What is the true position?
Type the basic X and Y from the drawing, the measured centre, and the position tolerance. The true position calculator gives the position deviation as a diameter, adds any bonus tolerance at MMC, and says pass or fail.
- True position
- 0.01 in
The true position is 0.01 in: Pass against an allowed 0.01 in.
- Result
- Pass
- Allowed tolerance
- 0.01 in
- Bonus tolerance
- 0 in
- Margin
- 0 in
- X deviation (dx)
- 0.003 in
- Y deviation (dy)
- -0.004 in
- Radial distance
- 0.005 in
True position: 0.01 in. The true position is 0.01 in: Pass against an allowed 0.01 in.
How to calculate
True position calculator for GD&T: the position deviation 2 × √(dx² + dy²) of a hole or pin from its basic location, with the bonus tolerance at MMC and a pass or fail against the position tolerance.
Example with the default inputs (Basic X 1 in, Basic Y 1 in, Measured X 1.003 in, Measured Y 0.996 in, Position tolerance 0.01 in, Material condition RFS): The true position is 0.01 in: Pass against an allowed 0.01 in.
Method: dx = measured X − basic X; dy = measured Y − basic Y; true position = 2 × √(dx² + dy²). Allowed = tolerance + bonus, with bonus = measured − MMC size (hole) or MMC size − measured (pin) at MMC, and 0 at RFS. Pass when true position ≤ allowed.
- A 2D position of a round feature with a diameter (⌀) tolerance zone; the datums set the basic X and Y.
- The measured size is within the size limits; a hole below MMC or a pin above MMC has no answer.
Worked examples
Each example is checked against the calculator on every build.
- Basic X 1 in, Basic Y 1 in, Measured X 1.003 in, Measured Y 0.996 in, Position tolerance 0.01 in, Material condition RFS gives True position 0.01 in, Result Pass, Margin 0 in, Radial distance 0.005 in.Source: GD&T Basics, True Position – Position Tolerance (position = 2 × √(dx² + dy²); bonus tolerance = measured hole size − MMC hole size), https://www.gdandtbasics.com/true-position/ (retrieved 2026-10-05)
- Basic X 1 in, Basic Y 1 in, Measured X 1.003 in, Measured Y 0.996 in, Position tolerance 0.008 in, Material condition MMC hole, MMC size 0.25 in, Measured size 0.254 in gives True position 0.01 in, Bonus tolerance 0.004 in, Allowed tolerance 0.012 in, Result Pass.Source: GD&T Basics, True Position – Position Tolerance (position = 2 × √(dx² + dy²); bonus tolerance = measured hole size − MMC hole size), https://www.gdandtbasics.com/true-position/ (retrieved 2026-10-05)
- Basic X 1.969 in, Basic Y 0.7874 in, Measured X 1.972 in, Measured Y 0.7913 in, Position tolerance 0.007874 in, Material condition MMC pin, MMC size 0.3937 in, Measured size 0.3917 in gives True position 0.0111 in, Bonus tolerance 0.002 in, Allowed tolerance 0.0098 in, Result Fail.Source: GD&T Basics, True Position – Position Tolerance (position = 2 × √(dx² + dy²); bonus tolerance = measured hole size − MMC hole size), https://www.gdandtbasics.com/true-position/ (retrieved 2026-10-05) (for a pin the bonus is MMC − measured size)
How it works
- Deviations dx = measured X − basic X; dy = measured Y − basic Y.
- Radial distance r = √(dx² + dy²).
- True position = 2 × r, a diameter.
- Bonus tolerance at RFS is 0. At MMC on a hole it is measured size − MMC size; on a pin, MMC size − measured size.
- Allowed tolerance = position tolerance + bonus.
- Result Pass when true position ≤ allowed tolerance, else Fail. The check is done exactly as 4 × (dx² + dy²) ≤ allowed².
- Margin = allowed − true position; negative on a fail.
Rules
- Coordinates from −10 m to 10 m; the tolerance, MMC size and measured size more than 0 and at most 10 m; type them in inches or millimetres (1 in = 25.4 mm exactly).
- A hole measured below its MMC size, or a pin above it, is outside its size limits and has no answer.
Output format
Every output is a length to 4 decimal places, in inches (US) or millimetres (Metric). Typed values are read back as exact decimals; dx, dy, the bonus and the allowed tolerance are exact, and the square root is exact when dx² + dy² is a square of a decimal (a float otherwise). Each value is rounded once.
Worked examples by hand
RFS, on the edge. Basic (1, 1) in, measured (1.003, 0.996) in: dx = 0.003, dy = −0.004, r = √(0.000009 + 0.000016) = 0.005 in, true position 0.010 in. Tolerance 0.010 in: 4 × 0.000025 = 0.0001 ≤ 0.010² = 0.0001, so it passes with a margin of 0.
A hole at MMC. The same hole with a 0.008 in tolerance at MMC, MMC size 0.250 in, measured 0.254 in: bonus 0.004 in, allowed 0.012 in, true position 0.010 in, pass, margin 0.002 in.
A pin at MMC. Basic (50, 20) mm, measured (50.1, 20.1) mm, tolerance 0.2 mm at MMC, MMC size 10 mm, measured 9.95 mm: true position 2 × √(0.01 + 0.01) = 0.28284 mm; bonus 0.05 mm, allowed 0.25 mm, so it fails by 0.03284 mm.
Other questions people ask
How do you calculate true position?
Find how far the measured centre is from the basic position in X and Y, then double the straight-line distance: true position = 2 × √(dx² + dy²). With dx = 0.003 in and dy = −0.004 in, it is 2 × 0.005 = 0.010 in.
Why is true position multiplied by 2?
The position tolerance is the diameter of a circle centred on the basic position. √(dx² + dy²) is a radius, so doubling it gives a diameter you can compare with the tolerance directly.
What is bonus tolerance?
When the position tolerance has the MMC modifier (Ⓜ), the feature gains extra tolerance as it departs from its maximum material size. For a hole the bonus is measured size − MMC size; for a pin it is MMC size − measured size.
What is MMC for a hole and for a pin?
Maximum material condition is the size with the most material left on the part: the smallest allowed hole, or the largest allowed pin.
Does a true position equal to the tolerance pass?
Yes. The feature passes when its true position is at most the allowed tolerance, so a position equal to the tolerance is on the edge of the zone and passes.
What does RFS mean?
Regardless of feature size: no material modifier, so there is no bonus and the tolerance stays the same at any size within the limits.