Home / Trade / Manufacturing / GD&T True Position

GD&T True Position

Calculate diametric true position from X/Y deviations. Instantly verify if a CNC milled hole or feature passes standard GD&T diametric tolerance limits.

CNC True Position Calculator (GD&T)

Compute the diametric true position (⌀TP) of a measured feature from its nominal location. Instantly verify GD&T tolerance compliance using first-principle coordinate geometry.

X Deviation (ΔX) — in

Measured X − Nominal X

Y Deviation (ΔY) — in

Measured Y − Nominal Y

Tolerance Zone (⌀) — in

Geometric tolerance from blueprint

TP = 2 × √(ΔX² + ΔY²) = 2 × √(0.0030² + 0.0040²) = 2 × 0.0050 = 0.0100 in | Deviation angle: 53.1°

Diametric True Position (⌀TP)

0.0100

in diametric

✓ PASS

Radial Error (from nominal center)

0.0050 in radial

Tolerance Zone Used

100.0% of ∅0.0100 in zone

Common GD&T Tolerance Tiers

Precision tooling: ⌀0.001–0.005"

Standard machined: ⌀0.005–0.020"

Structural/fab: ⌀0.030–0.060"

Practical Example

A CMM inspection report shows a bolt hole that measures 0.003" off in X and 0.004" off in Y from nominal. Using the GD&T formula: TP = 2 × √(0.003² + 0.004²) = 2 × √(0.000009 + 0.000016) = 2 × √0.000025 = 2 × 0.005 = ⌀0.010". If the blueprint calls out a True Position tolerance of ⌀0.010", this part is exactly on the boundary — it passes, but is right at the limit. The part should be flagged for engineering review before acceptance.

Email Link Text/SMS WhatsApp

What is Geometric Dimensioning & Tolerancing: True Position?

True Position is the most critical and widely used positional tolerance in modern manufacturing. Unlike old-school coordinate dimensioning (which creates a square tolerance box), GD&T True Position establishes a perfectly cylindrical tolerance zone. This means a hole is allowed the exact same amount of deviation in a diagonal direction as it is in the pure X or Y directions. This reflects the physical reality of how round pins fit into round holes.

Mathematical Foundation

Diametric True Position

TP = 2 \times \sqrt{\Delta X^2 + \Delta Y^2}

TP

= Diametric True Position — the diameter of the smallest theoretical cylinder, centered on the nominal position, that completely contains the actual axis of the measured feature.

\Delta X

= Deviation from nominal X coordinate (Measured X - Nominal X).

\Delta Y

= Deviation from nominal Y coordinate (Measured Y - Nominal Y).

\times 2

= Crucial factor: The Pythagorean theorem calculates radial deviation. GD&T callouts are almost always diametric (signified by the ⌀ symbol). Multiplying by 2 converts the radius into a diameter.

Laws & Principles

The Bonus Tolerance Myth: Coordinate ± tolerances create a square zone. The corners of that square are further from the center than the flat sides. True position eliminates these corners, creating a uniform circular zone. However, it effectively gives you 57% MORE allowable deviation in the diagonal directions than strict coordinate dimensioning.
The CMM ×2 Trap: Coordinate Measuring Machines (CMMs) naturally report radial deviation (how far the center point missed the target). Engineering drawings specify diametric tolerance zones. You MUST multiply your calculated hypotenuse by 2. Forgetting this means you are accepting parts that are twice as bad as the blueprint allows.
Maximum Material Condition (MMC): If the blueprint callout includes an (M) symbol, you get 'bonus tolerance'. If your hole is drilled larger than its smallest allowable size (its MMC limit), you can add that extra diameter to your allowable True Position zone. A nominally 'failed' hole can actually pass if it was drilled slightly oversized.
Datum Reference Frames: True position is meaningless without datums. The deviations (ΔX and ΔY) must be measured from the exact coordinate system established by the Primary, Secondary, and Tertiary datums called out in the feature control frame.

Step-by-Step Example Walkthrough

" An inspector measures a drilled hole on a CMM. Nominal location is X: 5.000', Y: 3.000'. Actual measured location is X: 5.004', Y: 2.997'. The drawing specifies a positional tolerance of ⌀0.010'. Does it pass? "

1. Calc X deviation: 5.004 - 5.000 = +0.004'.
2. Calc Y deviation: 2.997 - 3.000 = -0.003'.
3. Square the deviations: (0.004)² = 0.000016. (-0.003)² = 0.000009.
4. Add them: 0.000016 + 0.000009 = 0.000025.
5. take Square Root (Radial deviation): √0.000025 = 0.005'.
6. Multiply by 2 for Diameter: 0.005' × 2 = 0.010'.

Final Result: The True Position is exactly 0.010'. Since the tolerance is ⌀0.010', the part PASSES right on the absolute boundary limit. The CNC programmer should adjust their work offset by X-0.004' and Y+0.003' to re-center the process.

Quick Answer: How Do I Calculate GD&T True Position?

Enter your feature's measured X and Y coordinates along with the blueprint's nominal (exact) coordinates. This calculator computes the radial deviation using the Pythagorean theorem, then automatically multiplies it by 2 to output your Diametric True Position. Compare this final output directly to the ⌀ value in your engineering drawing's feature control frame.

Core GD&T Formula

True Position (Diametric)

TP = 2 × √ [ (Measured X - Target X)² + (Measured Y - Target Y)² ]

Always remember the 2× multiplier. The hypotenuse calculates the radius of your error, but GD&T positional callouts are practically always diametrical cylindrical zones.

Real-World Scenarios

✓ The Diagonal Advantage

A machinist cuts a hole that is off by X+0.003" and Y+0.003". Under old-school ±0.003" coordinate dimensioning, this part fails because the corner of the tolerance box has been breached. They beg the engineer to evaluate it under GD&T True Position. The calculation yields TP = 2 × √(0.003² + 0.003²) = 0.0084". The engineer updates the drawing to ⌀0.010" True Position. The part perfectly passes, and a $400 aerospace bracket goes to the customer instead of the scrap bin.

✗ The Sign Conversion Catastrophe

An operator uses a manual edge finder and writes down their offsets. The nominal location is X-1.000". Their measured location is X-1.005". When entering it into a poorly-made spreadsheet tool, they drop the negative signs and input 1.000 and 1.005, getting a 0.010" TP. The drawing allows 0.015", so they approve it. In reality, the hole was at X+1.005". The actual deviation was 2.005 inches. The part arrives at assembly completely backwards and gets scrapped instantly.

Coordinate Error vs True Position Quick Reference

X Deviation	Y Deviation	Radial Error	Diametric True Position
0.001	0.000	0.0010	⌀ 0.0020
0.001	0.001	0.0014	⌀ 0.0028
0.002	0.002	0.0028	⌀ 0.0056
0.003	0.003	0.0042	⌀ 0.0084
0.003	0.004	0.0050	⌀ 0.0100
0.005	0.005	0.0070	⌀ 0.0141
0.010	0.010	0.0141	⌀ 0.0282

Note: To pass a ⌀0.010 true position callout, your combined deviation cannot exceed exactly X:0.003" and Y:0.004" (a 3-4-5 triangle).

Pro Tips & Common Mistakes

Do This

✓Use a Dial Indicator on the machine. Don't wait for CMM results. After drilling a hole, put a coaxial indicator in the spindle, jog to the nominal X/Y coordinates, and sweep the drilled hole. The Total Indicator Reading (TIR) you see on the dial is exactly your Diametric True Position error.
✓Look for MMC modifiers. If your feature block has an (M) symbol, check the hole diameter! If the hole was supposed to be 0.500" ±0.005", and you measured it at 0.504", you get 0.009" of bonus tolerance added to your true position limit. This saves parts.
✓Compensate tool wear before scrapping. If a bolt-hole pattern fails true position identically across all holes, your part datum might be shifted or your spindle has thermal drift. Shift your G54 work offset to bring the entire pattern back to zero.

Avoid This

✗Don't forget the ×2 multiplier! This is the most common reason good parts get scrapped or bad parts get shipped. The equation calculates the distance from the center. GD&T specifies the diameter of the allowable zone. You must double your result.
✗Don't confuse form with location. If a hole is bored at a terrible taper or is severely out-of-round, its True Position might still calculate as perfectly zero if its center of mass is perfectly located. True position does not control the cilindricity of the hole itself.
✗Don't measure from the edge of the part. True Position is measured from the theoretical nominal coordinates established by the Datums. If you just measure the distance from the side of the part with calipers, you are ignoring the established coordinate framework and your measurement is invalid.

Frequently Asked Questions

Why do we multiply by 2?

The Pythagorean theorem (a² + b² = c²) calculates the hypotenuse, which is the distance from the exact target center to your measured center. That distance is a radius. Because GD&T engineering drawings specify True Position as a cylindrical zone (a diameter, marked with a ⌀ symbol), you must multiply that radius by 2 to compare apples to apples.

What does the (M) symbol mean next to the tolerance?

It stands for Maximum Material Condition, a core GD&T concept. It means that the positional tolerance applies when the hole is drilled at its smallest allowable diameter (maximum material left). If you drill the hole slightly larger, the mating pin has more wiggle room to fit. Therefore, you are granted 'bonus tolerance' added directly to your true position limit based on how much larger you drilled the hole.

What if my True Position result is negative?

A diametric True Position result can never be negative. While your X or Y coordinates might be negatively deviated from the target, squaring those deviations during calculation removes the negative signs entirely (a negative times a negative is a positive). The final TP represents a physical zone diameter, which must always be zero or positive.

Can True Position be used for a square slot?

Yes, but it won't be a diametric zone. If True Position is called out on a flat slot or keyway width without the ⌀ symbol, the tolerance zone is a set of two parallel planes rather than a cylinder. The calculation is different: the deviation is evaluated strictly perpendicularly to the feature center plane, without using the Pythagorean theorem.