than 0/90° | ∠ |
| ⊥ | Perpendicularity | Orientation | Required | 2 Planes / ⌀ Cyl | Perpendicular axis, wall | ⊥ |
| ∥ | Parallelism | Orientation | Required | 2 Planes | Parallel plates | ∥ |
| ⊕ | True Position | Location | Required | ⌀ Cylinder / 2 Planes | Holes, patterns | ⊕ |
| ◎ | Concentricity/Coaxiality | Location | Required | ⌀ Cylinder | Axis-on-axis (rotating) | ◎ |
| ⊙ | Symmetry | Location | Required | 2 Planes | Slots, splines | — |
| ↗ | Circular Runout | Runout | Required | 1 Cross-Section | Bearing seat | ↗ |
| ⇈ | Total Runout | Runout | Required | Full Surface | Entire cylinder | ⇈ |