AtlasCalcsUtility Calculation Suite
2026-07-30 8 min

ISO Tolerance Calculator

Calculate ISO 286 standard tolerance grades (IT1-IT18). Compute tolerance unit i, IT tolerance values, and fundamental deviations for any nominal size.

Calculator

Unit System
Nominal Size (mm)
Tolerance Grade (IT1-IT18)
Basic Deviation

Results

Normal

IT Grade

IT7

International Tolerance grade designation

Tolerance Value

21.453µm

Total tolerance zone width in micrometers

Tolerance Unit i

1.341µm

Standard tolerance unit: i = 0.45×∛D + 0.001×D (µm)

Standard Factor

16×i

Multiplier applied to tolerance unit i for this IT grade

Nominal Size

25mm

Basic size used for tolerance calculation

Deviation Value

0.000µm

Fundamental deviation for H: Lower (EI) = 0, Upper (ES) = +IT

Visualizations

Results Overview

7IT Grade
21.5Tolerance Value
1.3Tolerance Unit i
16Standard Factor
25Nominal Size

Formula

ISO 286 tolerance system computes tolerance unit i based on geometric mean of diameter range, then multiplies by grade-dependent factor to get the IT tolerance value.

i = 0.45 × ∛D + 0.001 × D, IT_n = Factor_n × i

Alternative Form

For IT1-IT3: IT = factor × (0.45×∛D + 0.001×D). For IT4-IT18: IT = factor × i

Variables

SymbolNameUnitDescription
DNominal DiametermmBasic size in millimeters
iTolerance UnitµmBasic tolerance unit: i = 0.45×∛D + 0.001×D
IT_nIT Grade ToleranceµmStandard tolerance value for grade n
Factor_nGrade Factor-Multiplier: IT6=10, IT7=16, IT8=25, IT9=40, IT10=64, IT11=100, IT12=160

Explanation

The ISO 286 tolerance system defines 18 standard tolerance grades (IT1 through IT18). The tolerance value for grades 5-16 is calculated as IT = factor × i, where i = 0.45×∛D + 0.001×D. For grades 1-4 and 17-18 slightly different formulas apply. The fundamental deviation (letter) positions the tolerance zone relative to the nominal size.

Derivation

The tolerance unit formula i = 0.45×∛D + 0.001×D was empirically derived to reflect the relationship between manufacturing difficulty and part size. The cubic root term accounts for size effect on manufacturing precision, while the linear term accounts for thermal expansion effects. Grade factors follow a geometric progression (Renard series R5) approximately doubling every 3 grades.

Step-by-Step Calculation

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

Step 1

Enter the nominal size in millimeters.

Nominal Size:25 mm
Result: D = 25 mm
Step 2

Select the IT tolerance grade (1-18).

Grade:7
Result: Factor = 16×i, Grade = IT7
Step 3

Calculate tolerance and review deviation.

i = 0.45×∛D + 0.001×D
Tolerance Unit i:1.341 µm
Intermediate: IT7 = 16 × 1.341 = 21.453 µm
Result: Tolerance: 21.453 µm (IT7)
Final Answer
IT7

Worked Examples

See how the calculator works with different scenarios.

Scenario

Calculate the standard IT7 tolerance for a 25 mm shaft or hole. IT7 is the most common grade for general mechanical engineering.

Inputs

Nominal Size:25 mm
Grade:IT7

Calculation

i = 0.45×∛25 + 0.001×25 = 0.45×2.924 + 0.025 = 1.341 µm IT7 = 16 × 1.341 = 21.5 µm Round to standard: 21 µm

Result

IT7 = 21 µm for 25 mm

Interpretation

A 25 mm H7 hole has tolerance range: 0 to +21 µm. This provides a standard precision hole for general engineering.

Understanding Your Result

Your Result: IT Grade: IT7

Typical range: IT1-IT4: Gage making and precision instruments. IT5-IT6: Precision fits and bearings. IT7-IT8: General engineering fits. IT9-IT11: Commercial manufacturing. IT12-IT18: Coarse/non-critical dimensions.

What This Means

ISO tolerance grades define the acceptable variation in part dimensions. The IT grade number indicates the width of the tolerance zone - smaller numbers mean tighter tolerances and higher manufacturing precision.

Why It Matters

Standardized tolerances ensure interchangeability of parts, enable global manufacturing, and provide a common language for design and production. Choosing the right IT grade balances function against manufacturing cost.

Professional Interpretation

The ISO tolerance system follows the principle that larger parts need larger tolerances for the same manufacturing process. The tolerance unit i increases with size, and the grade factor determines the precision level.

Recommendations

  • •Use IT5-IT6 for critical fits (bearings, precision shafts)
  • •Use IT7-IT8 for normal engineering fits (standard holes, shafts)
  • •Use IT9-IT10 for general manufacturing tolerances
  • •Use IT11-IT12 for castings, forgings, and rough dimensions
  • •Avoid specifying tighter grades (IT5-) unless functionally necessary
  • •Consider that IT7 costs approximately 2× IT9, and IT6 costs 4× IT9
  • •Use ISO 2768 general tolerances for non-critical dimensions

Educational Content

Introduction

The ISO 286 tolerance system is an internationally standardized system for defining dimensional tolerances on mechanical parts. It provides a systematic approach to specifying how much a manufactured dimension may vary from its nominal value.

Concept Explanation

The system has two components: (1) the IT grade (1-18), which defines the tolerance zone width (manufacturing precision), and (2) the fundamental deviation (letter), which defines the zone position relative to the nominal size. Combining these gives a complete tolerance specification.

Applications

▸Shaft and hole dimensioning for interchangeable parts
▸Fit classification (clearance, transition, interference)
▸Manufacturing tolerance specification on drawings
▸Quality control and inspection planning
▸Process capability analysis
▸International trade of mechanical components

Benefits

  • •Ensures global interchangeability of parts
  • •Standardizes communication between design and manufacturing
  • •Reduces ambiguity in tolerance specification
  • •Provides a rational basis for tolerance selection
  • •Supports statistical process control
  • •Enables consistent quality across suppliers

Limitations

  • •Does not cover geometrical tolerances (form, orientation, location)
  • •Assumes standard temperature conditions (20°C)
  • •May not suit all materials (especially plastics)
  • •Requires understanding of hole/shaft basis systems

Best Practices

  • •Always specify IT grade with fundamental deviation (e.g., H7, g6)
  • •Prefer hole-basis system (H) for general design
  • •Apply general tolerances (ISO 2768) to unspecified dimensions
  • •Consider manufacturing process capability when choosing grades
  • •Verify that tolerance stack-up in assemblies meets functional requirements
  • •Use tolerance analysis tools for complex assemblies

Common Misconceptions

Myth: Tighter tolerances always give better quality.
Truth: Unnecessarily tight tolerances increase cost without functional benefit. Optimal tolerances match precision to functional requirements.
Myth: ISO tolerances apply to all dimensions equally.
Truth: ISO tolerances are primarily for cylindrical features (shafts and holes). Other features may require different tolerance systems.
Myth: IT grade alone defines the complete tolerance.
Truth: Both IT grade (width) and fundamental deviation (position) are needed to fully define a tolerance zone.

Practical Tips

  • •For cost-effective manufacturing, use the coarsest IT grade that still meets functional requirements
  • •Tolerances tighter than IT6 typically require grinding or fine machining
  • •IT7-IT8 can be achieved with standard turning and boring operations
  • •IT9-IT11 are achievable with standard machining without special setup
  • •IT12+ can often be achieved without any machining (as-cast, as-forged)
  • •The cost of a tolerance increases exponentially as IT grade decreases
  • •Use the diameter range (not exact size) when looking up standard tolerance tables

Common Mistakes

Specifying IT grades that cannot be achieved economically
Match IT grade to manufacturing process: IT6 requires grinding, IT7-IT8 requires fine turning/boring, IT9-IT11 standard machining.
Using IT grades for non-cylindrical features
ISO 286 is primarily for linear sizes of cylindrical features. Use ISO 2768 for general dimensions and ISO 1101 for geometrical tolerances.
Confusing fundamental deviation with IT grade
The letter (H, g, p, etc.) defines POSITION of tolerance zone. The number (6, 7, 8, etc.) defines WIDTH. Both are needed for complete specification.
Applying hole tolerances to shaft features or vice versa
Per ISO 286, uppercase letters (A-ZC) are for holes (internal features), lowercase (a-zc) are for shafts (external features). Do not mix.

Assumptions

This calculator makes the following assumptions to provide estimates:

Standard Temperature: All tolerances are defined at 20°C reference temperature per ISO 1.
Steel as Reference Material: The tolerance system is based on steel manufacturing experience. Other materials may have different manufacturing characteristics.
Continuous Production: Assumes normal manufacturing conditions with statistical process control.
Measurement Uncertainty: Measurement uncertainty should be ≤ 20% of tolerance for reliable inspection per ISO 14253.

Limitations

Be aware of these limitations when using this calculator:

Approximated Values: Tolerance values are calculated using the i formula. Actual ISO 286 standard tables use rounded values for standardized diameter steps.
Diameter Steps: Actual ISO standard tolerances are tabulated for diameter steps (e.g., 18-30 mm, 30-50 mm). This calculator uses exact diameter, which may differ slightly.
Upper Grade Limitations: Grades IT1-IT3 use slightly different formulas than shown. For very high precision, consult standard tables directly.
Geometric Tolerances Not Included: Form, orientation, and location tolerances follow ISO 1101 and ASME Y14.5, not the IT system.

Frequently Asked Questions

Answers to common questions about this calculator.

What is ISO 286?
ISO 286 is the international standard for ISO code system for tolerances on linear sizes. It defines IT grades (IT1-IT18) and fundamental deviations for holes and shafts.
What is the tolerance unit i?
i = 0.45 × ∛D + 0.001 × D (µm), where D is the nominal diameter in mm. It represents the basic tolerance unit for IT grades 5-16.
What are IT grades?
International Tolerance (IT) grades 1-18 define the width of the tolerance zone. IT1 is the finest (0.8i), IT18 is the coarsest (2500i).
How is IT tolerance value calculated?
For IT4-IT18: IT = factor × i. Factors: IT4=3, IT5=5, IT6=10, IT7=16, IT8=25, IT9=40, IT10=64, IT11=100, IT12=160. For IT1-IT3: different formulas apply.
What is the difference between IT6 and IT7?
IT6 = 10i, IT7 = 16i. IT7 is 60% wider than IT6. For a 25 mm part, IT6 ≈ 13 µm, IT7 ≈ 21 µm.
What does H7 mean?
H7 means the hole has a fundamental deviation H (lower deviation = 0, i.e., at the nominal size) and an IT7 tolerance grade (16i).
What does g6 mean?
g6 means the shaft has a fundamental deviation g (upper deviation is negative, below nominal) and an IT6 tolerance grade (10i).
What is the most common IT grade?
IT7 is the most common grade for general engineering applications. IT6 is common for precision fits, and IT9 for general manufacturing.
How do I choose the right IT grade?
Consider functional requirements, manufacturing capability, and cost. IT5-IT6 for precision fits, IT7-IT8 for normal fits, IT9-IT11 for general use, IT12+ for non-critical.
What is the nominal size range for ISO 286?
ISO 286 covers sizes up to 3150 mm (standard) and up to 10000 mm (extended). Common diameter ranges are defined in standardized steps.
Can ISO tolerances be used for non-metallic materials?
Yes, but the standard was developed for metals. Plastics and other materials may need adjusted tolerances due to different thermal expansion and manufacturing behavior.
What is the difference between IT grade and fundamental deviation?
IT grade defines tolerance WIDTH (how much variation is allowed). Fundamental deviation defines POSITION (where the zone is located relative to nominal).
What is ISO 2768?
ISO 2768 provides general tolerances for linear and angular dimensions not individually specified. It has tolerance classes: fine (f), medium (m), coarse (c), very coarse (v).
How does temperature affect tolerances?
ISO tolerances are defined at 20°C. At different temperatures, thermal expansion changes actual part sizes. For critical measurements, control temperature to 20°C.
What measurement uncertainty is acceptable?
Per ISO 14253, measurement uncertainty should not exceed 20% of the tolerance band. For IT7 (21 µm), measurement uncertainty ≤ 4.2 µm.
How do IT grades relate to manufacturing processes?
IT5-IT6: grinding, honing. IT7-IT8: fine turning, boring, reaming. IT9-IT11: standard machining. IT12+: casting, forging, stamping.
What are the rules for hole/shaft designation?
Uppercase letters (A-ZC) = holes (internal). Lowercase letters (a-zc) = shafts (external). H is the basic hole (lower deviation = 0). h is the basic shaft (upper deviation = 0).
Can I use IT5 for a large 500 mm part?
Yes, but IT5 on large parts can be extremely difficult and expensive to achieve. IT5 at 500 mm ≈ 32 µm requires precision grinding and careful temperature control.
What is the cost impact of different IT grades?
Relative cost: IT9 = 1× (baseline), IT8 = 1.5×, IT7 = 2×, IT6 = 4×, IT5 = 10×. Cost increases exponentially for tighter grades.
What is the Renard series?
Renard series (R5, R10, R20) are geometric progressions used as preferred numbers. IT grade factors follow approximately an R5 progression (×1.6 per grade step).
How do I specify ISO tolerances on a drawing?
Use the pattern: nominal diameter + tolerance class. Examples: ø25 H7, ø25 g6, ø50 H7/g6 (fit). Per ISO 286 and ISO 14405-1.
What is the difference between IT grades and tolerance classes?
IT grade = the width, tolerance class = combination of fundamental deviation letter + IT grade number (e.g., H7, g6).
Can I convert between IT grades?
Not directly. Each grade defines a specific tolerance value. There is no fixed ratio (except approximately 1.6× per grade for the R5 progression).
What is the role of i in tolerance calculation?
i provides a size-dependent base unit. Larger parts need larger absolute tolerances for the same manufacturing process. i increases with the cubic root of diameter.
How are tolerance values rounded?
Calculated values are rounded to standard numbers following the Renard series. This calculator provides the calculated value before rounding.
What are preferred sizes?
Preferred sizes (ISO 3, ISO 497) are standard diameters that simplify design and reduce tooling variation. Use preferred sizes when possible.
How do I handle tolerances for assemblies?
Use the fit concept: combine hole and shaft tolerances into a fit designation (e.g., H7/g6). Analyze worst-case clearance/interference conditions.
What is the future of ISO tolerance system?
Integration with GPS (Geometrical Product Specifications) matrix and digital twin technology. ISO 8015 defines the GPS masterplan.
How do I verify ISO tolerances?
Use calibrated instruments with appropriate measurement uncertainty. Compare measured values against tolerance limits at 20°C reference temperature.

Related Calculators

Explore more calculators related to this topic.

Related Guides

Deepen your understanding with these educational resources.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Basic Deviation
The position of the tolerance zone relative to the nominal size, designated by a letter (A-ZC for holes, a-zc for shafts).
Fundamental Deviation
The deviation closest to the nominal size, defining the starting point of the tolerance zone.
Hole-Basis System
Preferred system where the hole has fixed deviation H (EI=0) and the shaft tolerance is varied for different fits.
IT Grade
International Tolerance grade (1-18) defining the width of the tolerance zone.
Lower Deviation
The algebraic difference between the minimum limit of size and the nominal size (EI for holes, ei for shafts).
Maximum Material Size
The largest shaft or smallest hole condition (maximum material).
Minimum Material Size
The smallest shaft or largest hole condition (minimum material).
Renard Series
Preferred number series (R5, R10) used as the basis for IT grade factor progression.
Shaft-Basis System
Alternative system where the shaft has fixed deviation h (es=0) and the hole tolerance is varied.
Tolerance Class
The combination of fundamental deviation letter and IT grade number (e.g., H7, g6, p6).
Tolerance Unit i
The basic tolerance unit: i = 0.45×∛D + 0.001×D (µm), used to calculate IT tolerance values.
Tolerance Zone
The range of acceptable sizes between the upper and lower limits of size.
Upper Deviation
The algebraic difference between the maximum limit of size and the nominal size (ES for holes, es for shafts).
Zero Line
The line representing the nominal size in a graphical tolerance representation.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ISO 286-1ISO 286-2ISO 2768-1ASME Y14.5MISO 8015ISO 1101ISO 5459

Was This Calculator Helpful?

Page Information

Last Updated:

2026-07-30

Version:

2.0.0

License:

Free to use for educational and professional purposes.