---
title: "Limits, fits and tolerance calculation"
subject: "Manufacturing and Production Processes"
chapter: 3
key: "semester_4/manufacturing_and_production_processes:limits-fits-tolerance-numerical"
source: https://www.bctengineer.com/q/semester_4/manufacturing_and_production_processes/limits-fits-tolerance-numerical
site: BCT Engineering
---

# Limits, fits and tolerance calculation

Manufacturing and Production Processes · Chapter 3: Properties of Manufactured Products

- Asked in: year not given, 3+5 marks
- Video: [LIMITS FITS AND TOLERANCES: What is limit fit & tolerance and its need? Animation](https://www.youtube.com/watch?v=joBy4BoJszo) — ADTW Study
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/manufacturing_and_production_processes/limits-fits-tolerance-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_4/manufacturing_and_production_processes/chapter-3

## Question

(a) Differentiate between unilateral and bilateral tolerance, and explain geometric tolerance with any four characteristic symbols. (b) A hole is dimensioned $\phi 40^{+0.039}_{0}$ mm. Three shafts are available: (i) $\phi 40^{-0.025}_{-0.050}$, (ii) $\phi 40^{+0.059}_{+0.043}$, (iii) $\phi 40^{+0.042}_{+0.026}$. For each, find the maximum and minimum clearance (or interference) and state the type of fit.

## Short answer

Unilateral tolerance varies only one way from basic size; bilateral varies both sides. Geometric tolerance controls form, orientation, location or run-out, with symbols such as straightness, flatness, parallelism and position. For hole 40+0.039/0: shaft (i) clearance fit, clearances 0.025-0.089 mm; shaft (ii) interference fit, interferences 0.004-0.059 mm; shaft (iii) transition fit, 0.013 mm clearance to 0.042 mm interference.

## Answer

#### (a) Unilateral and bilateral tolerance; geometric tolerance

| Point | Unilateral | Bilateral |
|---|---|---|
| Variation | In one direction only from basic size | On both sides of basic size |
| Example | $40^{+0.04}_{0}$ | $40 \pm 0.02$ |
| Use | Hole basis / shaft basis systems, easy fits | Positioning, centre distances |

**Geometric tolerance** limits the form, orientation, location and run-out of a feature, not just its size. It is given in a feature control frame on the drawing. Characteristic symbols:

- Straightness (a straight line) and flatness (a parallelogram) - form.
- Parallelism (two parallel lines) and perpendicularity (a right-angle) - orientation.
- Concentricity (two circles) and position - location.
- Circular run-out (arrow) - run-out.

#### (b) Fit calculation

Hole: maximum size $= 40.039$ mm, minimum size $= 40.000$ mm.

Maximum clearance $= $ hole max $-$ shaft min; minimum clearance $= $ hole min $-$ shaft max (negative value = interference).

**Shaft (i):** shaft max $= 39.975$, min $= 39.950$

$$
C_{max} = 40.039 - 39.950 = 0.089\ \text{mm},\qquad C_{min} = 40.000 - 39.975 = 0.025\ \text{mm}
$$

Both positive, so it is a **clearance fit** (running fit).

**Shaft (ii):** shaft max $= 40.059$, min $= 40.043$

$$
C_{max} = 40.039 - 40.043 = -0.004\ \text{mm},\qquad C_{min} = 40.000 - 40.059 = -0.059\ \text{mm}
$$

Both negative, so maximum interference $= 0.059$ mm and minimum interference $= 0.004$ mm: an **interference (press) fit**.

**Shaft (iii):** shaft max $= 40.042$, min $= 40.026$

$$
C_{max} = 40.039 - 40.026 = 0.013\ \text{mm},\qquad C_{min} = 40.000 - 40.042 = -0.042\ \text{mm}
$$

The result can be clearance or interference, so it is a **transition fit**.

| Shaft | Max clearance (mm) | Min clearance (mm) | Fit |
|---|---|---|---|
| (i) | 0.089 | 0.025 | Clearance |
| (ii) | $-0.004$ | $-0.059$ | Interference |
| (iii) | 0.013 | $-0.042$ | Transition |

**Answer:** (i) clearance fit, 0.089 to 0.025 mm; (ii) interference fit, 0.004 to 0.059 mm; (iii) transition fit, 0.013 mm clearance to 0.042 mm interference.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is a bilateral tolerance?
   A. 40 +0.04/0
   B. 40 +0.00/-0.04
   C. 40 +/- 0.02
   D. 40 +0.04/+0.02 only
   Answer: C. A bilateral tolerance varies on both sides of the basic size, as in 40 +/- 0.02; unilateral varies in one direction only. (Key point: Unilateral vs bilateral tolerance)

2. How are maximum and minimum clearance calculated?
   A. Max = hole max - shaft min; min = hole min - shaft max
   B. Max = hole max - shaft max; min = hole min - shaft min
   C. Max = shaft max - hole min; min = shaft min - hole max
   D. Max = hole min - shaft min
   Answer: A. Maximum clearance uses the largest hole and smallest shaft; minimum uses smallest hole and largest shaft; negative means interference. (Key point: Max clearance formula)

3. For shaft (i) (39.950 to 39.975) with the hole 40.000 to 40.039, the clearances and fit are
   A. 0.089 and 0.025 mm; clearance fit
   B. 0.064 and 0.025 mm; transition fit
   C. -0.004 and -0.059 mm; interference fit
   D. 0.089 and -0.025 mm; transition fit
   Answer: A. 40.039 - 39.950 = 0.089 and 40.000 - 39.975 = 0.025, both positive, so clearance fit. (Key point: Shaft (i) clearance fit)

4. Shaft (iii) gives C_max = +0.013 mm and C_min = -0.042 mm. The fit is
   A. Clearance
   B. Interference
   C. Transition
   D. Running
   Answer: C. When the result can be either clearance or interference, the fit is a transition fit. (Key point: Transition fit)

## Related in Manufacturing and Production Processes

- [Blanking force, clearance and die sizes](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Ablanking-punching-force-clearance-numerical) — Manufacturing and Production Processes, chapter 6

## Related in other subjects

- [Limits of a 40 H7/g6 hole-shaft fit](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Afit-40-h7-g6-calculation) — Metrology, chapter 9
- [Unilateral and bilateral tolerance conversion](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Aunilateral-bilateral-tolerance) — Metrology, chapter 9
- [Assembly constraints and tolerance fit calculation](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Aassembly-constraints-tolerance-fit) — Computer Aided Design, chapter 5
- [Clearance, transition and interference fits](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Atypes-of-fits-with-examples) — Metrology, chapter 9