Select a relative-deviation solve task, dimensional limits, or the Goldschmidt factor. Compare dimensions with an optional specification or calculate ionic-radius geometry; the factor alone does not identify a perovskite crystal phase.
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Tolerance Factor Formula
The following formula gives the relative dimensional factor. Select an explicit solve task and enter its known values; nominal size must be positive. Optional allowed tolerance compares the absolute percentage with a symmetric ยฑ limit.
Variables:
- TF is the dimensionless signed relative deviation; percentage deviation is 100 ร TF
- AS is the actual size of the component (mm)
- NS is the nominal size of the component (mm)
To calculate the tolerance factor, subtract the nominal size from the actual size, then divide by the nominal size. The result is a dimensionless signed relative difference. The calculator leads with 100 ร TF as a percentage and shows TF separately. Convert actual and nominal sizes to the same unit before subtracting.
What is a Tolerance Factor?
A tolerance factor is a numerical value that represents the deviation of an actual measured size from its nominal size, relative to the nominal size itself. It is a critical measure in quality control and manufacturing processes to ensure that parts meet specified tolerances and fit together properly in assemblies.
How to Calculate Tolerance Factor?
The following steps outline how to calculate the Tolerance Factor.
- First, determine the nominal size of the component (NS) in millimeters.
- Next, measure the actual size of the component (AS) in millimeters.
- Use the formula TF = (AS - NS) / NS to calculate the tolerance factor.
- Finally, compare the calculated tolerance factor with the acceptable tolerance range for the component.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Nominal size of the component (NS) = 50 mm
Actual size of the component (AS) = 50.05 mm. Then TF = 0.001 and the signed deviation is 0.1%.
For dimensional limits, lower = nominal โ minus tolerance and upper = nominal + plus tolerance. Blank tolerance magnitudes mean zero; blank actual size omits pass/fail. Limits are inclusive and negative physical-size limits are rejected.
For ABXโ ionic-radius geometry, t = (rA + rX) / [โ2(rB + rX)] and ฮผ = rB/rX. Enter positive radii appropriate to the ion, oxidation state and coordination; 1 ร = 100 pm. These are geometric descriptors, not reliable standalone predictions of phase, symmetry or thermodynamic stability. Primary research explains these limits.
