Tolerance stack up analysis calculation is done to find out essentially the deviation of gap of the surfaces between two specified parts.

**How?**

Following steps shows how to do the tolerance stack up analysis for absolute tolerance system or worst case method. The steps explained will be clearer when we will go through the example at later part of this tutorial.

**Step-1: Dimension Chain**

Find the dimensions chain describing the gap you are interested on.

**Step-2: Gap Nominal Value Calculation**

For calculating the nominal value of the gap, you have to start from one end of the gap and keep adding dimensions of the dimension chain considering the direction towards which you are going. If you consider **+ve **for going towards right then have to consider **–ve** while going left.

**Step-3: Gap Tolerance Calculation**

Sum up all the tolerance values of all the dimensions without considering the sign to get the tolerance range of the gap.

**Solved Example**

**Problem: **The bolt shown in the picture below contains four sleeves and a nuts. The necessary dimensions are as below:

V=6±0.06 mm

W=1.10±0.02 mm

X=1.25±0.03 mm

Y=1.40±0.04 mm

Z=1.25±0.01 mm

Calculate nominal, max and min value of the gap between the points **A **and **B**.

**Solution:**

**Step-1:**

The dimension chain surrounding the gap starts from the point **A **and go through the dimensions **Z , Y, X, W, V** and ends at point **B.**

**Step-2:**

Nominal value of the gap,

**G= -Z-Y-X-W+V = -1.10 – 1.25 – 1.40 – 1.25 + 6 = 1 mm**

**Step-3:**

Gap tolerance,

**t = 0.01 + 0.04 + 0.03 + 0.02 + 0.06 = 0.16 mm**

Overall dimension of the gap = **1 ±0.16 mm**

The maximum dimension of the gap,

**Gmax = G + t = 1 + 0.16 = 1.16 mm**

The minimum dimension of the gap,

**Gmin = G – t = 1 – 0.16 = 0.84 mm**

The tolerance stack up calculation procedure shown above is the simplest one, more sophisticated methods are: standard deviation method and monte carlo simulation.