# Bilateral and Unilateral Tolerance Converter

> Source: https://netray.co/tools/bilateral-unilateral-tolerance-converter-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Turn any plus/minus tolerance, even an unequal or one-sided one, into upper and lower limits, a mid-limit target and an equal bilateral equivalent that CNC programmers can aim at.

## Category

engineering-plm

## Industry

Discrete Manufacturing

## Audience

- Design engineer
- CNC programmer
- Quality engineer
- Machinist

## Tool

**Kind:** calculator

**Inputs:**

#### Nominal dimension

**Key:** nominal

**Type:** number

**Default:** 50

**Step:** 0.01

**Unit:** mm

#### Plus tolerance

**Key:** plus_tol

**Type:** number

**Default:** 0.05

**Min:** 0

**Step:** 0.005

**Unit:** mm

**Help:** Enter as a positive number.

#### Minus tolerance

**Key:** minus_tol

**Type:** number

**Default:** 0.02

**Min:** 0

**Step:** 0.005

**Unit:** mm

**Help:** Enter as a positive number, for example 0.02 for a -0.02 callout.

#### Expected process spread (1 sigma)

**Key:** std_dev

**Type:** number

**Default:** 0.008

**Min:** 0

**Step:** 0.001

**Unit:** mm

**Help:** Used only to estimate yield when aiming at the mid-limit.

**Outputs:**

#### Upper limit

**Key:** upper

**Expr:** nominal + plus_tol

**Format:** decimal

#### Lower limit

**Key:** lower

**Expr:** nominal - minus_tol

**Format:** decimal

#### Mid-limit target (program to this)

**Key:** mid

**Expr:** (upper + lower) / 2

**Format:** decimal

**Primary:** true

#### Equal bilateral tolerance about mid-limit (+/-)

**Key:** sym

**Expr:** (upper - lower) / 2

**Format:** decimal

**Primary:** true

#### Total tolerance band

**Key:** band

**Expr:** upper - lower

**Format:** decimal

#### Estimated yield if centered on mid-limit

**Key:** yield_mid

**Expr:** if(gt(std_dev, 0), (normsdist(sym / std_dev) - normsdist(0 - sym / std_dev)) * 100, 100)

**Format:** percent

**Description:** Assumes a normal distribution and no drift.

#### Estimated yield if centered on nominal

**Key:** yield_nom

**Expr:** if(gt(std_dev, 0), (normsdist((upper - nominal) / std_dev) - normsdist((lower - nominal) / std_dev)) * 100, 100)

**Format:** percent

**Chart:**

#### Yield centered on mid-limit vs process spread

**Type:** line

**X:** std_dev

**From:** 0.002

**To:** 0.03

**Steps:** 15

**Series:**

- yield_mid
- yield_nom

**Disclaimer:** Yield figures are normal-distribution estimates for planning, not a substitute for a capability study on real data.

## Content

**Intro:** 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.

**Sections:**

#### How to use it

**Body:** 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

**Body:** 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.

**Bullets:**

- 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

**Body:** 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.

**Cta:** If you need drawing tolerances and target values flowing into routings or inspection plans in your ERP, Netray can help scope that integration.

**Faq:**

#### What is a unilateral tolerance?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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.

## Search terms

bilateral tolerance calculator, unilateral tolerance converter, convert unequal tolerance to equal bilateral, mid tolerance dimension, tolerance limits calculator, plus minus tolerance calculator, cnc target dimension mid tolerance, limit dimensions from tolerance

---
Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json