Geometric tolerancing calculators covering all 14 GD&T characteristics. Use the sidebar to jump to any tool.
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True position defines the exact location a feature must be in relation to its datums. Enter your nominal and actual coordinates to determine the deviation — with a clear PASS or FAIL against your specified tolerance.
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Enter values above and press CALCULATE
TRUE POSITION VALUE
Ø 0.0000
ΔX deviation
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ΔY deviation
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Tolerance (Ø)
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Formula
TP = 2√(ΔX² + ΔY²)
ΔX = Xactual − Xnominal
ΔY = Yactual − Ynominal
TP is expressed as a diameter — compare directly against the tolerance value on the drawing.
PASS if TP ≤ Tolerance
FAIL if TP > Tolerance
Maximum Material Condition (MMC) and Least Material Condition (LMC) modifiers unlock additional positional tolerance — called bonus — based on the actual measured size of a feature. As the hole departs from its critical condition, the tolerance zone grows by the same amount.
For MMC on a hole, the critical condition is the smallest allowed size. A larger actual hole earns bonus equal to the departure. For LMC, the critical condition is the largest allowed size — used where minimum wall thickness is the design concern. A smaller actual bore earns the bonus.
MMC — bigger hole gains bonus tolerance
LMC — smaller bore, thicker wall, bonus tolerance gained
A larger actual hole earns bonus tolerance. Bonus = Actual Ø − MMC Ø (lower size limit).
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Enter values above and press CALCULATE
TRUE POSITION VALUE
Ø 0.0000
MMC Size (Ø)
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Actual Size (Ø)
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Bonus Tol (Ø)
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Total Tol (Ø)
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Formula
Bonus = Øact − ØMMC
Total = Stated + Bonus
TP = 2√(ΔX² + ΔY²)
ØMMC = lower size limit (min hole)
ΔX = Xactual − Xnominal
ΔY = Yactual − Ynominal
TP is expressed as a diameter — compare directly against the tolerance value on the drawing.
PASS if TP ≤ Total tolerance
FAIL if TP > Total tolerance
Enter a nominal diameter and a single ISO 286 tolerance code — exactly as it appears on the engineering drawing, such as H7 for a hole or g6 for a shaft — to calculate the exact tolerance limits for that feature.
Uppercase letters denote a hole (H, G, F, E, D). Lowercase letters denote a shaft (h, g, f, e, d, k, m, n, p, r, s, u). The number is the IT tolerance grade. The calculator detects hole vs. shaft automatically from the letter case.
Common Tolerance Codes
Holes
| H7 | General precision |
| H8 | General purpose |
| H9 | Loose / generous |
| G7 | Close clearance |
Shafts
| g6 | Precision clearance |
| f7 | Free running |
| k6 | Transition |
| p6 | Light press |
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Enter a nominal size and tolerance code above, then calculate.
H7 — Ø25 mm
HOLEMin Ø (Lower Limit)
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EI deviation
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Max Ø (Upper Limit)
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ES deviation
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Tolerance Band
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IT grade width
Deviation from Nominal
Reference
How to read the code
Letter = deviation family
Number = IT tolerance grade
Uppercase → HOLE
Lowercase → shaft
Hole Letters
H — zero lower deviation
G, F, E, D — clearance holes
Shaft Letters
d e f g — clearance shafts
h — zero upper deviation
k m n — transition shafts
p r s u — interference shafts
IT Grade Range
IT5 (fine) → IT12 (coarse)
Nominal range: 0–500 mm
Standard: ISO 286-1:2010
A 1D tolerance stackup sums contributing dimensions and their tolerances to find the total variation at a critical gap or resultant dimension. Worst-case analysis guarantees every part within tolerance will assemble correctly. RSS (root sum square) gives the statistical expectation — typically 3× more permissive for many-component assemblies.
Enter each contributing dimension with its bilateral (±) tolerance. To model closing dimensions, enter a negative nominal value. Leave unused rows blank.
Component name (optional)
Nominal (mm)
± Tolerance (mm)
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Enter component values above and press CALCULATE
NOMINAL RESULTANT
0.0000 mm
Worst Case
Total variation (±)
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Resultant range
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RSS Statistical
Total variation (±)
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Resultant range
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Worst Case
PASS
RSS
PASS
Formulas
N = Σnᵢ
WC = ±Σtᵢ
RSS = ±√(Σtᵢ²)
nᵢ = nominal of each component
tᵢ = bilateral tolerance of each part
PASS if (N − variation) ≥ min gap
RSS is statistically valid when tolerances are independent and normally distributed.
GO and NOGO gauges verify that a manufactured feature falls within its size limits without measuring the actual size. The GO gauge must pass — confirming the feature is at least the minimum size. The NOGO gauge must not pass — confirming the feature does not exceed the maximum size.
Gauge tolerances are set by the 10% rule (workshop grade II) or 5% rule (inspection grade I) per BS 969 / ISO 1938-1. For holes, plug gauges are used. For shafts, ring gauges are used.
GO plug must enter the hole; NOGO plug must not. GO is made to lower limit; NOGO is made to upper limit.
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Enter limits above and press CALCULATE
Workpiece Tol.
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Gauge Tol.
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GO — Maker's size
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GO limits
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NOGO — Maker's size
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NOGO limits
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Size Range — Workpiece & Gauge Positions
10% Rule (BS 969)
Gauge tolerance
Grade II = T × 10%
Grade I = T × 5%
GO gauge (hole)
Maker's size = lower limit
Range: LL → LL + gauge tol
NOGO gauge (hole)
Maker's size = upper limit
Range: UL − gauge tol → UL
Standard: BS 969 / ISO 1938-1. Gauge tol is applied on the workpiece tolerance side (unilateral).
Circular runout controls the variation of each circular cross-section around the datum axis — measured with a dial gauge at one axial position at a time. Total runout controls variation across the entire surface simultaneously, combining both concentricity and cylindricity errors.
Both are measured as TIR — Total Indicator Reading (full dial gauge swing from min to max in one rotation). TIR must not exceed the drawing tolerance. Eccentricity = TIR ÷ 2 (the offset of the actual axis from the datum).
Measured at a single cross-section. Controls concentricity and roundness of each circular element.
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Enter values above and press CALCULATE
MEASURED TIR
0.0000 mm
Tolerance
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Eccentricity (e)
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Margin / Overshoot
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Key Relationships
e = TIR ÷ 2
PASS if TIR ≤ tol
TIR = total dial gauge swing
e = axis eccentricity
Circular runout
Checks each cross-section independently. Concentricity + roundness errors combined.
Total runout
Checks entire surface simultaneously. Also controls cylindricity and taper.
Used for threaded inserts, press-fit pins, and studs where the mating part must clear the fastener above the surface. A pin can be perfectly positioned at the surface but still fail if it tilts — its tip can deviate outside the tolerance zone projected above the part.
The calculator finds the effective position deviation at the projection height P given the radial deviation at the surface and the feature's tilt angle. Annotated on drawings as Ⓟ with a projection height value.
Radial distance from nominal axis at entry point.
Angle of pin/hole axis from true (vertical) axis.
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Enter values above and press CALCULATE
DEVIATION AT PROJECTION HEIGHT
0.0000 mm
At surface (d)
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Tilt addition
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Tol. radius (t÷2)
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Formula
dev = d + P·tan θ
PASS if dev ≤ t/2
d = radial deviation at surface
P = projection height
θ = tilt angle of feature
t = stated tolerance (diameter)
The tolerance is a diameter zone, so the radial limit is t÷2. Used on drawings with the Ⓟ symbol and a projection height value.
When a datum feature is called up at Maximum Material Boundary (Ⓜ after datum letter), the entire feature pattern is allowed to shift as the datum feature departs from its virtual condition. This is equivalent to a bonus tolerance for the whole pattern — not individual features.
The virtual condition (VC) of a datum is calculated from its size limits and its own geometric tolerance. Any departure from VC in a more generous direction earns datum shift equal to that departure.
VC = lower limit − datum position tol. Shift = actual − VC (if actual > VC).
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Enter values above and press CALCULATE
DATUM SHIFT AVAILABLE
0.0000 mm
Virtual Condition (VC)
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Actual Size
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Pattern Shift
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Virtual Condition
Hole (internal datum)
VC = lower limit − datum tol
Shift = actual − VC
Pin / Boss (external)
VC = upper limit + datum tol
Shift = VC − actual
Datum shift applies to the whole pattern — every feature in the group shifts together. Not the same as individual feature bonus tolerance.
Profile of a surface controls the form, orientation, and location of any surface relative to the true profile. The tolerance zone is a band of width t distributed around the true profile, which can be split equally (bilateral), unequally (unilateral or unequal bilateral), or placed entirely on one side.
Enter the nominal profile value and tolerance, select the distribution, and optionally enter an actual measured deviation to get a PASS/FAIL result.
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Enter values above and press CALCULATE
TOLERANCE ZONE BOUNDARIES
Upper Boundary (+)
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outside limit
Lower Boundary (−)
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inside limit
Zone Width
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Distribution
Equal bilateral
Upper = nom + t/2, Lower = nom − t/2
Unilateral outside
Upper = nom + t, Lower = nom
Unilateral inside
Upper = nom, Lower = nom − t
Unequal bilateral
Upper = nom + u, Lower = nom − v
Deviation is measured normal to the true profile surface. PASS if actual deviation falls within upper and lower boundaries.
Cp measures the potential capability of a process — how well it could perform if perfectly centred within the spec limits. Cpk measures actual capability, penalising any offset of the process mean from the centre of the tolerance band. A process with Cpk < 1.0 is producing parts outside specification.
Industry standard requires Cpk ≥ 1.33 for a capable process (4-sigma). Critical or safety features often require Cpk ≥ 1.67 (5-sigma). Enter your spec limits, the measured process mean, and the process standard deviation.
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Enter spec limits and process statistics above, then press CALCULATE
Cpk — PROCESS CAPABILITY INDEX
1.0000
Cp — Potential
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centred capability
Cpk — Actual
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min(CPU, CPL)
CPU — Upper
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distance to USL
CPL — Lower
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distance to LSL
CAPABLE
Process Distribution vs Specification Limits
Formulas
Cp = (USL−LSL) / 6σ
CPU = (USL−μ) / 3σ
CPL = (μ−LSL) / 3σ
Cpk = min(CPU, CPL)
Capability ratings
≥ 1.67 — Excellent (5σ)
≥ 1.33 — Capable (4σ) ✓
≥ 1.00 — Marginal (3σ)
< 1.00 — Not capable ✗
Cp measures potential (centred). Cpk measures actual (off-centre penalty). If Cp = Cpk the process is perfectly centred.