Bilateral and Unilateral Tolerance Converter
A drawing may call out 50.00 +0.05 / -0.02 while the shop works to 50.015 +/-0.035. This converter does the arithmetic, shows the limits and estimates why programming to the middle of the band gives more good parts than aiming at nominal.
Your numbers
Enter as a positive number.
Enter as a positive number, for example 0.02 for a -0.02 callout.
Used only to estimate yield when aiming at the mid-limit.
Your results
Yield figures are normal-distribution estimates for planning, not a substitute for a capability study on real data.
Yield centered on mid-limit vs process spread
Sweeps Expected process spread (1 sigma) from 0.002 to 0.03, holding your other inputs fixed.
Put target dimensions into your routings
Optional: a short note on carrying mid-limit targets from drawings into ERP routings and inspection plans.
Optional. The tool and every export work without this. No spam.
How to use it
Enter the nominal size and the plus and minus values as positive numbers. A unilateral tolerance such as +0.05 / -0 is entered with a minus value of zero. The tool returns upper and lower limits, the mid-limit and the equal bilateral tolerance around that mid-limit. Add your expected process standard deviation to compare the yield when you aim at nominal with the yield when you aim at the mid-limit. The chart sweeps process spread so you can see how quickly an off-center target loses parts.
The arithmetic
Upper limit is nominal plus the plus tolerance and lower limit is nominal minus the minus tolerance. The mid-limit is the average of the two and the equal bilateral tolerance is half the band. Programming to the mid-limit puts the process in the middle of the allowable band, which maximizes yield for a centered process. The yield estimate uses the standard normal distribution on the distance from the target to each limit divided by sigma.
- Example: 50 +0.05 / -0.02 gives limits 50.05 and 49.98
- Mid-limit 50.015, equal bilateral +/-0.035
- Unilateral limits shift the ideal target away from nominal
Practical notes and mistakes
Do not change the drawing just because the shop programs to the mid-limit, the drawing limits still govern acceptance. Tool wear tends to move size in one direction, so many shops bias the target slightly toward the side that wear moves away from. A common error is entering the minus tolerance with a negative sign, which doubles the sign and gives wrong limits. Another is applying the mid-limit method to a feature where one limit is a hard functional boundary, such as an interference fit, where you may deliberately aim away from that limit.
Frequently Asked Questions
What is a unilateral tolerance?
A unilateral tolerance allows variation in one direction only from the nominal, for example +0.05 / -0.00. A bilateral tolerance allows variation in both directions. Unequal bilateral tolerances like +0.05 / -0.02 are common and are converted here to an equal form.
Why program to the mid-limit?
Because a process centered in the allowable band produces the fewest out-of-tolerance parts. Aiming at nominal when the band is asymmetric wastes part of the band and increases scrap.
Does converting change what the drawing allows?
No. The limits of size are identical, only the way they are expressed changes. Inspection still accepts parts between the original lower and upper limits.
How is the yield estimated?
The tool assumes a normal distribution with the given standard deviation and a perfectly centered process at the chosen target, then calculates the probability that a part lands between the limits. Real processes drift, so treat it as an optimistic planning number.
If you need drawing tolerances and target values flowing into routings or inspection plans in your ERP, Netray can help scope that integration.
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