Geometric Dimensioning & Tolerancing · ASME Y14.5 / ISO 1101
GD&T Calculator — True Position, Flatness & Runout (ASME Y14.5 / ISO 1101)
Governing standard: ASME Y14.5· ASME Y14.5-2018 · ISO 1101:2017
Page last updated
The MechanixCalc GD&T calculator evaluates the full family of geometric tolerances to ASME Y14.5-2018 and ISO 1101. Enter the measured feature coordinates, surface points or radii, and the drawing tolerance, and the tool returns an instant verdict — PASS, FAIL, or NOT PROVEN where the measurement only bounds the quantity — with a tolerance-zone chart, covering true position (cylindrical zone, with MMC bonus), flatness, circularity, cylindricity, circular runout, total runout, perpendicularity, parallelism, and an MMC / LMC bonus tolerance panel with virtual condition.
It is built for quality and inspection engineers, CMM operators, and design engineers who need to confirm that a manufactured feature is within its drawing callout without reaching for a spreadsheet. Every result is traceable to the ASME Y14.5 definition so it can be attached directly to an inspection record or referenced in a non-conformance report.
What this calculator does
- True position (ASME Y14.5) with cylindrical tolerance zone — instant PASS/FAIL against the drawing callout
- MMC and LMC bonus tolerance: automatic bonus calculation for holes and external features (shafts/pins)
- Flatness check from up to 20 CMM or height-gauge points, with per-point deviation bar chart
- Circularity from radii and cylindricity screening from multi-section two-point diameters, with radar chart — FAIL only when proven, otherwise NOT PROVEN
- Circular and total runout (TIR) — FAIL when a reading exceeds the tolerance; within it, NOT PROVEN (one section, or per-station readings)
- Perpendicularity and parallelism deviation with remaining tolerance readout
- Bonus tolerance panel with virtual condition (VC) and feature size range check
- Branded PDF engineering report with the full method shown (True Position tab)
Method & formulas
True position (ASME Y14.5 cylindrical zone)
True position quantifies how far a feature's actual centre lies from its theoretically exact (TED) location. ASME Y14.5 defines the positional error as the diameter of the smallest circle centred on the TED that encloses the actual feature centre — which is twice the radial deviation from the TED. The tolerance zone is cylindrical (a diameter), so the measured positional deviation must be smaller than or equal to the stated diameter tolerance for the feature to pass.
When an MMC modifier is applied, each unit of departure from the maximum material condition (smallest hole or largest shaft) adds an equal unit of bonus tolerance, expanding the allowed zone. The total effective tolerance is the stated value plus the bonus. The virtual condition is the extreme boundary formed by the worst-case combination of size and position.
TP = 2 × √(Δx² + Δy²)where TP = true position diameter (mm); Δx = actual X − nominal X; Δy = actual Y − nominal Y. Pass if TP ≤ total tolerance zone diameter.
T_total = T_stated + bonus; hole: bonus = max(0, actual_size − MMC_size); shaft: bonus = max(0, MMC_size − actual_size)where T_stated = tolerance on the drawing (mm); bonus = departure from MMC; MMC_size = smallest hole diameter or largest shaft diameter (mm). The sign follows the feature type — a feature on the wrong side of MMC has violated it rather than departed from it, so it earns no bonus. The bonus is not |actual − MMC|, which would award tolerance to precisely the parts that must be rejected.
Form tolerances — flatness, circularity and cylindricity
Flatness, circularity and cylindricity are evaluated from a set of measured surface points. In each case the tolerance zone is the width between two parallel bounding elements (planes, circles or cylinders). The calculator takes the peak-to-valley range of the measured points. Because sampled points only bound the true minimum-zone value, no form check ever PASSES: a result within tolerance is NOT PROVEN. A FAIL is reported only when non-conformance is proven — circularity when the radius range exceeds the tolerance, and cylindricity when the two-point diameter variation Vd exceeds twice the tolerance (the radial zone is Vd/2, so Vd/2 > t). Flatness from heights without X-Y positions is never proven either way, because the peak-to-valley includes any tilt of the measuring setup: over tolerance it reads NOT PROVEN, not FAIL.
Form error = max(measured values) − min(measured values)where For flatness: values are surface heights from a reference plane (mm). For circularity: values are radii at equally-spaced angles (mm). For cylindricity: the inputs are two-point DIAMETERS, and the value is the diameter variation Vd = max diameter − min diameter across all axial sections and angles. Vd is a diametral quantity — twice the radial width between two coaxial cylinders — so the proven lower bound on cylindricity is Vd/2. Verdicts: circularity FAIL when the range exceeds the tolerance; cylindricity FAIL only when Vd > 2 × tolerance (NOT PROVEN for tolerance < Vd ≤ 2 × tolerance); flatness over tolerance is NOT PROVEN (setup tilt). Within tolerance every form check is NOT PROVEN, because sampled points cannot prove the whole surface conforms — nothing in the form family PASSES.
Runout and orientation
Circular runout is the total indicator reading (TIR) at a single cross-section during one full revolution about the datum axis. The calculator compares the entered TIR directly against the stated runout tolerance; because circular runout applies at every circular element and one section proves only that section, a reading within tolerance is NOT PROVEN, while a reading above it FAILS. Total runout takes the maximum TIR across the entered cross-sections; because that is built from per-station readings rather than one continuous sweep, it is a lower bound on total runout — it can prove non-conformance but not conformance, and it cannot see taper that is coaxial with the datum axis.
Perpendicularity is converted from the measured angular deviation: the linear deviation over the feature's length is L·tan(α), evaluated as a magnitude, since a perpendicularity deviation is a zone width and has no sign. One angular reading assumes a straight axis, so it bounds the deviation from below: exceeding the tolerance FAILS, staying within it is NOT PROVEN. Parallelism is the absolute height difference between two measured reference points, which likewise bounds — rather than proves — the surface's containment within the tolerance zone.
deviation = |L × tan(α)|where L = feature length (mm); α = measured angular deviation from perpendicular (degrees), |α| < 90. Pass if deviation ≤ perpendicularity tolerance.
Worked example
Check whether a drilled hole at nominal position (X = 0, Y = 0) passes a true-position callout of ⌀ 0.30 mm, given that the CMM measures the hole centre at X = 0.10 mm, Y = 0 mm (no MMC modifier).
Given
- Nominal X0 mm
- Nominal Y0 mm
- Actual X (CMM)0.10 mm
- Actual Y (CMM)0 mm
- Positional tolerance zone diameter⌀ 0.30 mm
Result
- True position TP⌀ 0.20 mm
- Tolerance zone⌀ 0.30 mm
- Remaining tolerance0.10 mm
- VerdictPASS
- Compute the coordinate deviations from nominal: Δx = 0.10 − 0 = 0.10 mm; Δy = 0 − 0 = 0 mm.
- Apply the true-position formula: TP = 2 × √(Δx² + Δy²) = 2 × √(0.10² + 0²) = 2 × √0.01 = 2 × 0.10 = 0.20 mm.
- Compare to the tolerance zone: 0.20 mm ≤ 0.30 mm — the hole centre lies inside the cylindrical tolerance zone.
- Remaining tolerance = 0.30 − 0.20 = 0.10 mm.
Illustrative example only — verify against your own CMM measurements. No MMC modifier is used here; adding an MMC bonus would expand the allowable zone further.
Frequently asked questions
Which standard does this GD&T calculator use?
True position (with MMC bonus), the MMC / LMC bonus panel, flatness, circularity, cylindricity, runout, perpendicularity and parallelism are evaluated to ASME Y14.5-2018 (the current US standard for geometric dimensioning and tolerancing) and ISO 1101:2017 (the international equivalent). The form, runout and orientation checks are evaluated from the measurement points you enter, so they bound the true minimum-zone value rather than replacing a CMM's own evaluation. The governing standard is shown in the generated PDF report.
How does MMC bonus tolerance work in the calculator?
When you enable the MMC modifier, the tool computes the bonus as the feature's departure from its maximum material condition: for a hole, bonus = actual size − MMC size (smallest hole); for a shaft or pin, bonus = MMC size (largest pin) − actual size. The total effective tolerance is the drawing-stated value plus the bonus. A virtual condition is also displayed — the extreme boundary that must never be violated regardless of the bonus.
What is the difference between circular runout and total runout?
Circular runout (ASME Y14.5 symbol: single arrow) is the TIR (total indicator reading) measured at one cross-section during a full 360° rotation about the datum axis. It controls both radial variation and eccentricity at that section only. Total runout (double arrow) is a composite control: every reading from one setup, along the full axial length, must lie between two coaxial cylinders t apart — a stricter control that also covers taper and profile error along the axis. The calculator takes the maximum of per-station TIR readings, which is only a LOWER BOUND on total runout: it cannot see taper coaxial with the datum (a perfect cone reads TIR 0 at every station), so it can prove non-conformance but not conformance.
Can I use this calculator alongside a CMM report?
Yes. Enter the actual coordinates or radii from your CMM report directly and attach the generated PDF to your inspection record. Note that the form and runout checks are evaluated from the points you enter: they can prove a feature is out of tolerance, but proving conformance needs your CMM's own minimum-zone evaluation over the full measured surface. An ISO 14253-1 measurement-uncertainty guardband decision (U95, bias correction, Accept / Reject / Inconclusive) is available through the MechanixCalc API at /api/v1/gdt.
Is the GD&T calculator free?
Yes — you can use every GD&T check with no sign-up during a free 30-minute preview, and a free 14-day account trial unlocks the full calculator suite with no credit card required. The branded PDF engineering report and saved calculations are included in the free 14-day trial and in every paid plan.
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- Shaft AnalysisVerify shaft diameters and runout allowances that the GD&T runout callout must be consistent with.
- Press Fit (ISO 286)Size interference fits whose bore and shaft size tolerances interact directly with GD&T position and size requirements.
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