True Position Calculator
Check a measured hole or shaft center against its diametrical position tolerance, including optional MMC or LMC bonus tolerance.
Inspection inputs
Feature size
Drawing and measured center
Inspection result
Position variationThe measured axis is inside the available diametrical tolerance by 0.0779 mm.
Position offset summary
Calculation detail
| Check | Drawing / limit | Measured / calculated | Difference |
|---|---|---|---|
| Datum B coordinate | 25.0000 mm | 25.0300 mm | +0.0300 mm |
| Datum C coordinate | 40.0000 mm | 39.9800 mm | – 0.0200 mm |
| Feature size | 10.0000 – 10.1000 mm | 10.0500 mm | Within size limits |
| Position tolerance | 0.1500 mm total | 0.0721 mm variation | 0.0779 mm margin |
The position result is a diametrical value: twice the radial distance between the measured center and the basic center. This calculator checks location only; a complete inspection may also need size, form, orientation, datum simulation, and drawing-specific requirements.
How to use the true position calculator
What this calculator does
This calculator evaluates the two-dimensional location of a hole, bore, shaft, or pin axis relative to a theoretically exact center defined by basic dimensions. It converts the B- and C-direction coordinate errors into one diametrical position variation, then compares that variation with the drawing tolerance plus any valid bonus tolerance from MMC or LMC. It is useful for a quick inspection check, process troubleshooting, first-article review, and verifying hand calculations. It does not replace the complete drawing, datum setup, a calibrated coordinate measuring system, or the full interpretation rules in the governing GD&T standard.
When to use it
Use it when checking a single feature center from CMM or layout measurements, when investigating why a feature failed a coordinate-tolerance report, when estimating the effect of feature-size departure from MMC or LMC, or when teaching how rectangular X/Y offsets become a circular or cylindrical position zone. NIST explains how model-based product and manufacturing information supports dimensional inspection in its PMI validation and conformance testing program.
How to calculate
- The calculator opens with a complete millimeter demonstration and a ready Excel workbook. Replace the sample values with the drawing and measured values for your feature.
- Choose Units, Material condition, and Feature type. Unit changes convert all existing dimensional entries.
- Enter the stated Position tolerance (diametrical). For MMC or LMC, also enter nominal size, plus/minus size tolerances, and the measured feature size.
- Enter the basic distances from datums B and C and the corresponding measured distances. Results update immediately.
- Read Position variation, Total tolerance, the pass/fail verdict, and the signed Tolerance margin. Download Excel exports the current typed model. Reset clears the demonstration and may disable export until all required values are complete again.
Input guide
Units selects millimeters or decimal inches and is required. Material condition accepts RFS, MMC, or LMC. RFS uses only the stated position tolerance; MMC and LMC can add bonus tolerance. Position tolerance (diametrical) is a required positive decimal such as 0.10 mm. Do not enter a radius or a ± coordinate value. Feature type is hole/bore or shaft/pin and controls which size limit represents MMC or LMC.
Nominal feature size is the basic diameter, such as 10.00 mm. Measured feature size is the actual diameter, such as 10.05 mm. Size tolerance (+) and Size tolerance ( – ) are nonnegative magnitudes; enter 0.10 and 0.00 for a 10.00 +0.10/ – 0.00 hole. The measured size must stay within those limits. For a hole, MMC is the smallest allowed diameter; for a shaft, MMC is the largest. LMC is the opposite. A common error is applying hole logic to a shaft.
Basic distance from datum B and Basic distance from datum C are the theoretically exact coordinates. Measured distance from datum B and Measured distance from datum C are the inspected coordinates. Signed coordinates are accepted. Use a period as the decimal separator; grouped numbers, scientific notation, and ambiguous decimal-comma input are rejected.
Output guide
Offset from datum B and Offset from datum C are measured minus basic coordinates. Positive and negative signs show direction, but both contribute positively after squaring. Position variation is the diametrical result, not a radial distance. Drawing position tolerance repeats the stated callout. Bonus tolerance is zero under RFS and otherwise equals valid departure from the applicable material boundary. Total tolerance is drawing tolerance plus bonus. Tolerance margin is total tolerance minus position variation: positive means pass, zero is exactly at the boundary, and negative means the amount of excess. The detail table cross-checks coordinates, size limits, and the final comparison.
Worked example
The startup example uses a 10.00 mm hole with +0.10/ – 0.00 size tolerance, MMC position tolerance of 0.10 mm, and measured diameter of 10.05 mm. The basic center is B = 25.00 mm and C = 40.00 mm; the measured center is B = 25.03 mm and C = 39.98 mm. Therefore ΔB = +0.03 mm and ΔC = – 0.02 mm. The formula is:
Position variation = 2 × √(ΔB² + ΔC²)This gives 2 × √(0.03² + 0.02²) = 0.0721 mm. The hole is 0.05 mm larger than its MMC size of 10.00 mm, so bonus tolerance is 0.0500 mm and total tolerance is 0.1500 mm. The remaining margin is 0.1500 – 0.0721 = 0.0779 mm, so the example passes.
Formula, material boundaries, and interpretation
The core coordinate calculation is an exact Euclidean identity: subtract each basic coordinate from its measured coordinate, combine the perpendicular offsets with the Pythagorean theorem, and multiply the radial distance by two because position tolerance is commonly reported as a diameter. The U.S. National Institute of Standards and Technology maintains dimensional metrology resources through its dimensional metrology program, while ASME publishes the Y14.5 dimensioning and tolerancing standard used widely for GD&T practice.
Bonus tolerance is not automatic simply because a measured size differs from nominal. It applies only when the feature control frame includes a material condition modifier and when the actual size is within its permitted limits. Under MMC, a hole earns bonus as it becomes larger than its smallest allowed size, while a shaft earns bonus as it becomes smaller than its largest allowed size. Under LMC, the directions reverse. RFS keeps bonus at zero. Always read the feature control frame, datum references, projected tolerance zones, composite controls, and any drawing notes before accepting a part.