Engineering Tolerances Calculator — Fits & Limits

Engineering Tolerances, Fits & Limits — A Friendly Primer

In precision manufacturing, two parts rarely measure exactly their nominal size. Instead, drawings specify a basic size plus permitted tolerances, producing a range of acceptable dimensions called limits. For mating parts (a hole and a shaft), these limits determine the fit: whether assembly results in guaranteed clearance, guaranteed interference, or a transition where either outcome is possible. This calculator lets you explore limits and fits either by entering deviations directly (µm) or by using a quick ISO-style helper with IT grades and simple bases (H/h/js).

Key Terms (Plain English)

• Basic size (D): The nominal size from which limits are derived (e.g., 25 mm).
• Deviation: Offset from the basic size. For holes we use \(E_i, E_s\); for shafts \(e_i, e_s\) (in µm).
• Limits: The smallest and largest permissible sizes (e.g., 25.000–25.025 mm).
• Clearance: Hole diameter minus shaft diameter. Positive = “slack”, negative = overlap.
• Fit types: Clearance (always +), Interference (always −), Transition (can be + or −).

How Limits & Fits Are Computed

Deviations are given in micrometres (µm). Converting to millimetres is simply division by 1000. If the basic size is \(D\) (mm), then:

• Hole limits: \(D_\text{hole,min} = D + E_i/1000\),   \(D_\text{hole,max} = D + E_s/1000\).
• Shaft limits: \(D_\text{shaft,min} = D + e_i/1000\),   \(D_\text{shaft,max} = D + e_s/1000\).
• Minimum clearance: \(C_\text{min} = D_\text{hole,min} - D_\text{shaft,max}\).
• Maximum clearance: \(C_\text{max} = D_\text{hole,max} - D_\text{shaft,min}\).

Classification is then straightforward: both clearances > 0 → clearance fit; both < 0 → interference fit; mixed signs → transition fit.

What Are IT Grades?

ISO 286 defines tolerance “grades” (IT5, IT6, … IT10) that scale with size using a tolerance unit \(i\) (µm). A common approximation is: \( i \approx 0.45\,\sqrt[3]{D} + 0.001\,D \) (with \(D\) in mm). Typical grade widths are: IT5 = 7\(i\), IT6 = 10\(i\), IT7 = 16\(i\), IT8 = 25\(i\), IT9 = 40\(i\), IT10 = 64\(i\). Our helper uses these to build simple hole/shaft limits for the popular bases:

• H hole: lower deviation \(E_i = 0\); hole lies entirely above the basic size.
• h shaft: upper deviation \(e_s = 0\); shaft lies entirely below the basic size.
• js shaft: deviations are symmetric about 0 (±IT/2).

Real ISO tables include many more letters (a–zC) with specific fundamental deviations. Use official tables for certification work; this tool is an educational shortcut for quick planning and sanity checks.

Selecting a Fit (Rule-of-Thumb)

• Free sliding: H8/h7 or H9/h9 for general assemblies that must move without binding.
• Location/transition: H7/js6 where some parts may be tight, others loose; alignment prioritized.
• Light press: H7/p6 or H7/k6 for locating with light interference (bearing inner rings on shafts often use k/m).
• Heavy press/shrink: H7/u6 or similar for permanent joints. Thermal methods are common for assembly.

Common Pitfalls (and Easy Fixes)

• Forgetting units: Deviations are in µm, basic size and limits in mm. Convert consistently.
• Mismatched grade severity: A very tight hole with a very loose shaft can yield unpredictable fits. Pair grades sensibly (e.g., H7/h6).
• Ignoring process capability: Choose grades your machining process and metrology can actually hit.
• Skipping function: Rotating parts may need clearance for thermal growth and lubrication; static pins may require interference.

Practical Tips

• Prototype with slightly looser combinations first; tighten once function is proven.
• For bearings, consult the manufacturer’s fit recommendations—load direction and rotation matter.
• Consider environment: temperature swings, corrosion allowance, coatings/plating thickness, and surface finish all influence real fits.

Disclaimer: This primer and calculator provide engineering approximations for education and early planning. For production drawings, QA, or regulated applications, verify with ISO 286 tables and your organization’s standards.