2026-07-30 8 min

Hole Tolerance Calculator

Calculate hole tolerances per ISO 286 standards. Determine upper and lower deviations, IT grades, GO and NO-GO diameters for hole features.

Calculator

Unit System

Nominal Size (mm)

Hole Type

IT Grade

Deviation Mode

Results

Normal

Tolerance (IT value)

27.3250mm

Total tolerance zone width for the hole

Upper Deviation (ES)

27.3250mm

Upper deviation from nominal (ES for internal features)

Lower Deviation (EI)

0.0000mm

Lower deviation from nominal (EI for internal features)

GO Diameter (MMC)

50.0000mm

GO gauge limit - smallest acceptable hole diameter

NO-GO Diameter (LMC)

77.3250mm

NO-GO gauge limit - largest acceptable hole diameter

IT Grade

IT7

ISO tolerance grade for the hole

Tolerance Unit (i)

1.708mm

Standard tolerance unit i per ISO 286

Visualizations

Results Overview

27.3mmTolerance

27.3mmUpper Deviation

50mmGO Diameter

77.3mmNO-GO Diameter

7mmIT Grade

1.7mmTolerance Unit

Formula

ISO 286 defines the standard tolerance system for holes based on geometric mean diameter and the tolerance unit i. The fundamental deviation determines the position of the tolerance zone relative to the nominal size.

D = sqrt(0.5×N × 2×N), i = 0.45×∛D + 0.001×D, IT7 = 16×i, EI = deviation table, ES = EI + ITn

Alternative Form

For hole H7: EI = 0, ES = +IT7. For hole K7: EI = -IT7, ES = 0.

Variables

Symbol	Name	Unit	Description
D	Geometric Mean	mm	Geometric mean of the diameter range limits
i	Tolerance Unit	mm	Standard tolerance unit per ISO 286
ITn	IT Grade Tolerance	mm	Tolerance value for the specified IT grade
EI	Lower Deviation	mm	Lower deviation (fundamental deviation for holes)
ES	Upper Deviation	mm	Upper deviation (lower deviation + tolerance)

Explanation

ISO 286 provides a systematic framework for assigning tolerances to hole features. The tolerance unit i accounts for the non-linear relationship between diameter size and achievable manufacturing precision. Higher IT grades (lower numbers) give tighter tolerances.

Derivation

The tolerance unit i = 0.45×∛D + 0.001×D is derived from empirical manufacturing data. The multiplier for each IT grade follows the Renard series (R5/R10) to provide geometrically progressive tolerance values.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Calculate geometric mean of the diameter range.

Nominal Size:50.0000 mm

Result: D = sqrt(min_range × max_range) = 50.000 mm

Step 2

Compute standard tolerance unit i.

i = 0.45 × ∛D + 0.001 × D

Geometric Mean D:50.000 mm

Result: i = 1.708 mm

Step 3

Apply tolerance grade multiplier and hole type deviation.

ITn = multiplier × i, EI = deviation table, ES = EI + ITn

IT Grade:IT7

Hole Type:H

Intermediate: Upper Dev (ES) = 27.3250 mm, Lower Dev (EI) = 0.0000 mm

Result: GO = 50.0000 mm, NO-GO = 77.3250 mm

Final Answer

27.3250

Worked Examples

See how the calculator works with different scenarios.

Scenario

A 50 mm hole with H7 tolerance. H gives zero lower deviation (EI=0). IT7 tolerance is applied.

Inputs

Nominal:50 mm

Type:H

Grade:IT7

Calculation

D = sqrt(30 × 100) = 54.77 mm i = 0.45×∛54.77 + 0.001×54.77 = 1.72 + 0.055 = 1.78 μm IT7 = 16 × 1.78 = 28.4 μm ≈ 0.028 mm

Result

Upper Deviation = +0.028 mm, Lower Deviation = 0, GO = 50.000 mm, NO-GO = 50.028 mm

Interpretation

H7 is the most common hole tolerance for general engineering. The GO gauge checks the minimum diameter (50.000 mm) and the NO-GO checks the maximum (50.028 mm).

Understanding Your Result

Your Result: Tolerance (IT value): 27.3250 mm

Typical range: IT5-IT6: Precision fits (bearings, instruments). IT7-IT8: General engineering (most common). IT9-IT11: Wide tolerances (coarse work). IT12+: Rough/clearance applications.

What This Means

Hole tolerance per ISO 286 defines the acceptable range of hole diameters based on the nominal size and the required fit type. Holes are designated by a letter (deviation position) and an IT grade number.

Why It Matters

Proper hole tolerance selection ensures correct assembly characteristics (clearance, transition, or interference) with mating shafts. The ISO 286 system provides international standardization for interchangeable manufacturing.

Professional Interpretation

H7 is the default hole tolerance for general engineering (80% of applications). The hole-basis system (H) is preferred because holes are harder to produce than shafts of equivalent tolerance.

Recommendations

•Use H7 as the default hole tolerance for general engineering applications
•Select H6 for precision bearing seats and critical alignment features
•Use H8 or H9 for sliding fits and clearance applications
•Apply P, S, or U holes for interference fits with appropriate shaft tolerances
•Consider manufacturing capability when selecting IT grades
•Verify fit calculations with the corresponding shaft tolerance simultaneously

Educational Content

Introduction

ISO 286 is the international standard for limits and fits in mechanical engineering. The hole basis system uses the letter H to represent zero fundamental deviation, with other letters (J through U) providing progressively more negative deviations.

Concept Explanation

The tolerance is a function of the nominal diameter. Smaller diameters can be manufactured to tighter absolute tolerances. The tolerance unit i normalizes tolerance values across the diameter range. IT grades follow a geometric progression (Renard series) for systematic tolerance selection.

Applications

▸Bearing housing bores (typically H6 or H7)

▸Cylinder bores for hydraulic/pneumatic systems (H7-H9)

▸Slideway guides and linear bearing mounts (H7-H8)

▸Pin and bushing holes for linkages (H7)

▸Die and mold insert cavities (H6-H7)

▸Valve body bores for spool fit (H6-H8)

▸Gear box housing bearing seats (H7)

Benefits

•Internationally standardized system for interchangeability
•Systematic tolerance selection based on diameter and function
•Hole-basis system simplifies shaft manufacturing (turn down)
•Clearance, transition, and interference fits available
•Comprehensive tables cover diameters from 1 mm to 500 mm
•Compatible with ISO 2768 general tolerances

Limitations

•Does not cover geometric tolerances (requires ISO 1101)
•May not be optimal for non-cylindrical features
•Standard tolerance values are for general manufacturing
•Does not consider material properties or thermal effects
•Very large diameters have limited ISO 286 coverage

Best Practices

•Always use hole-basis system (H) unless shaft-basis is specifically required
•Select IT grade based on functional requirements and manufacturing capability
•Reference ISO 286 tables for exact values at nominal diameters
•Consider using H7/g6 for clearance fits and H7/p6 for interference fits
•Document tolerance selections on drawings with clear ISO references
•Train designers on proper fit selection for manufacturing

Common Misconceptions

Myth: A smaller IT number always means higher cost.

Truth: While IT5 and IT6 are more expensive than IT7-IT8, the cost increase for IT7 vs IT8 is minimal. Select the tightest feasible grade for function.

Myth: The hole basis system is always preferred.

Truth: Shaft-basis is preferred when using standard shafts (e.g., drawn shafting) or when multiple components fit on a single shaft.

Myth: ISO 286 covers all sizes and tolerances.

Truth: ISO 286 primarily covers diameters from 1-500 mm. For larger or smaller sizes, special tolerance calculations or other standards apply.

Practical Tips

•Use H7 as the default starting point for most general engineering holes
•For sliding fits with lubrication, consider H7/f7 or H8/f8
•Transition fits (H7/k6, H7/m6) provide light interference for moderate locating
•Interference fits (H7/p6, H7/s6) require significant press force for assembly
•Verify surface finish requirements - tighter tolerances require finer finishes
•Consider using H6 for ball bearing seats and H9 for non-critical sliders
•Document the complete fit designation (e.g., 50H7/g6) on assembly drawings

Common Mistakes

Selecting too tight a tolerance for the application

Use the loosest tolerance that meets functional requirements to reduce manufacturing cost and scrap rates.

Confusing hole and shaft deviation signs

For holes: positive deviations increase the hole size. For shafts: negative deviations decrease the shaft size.

Ignoring tolerance accumulation in assemblies

Perform tolerance stack analysis to ensure the total assembly tolerance meets functional requirements.

Using IT grades inconsistently between hole and shaft

Aim for about 1-2 IT grades difference between hole and shaft (e.g., H7 hole with g6 shaft for precision clearance fits).

Assumptions

This calculator makes the following assumptions to provide estimates:

ISO 286 Defaults: Deviations are calculated per ISO 286 standard tables. Actual values may vary slightly from official ISO tables due to rounding.

Temperature at 20°C: All dimensions are referenced to 20°C per ISO 1. Actual dimensions at other temperatures require thermal expansion compensation.

Cylindrical Features: The calculator assumes round cylindrical holes. Non-circular holes or complex profiles require different tolerance analysis.

Standard Diameter Ranges: Nominal diameters are assumed to fall within standard ISO 286 size ranges (1-500 mm).

Limitations

Be aware of these limitations when using this calculator:

Simplified Deviation Tables: The calculator uses approximate deviation values. Consult official ISO 286 tables for exact values, especially at size range boundaries.

No Geometric Tolerance: This calculator covers only size tolerance. Geometric tolerances (position, concentricity, etc.) require separate analysis per ISO 1101.

Limited Hole Types: Only common hole types (H, J, K, M, N, P, S, U) are implemented. Special deviations like A-G and V-ZC require additional tables.

Single Range Only: For diameters near the boundaries of ISO size ranges (e.g., 30 mm, 50 mm, 80 mm), confirm the correct range limits against ISO tables.

Frequently Asked Questions

Answers to common questions about this calculator.

What is ISO 286?

ISO 286 is the international standard for limits and fits in mechanical engineering. It defines tolerance grades (IT5-IT18) and fundamental deviations for holes and shafts.

What does H7 mean?

H7 is an ISO hole tolerance: H = zero fundamental deviation (lower deviation = 0), 7 = IT grade 7. It is the most common hole tolerance for general engineering.

What is the hole basis system?

In the hole basis system, the hole tolerance is fixed (usually H) and the shaft tolerance is varied to achieve the desired fit. This is preferred because holes are harder to produce.

What is the difference between H7 and H8?

H8 has a wider tolerance than H7 (IT8 = 25×i vs IT7 = 16×i). H7 is used for medium precision, H8 for sliding fits with more clearance.

How is the tolerance unit i calculated?

i = 0.45 × ∛D + 0.001 × D, where D is the geometric mean of the diameter range limits. i is in microns.

What is the geometric mean diameter?

The geometric mean D = sqrt(d_lower × d_upper), where d_lower and d_upper are the limits of the ISO size range containing the nominal diameter.

What are the common H fits and their applications?

H6: Precision bearing seats. H7: General engineering. H8: Sliding fits. H9: Wide clearance. H11: Coarse tolerances for casting/forging.

What is the difference between H7 and H6?

H6 (IT6 = 10×i) is about 60% of the H7 tolerance (IT7 = 16×i). H6 is used for precision fits like ball bearing inner rings.

What hole types are available?

H (zero deviation), J (transition), K (transition), M (transition/interference), N (light interference), P (interference), S (heavy interference), U (very heavy interference).

What is the purpose of fundamental deviations?

Fundamental deviations (letters A-ZC) position the tolerance zone relative to the nominal size. This determines whether a fit is clearance, transition, or interference.

How do I choose the right hole tolerance?

Start with H7 for general use. Use H6 for precision, H8 for loose fits, and H11 for rough work. Select deviation letter based on desired fit type with the mating shaft.

What is the GO gauge for a hole?

The GO gauge for a hole checks the minimum acceptable diameter (MMC). It should enter the hole freely. For an H7 hole, GO = nominal + lower deviation.

What is the NO-GO gauge for a hole?

The NO-GO gauge checks the maximum acceptable diameter (LMC). It should NOT enter the hole. For an H7 hole, NO-GO = nominal + upper deviation.

What is the relationship between IT grade and manufacturing cost?

Tighter IT grades (IT5-IT6) can increase manufacturing cost by 50-200% compared to IT7-IT8 due to the need for grinding and specialized processes.

Can I use both hole and shaft basis in one assembly?

Yes, but it is recommended to standardize on one basis. Most engineering drawings use the hole basis system (H) for consistency.

What is the tolerance for a 50H7 hole?

Approximately 0.025 mm (25 microns) for a 50 mm diameter. The exact value depends on the ISO size range for 50 mm.

How does surface finish affect hole tolerance?

Surface roughness reduces the effective diameter for fit calculation. As a rule of thumb, surface finish should be 1/10 of the tolerance or better.

What is the difference between IT and ISO tolerance?

IT (International Tolerance) grades are the tolerance values defined by ISO 286. IT5 through IT18 cover from very fine to very coarse tolerances.

What is the standard temperature for ISO 286?

The reference temperature is 20°C (68°F) per ISO 1. All dimensions and tolerances are defined at this temperature.

How do I specify a hole tolerance on a drawing?

Write the nominal size followed by the ISO tolerance: e.g., 50H7 means a 50 mm hole with H7 tolerance. The shaft fit would be shown as 50H7/g6 for an assembly.

What is a transition fit?

A transition fit can produce either a clearance or light interference depending on actual sizes. Examples: H7/k6, H7/m6, H7/n6.

What is a clearance fit?

A clearance fit always provides a gap between the hole and shaft. Common examples: H7/g6 (close running), H7/f7 (normal running), H8/e8 (easy running).

What is an interference fit?

An interference fit always requires force to assemble. Examples: H7/p6 (press fit), H7/s6 (heavy press), H7/u6 (permanent assembly).

What is the ISO size range for a 50 mm diameter?

50 mm falls in the 30-50 mm range (for IT grades) or the 50-80 mm range (for some deviation calculations). Always check the specific range in ISO 286 tables.

How do I calculate fit tolerance?

Fit tolerance = hole tolerance + shaft tolerance. The maximum clearance = hole max - shaft min. The minimum clearance = hole min - shaft max.

What is the difference between unilateral and bilateral tolerance?

Unilateral tolerance extends in one direction from nominal (e.g., H7: +0.025/0). Bilateral tolerance extends both ways (e.g., ±0.0125 mm).

What are ISO general tolerances (ISO 2768)?

ISO 2768 defines general tolerances for linear and angular dimensions when specific tolerances are not individually assigned on the drawing.

How does material affect tolerance capability?

Material hardness, stability, and machinability affect achievable tolerances. Hardened steel can hold tighter tolerances than aluminum or plastic.

What is the difference between IT grades for holes vs shafts?

IT grades are the same for both holes and shafts, but the deviation letters differ. Holes use uppercase (H7), shafts use lowercase (g6).

Can I interpolate ISO 286 values for intermediate sizes?

Yes, linear interpolation between ISO size range boundaries is acceptable for intermediate diameters. For critical applications, use the exact ISO table values.

Related Calculators

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Related Guides

Deepen your understanding with these educational resources.

ISO 286 Limits and Fits Selection Guide

Engineering Toolbox guide to ISO limits and fits

Hole Basis System Design Guide

Mitutoyo metrology education resources

Practical Tolerance Selection Handbook

NIST measurement and calibration guides

Glossary

Technical terms used in mortgage calculations explained in plain language.

EI: Lower deviation of a hole (Écart Inférieur). The difference between the minimum limit of size and the nominal size for internal features.
ES: Upper deviation of a hole (Écart Supérieur). The difference between the maximum limit of size and the nominal size for internal features.
IT Grade: International Tolerance grade - a standardized tolerance value defined by ISO 286. Grades range from IT5 (finest) to IT18 (coarsest).
Fundamental Deviation: The deviation closest to the nominal size. For holes, it is usually EI (lower deviation). Determines the position of the tolerance zone.
Tolerance Unit (i): The standard tolerance unit per ISO 286, calculated from the geometric mean diameter. Used to derive IT grade values.
Hole Basis System: A system where the hole tolerance is fixed (usually H) and the shaft tolerance is varied to achieve the required fit type.
Clearance Fit: A fit that always provides a positive clearance between hole and shaft when assembled.
Transition Fit: A fit that may provide either clearance or light interference depending on the actual sizes of the hole and shaft.
Interference Fit: A fit that always provides negative clearance (interference) between hole and shaft, requiring force for assembly.
GO/NO-GO: Limit gauge system. GO checks the MMC limit (smallest hole), NO-GO checks the LMC limit (largest hole).

Authoritative References

Trusted sources and standards referenced by this calculator.

ISO 286-1:2010 - ISO System of Limits and Fits ISO 286-2:2010 - Tables of Tolerance Grades and Deviations ISO 2768-1:1989 - General Tolerances ASME B4.1-1967 - Preferred Limits and Fits ISO 1101:2017 - Geometrical Product Specifications (GPS) ISO 8015:2011 - Fundamental Principles of GPS

Applicable Standards

ISO 286ISO 2768ASME B4.1ISO 1101ISO 8015ISO 5459

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Last Updated:

2026-07-30

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.