AtlasCalcsUtility Calculation Suite
2026-07-30 8 min

Cylindricity Calculator

Calculate cylindricity error from multiple cross-section roundness measurements, taper estimates, and surface deviation per ASME Y14.5 and ISO 12180.

Calculator

Unit System
Cross-Section Readings (mm, semicolon-separated sections)
Number of Cross-Sections
Section Spacing (mm)
Nominal Radius (mm)
Cylindricity Tolerance (mm)

Results

Caution

Cylindricity Error

0.0500mm

Overall form error combining all cross-sections

Max Cross-Section Roundness Error

0.0500mm

Largest roundness error among all measured cross-sections

Avg Roundness Error

0.0467mm

Average roundness error across all cross-sections

Taper Estimate

0.0000mm/mm

Estimated taper of the cylindrical surface (dr/dl)

Visualizations

Results Overview

0.1mmCylindricity Error
0.1mmMax Cross-Section Roundness Error
0mmAvg Roundness Error

Formula

Cylindricity is a 3D form tolerance controlling all surface points of a cylindrical feature. The tolerance zone is the space between two coaxial cylinders. It combines roundness, straightness, and taper into a single control.

CylindricityError = max(all_radii) - min(all_radii)

Alternative Form

TaperEstimate = |R_avg_last - R_avg_first| / L_total

Variables

SymbolNameUnitDescription
R_i_jRadius at Section i, Point jmmRadial measurement at cross-section i, angular position j
R_maxMaximum RadiusmmLargest radius across all sections and angles
R_minMinimum RadiusmmSmallest radius across all sections and angles
LTotal LengthmmTotal length of measured cylindrical surface
TTolerancemmAllowable cylindricity deviation

Explanation

Cylindricity evaluates the entire 3D surface of a cylinder. The difference between the overall maximum and minimum radius (peak-to-valley) represents the total form error. Unlike roundness (2D, single cross-section), cylindricity captures taper, barreling, hourglass shapes, and axis curvature. The tolerance zone is two coaxial cylinders separated by the tolerance value.

Derivation

Cylindricity error is the peak-to-valley of all radial measurements from all cross-sections. The taper estimate uses the difference in average radius between the first and last section divided by the total length. The average roundness error indicates the average cross-sectional form quality.

Step-by-Step Calculation

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

Step 1

Measure radial readings at multiple cross-sections along the cylinder axis.

Sections:3
Spacing:50 mm
Total Length:100 mm
Result: Radii range across all sections
Step 2

Compute per-section roundness errors and overall cylindricity from all data.

Cylindricity = max(R_ij) - min(R_ij)
Overall Max Radius:50.0300 mm
Overall Min Radius:49.9800 mm
Intermediate: Section roundness errors: max=0.0500 mm, avg=0.0467 mm
Result: Cylindricity Error: 0.0500 mm
Step 3

Estimate taper and compare cylindricity against tolerance.

%Tolerance = (Cylindricity / Tolerance) × 100%
Cylindricity Error:0.0500 mm
Taper Estimate:0.0000 mm/mm
Tolerance:0.1000 mm
Intermediate: %Tolerance = (0.0500 / 0.1000) × 100%
Result: Cylindricity: 0.0500 mm — Pass
Final Answer
0.0500

Worked Examples

See how the calculator works with different scenarios.

Scenario

A 100 mm long cylinder (50 mm radius) measured at 3 sections, 8 points each. Section data: [50.02,50.01,49.99,50.00,50.03,49.98,50.01,50.00]; [50.01,50.00,50.02,49.99,50.01,50.02,49.98,50.00]; [50.03,50.02,50.00,49.98,50.02,50.01,50.00,49.99]. Tolerance: 0.1 mm.

Inputs

Sections:3
Spacing:50 mm
Tolerance:0.1 mm

Calculation

Section 1 roundness: 0.05 mm Section 2 roundness: 0.04 mm Section 3 roundness: 0.05 mm Cylindricity (overall): 0.05 mm Taper: 0.0000 mm/mm

Result

Cylindricity: 0.0500 mm, Status: Pass (50% of tolerance)

Interpretation

The cylinder is well within the 0.1 mm cylindricity tolerance with consistent roundness across sections.

Understanding Your Result

Your Result: Cylindricity Error: 0.0500 mm

Typical range: Engine cylinder bores: 0.005-0.020 mm. Hydraulic cylinders: 0.02-0.08 mm. Precision shafts: 0.005-0.025 mm. General turned cylinders: 0.05-0.20 mm. Drawn tubing: 0.10-0.50 mm.

What This Means

Cylindricity controls the total 3D form of a cylindrical surface. It combines roundness (cross-sectional), straightness (axial), and taper into a single tolerance. A cylindricity of 0.1 mm means all surface points lie between two coaxial cylinders 0.1 mm apart.

Why It Matters

Cylindricity is essential for engine cylinders, hydraulic bores, precision shafts, and any cylindrical mating surface. Poor cylindricity causes leakage, binding, uneven wear, and reduced performance in rotating or reciprocating assemblies.

Professional Interpretation

Cylindricity is the most comprehensive form tolerance. Per ASME Y14.5, it controls the entire surface of a cylinder, including roundness, straightness, and taper. It does not require a datum. The evaluation uses all surface points, and the tolerance zone is defined by two coaxial cylinders.

Recommendations

  • •Use minimum 3 cross-sections for meaningful cylindricity evaluation
  • •Measure 8+ points per cross-section at uniform angular intervals
  • •Consider both form error and taper separately to identify dominant error source
  • •Use cylindrical grinding or honing to correct cylindricity errors
  • •Check for lobing patterns that may vary along the cylinder axis
  • •Document measurement locations on a cylindrical coordinate map

Educational Content

Introduction

Cylindricity is a GD&T form tolerance that controls the entire 3D surface of a nominally cylindrical feature. It is the most comprehensive cylindrical form control, combining roundness, straightness, and taper into a single requirement.

Concept Explanation

The cylindricity tolerance zone consists of two coaxial cylinders spaced the tolerance value apart. All points on the actual surface must lie between these two cylinders. The axis of the tolerance zone is not constrained - it can shift and tilt to best fit the measured data.

Applications

▸Engine cylinder bores and liners
▸Hydraulic and pneumatic cylinder tubes
▸Precision shafts and spindles
▸Compressor and pump cylinders
▸Bearing journals and races
▸Injection molding barrel liners
▸Gun barrels and rifled tubes

Benefits

  • •Single tolerance controls all cylindrical form errors
  • •Ensures proper piston ring sealing in engines
  • •Reduces leakage in hydraulic systems
  • •Improves bearing load distribution along the axis
  • •Simplifies drawing callouts (one control instead of three)
  • •Provides comprehensive quality assessment of cylindrical features

Limitations

  • •More complex to measure than roundness or straightness alone
  • •Requires multiple cross-sections for proper evaluation
  • •Cannot be used with material condition modifiers
  • •Measurement is time-consuming compared to simpler controls

Best Practices

  • •Use a CMM with rotary table or dedicated cylindricity measuring machine
  • •Select cross-sections that cover the full cylinder length
  • •Include sections near the ends and at regular intervals
  • •Use sufficient measurement points per section (minimum 8)
  • •Apply appropriate filtering to separate form from waviness
  • •Center and level the part carefully on the measurement axis
  • •Document all measurement conditions and equipment used

Common Misconceptions

Myth: Cylindricity is just roundness plus straightness.
Truth: Cylindricity is a single comprehensive control. Separate roundness and straightness tolerances may not capture combined effects (e.g., a barrel shape).
Myth: Cylindricity requires a datum axis.
Truth: Like other form tolerances, cylindricity does not require a datum. The tolerance zone is self-referencing.
Myth: Cylindricity and total runout are the same.
Truth: Cylindricity controls form only. Total runout controls both form and position relative to a datum axis.

Practical Tips

  • •Minimum 3 cross-sections recommended for reliable cylindricity evaluation
  • •Use 8+ measurement points per cross-section at uniform angular spacing
  • •Check section spacing is appropriate for the cylinder length
  • •Consider taper as a separate indicator of process issues
  • •Use cylindrical grinding to correct cylindricity errors
  • •For thin-walled parts, support to avoid clamping distortion
  • •Document all cross-section positions for traceability

Common Mistakes

Using too few cross-sections for long cylinders
Use minimum 3 sections for cylinders up to 200 mm, add one section per additional 100 mm length.
Not detecting taper separate from roundness
Review average radius per section to identify taper trends independent of roundness.
Confusing cylindricity with total runout on inspection reports
Cylindricity controls form without datum; total runout controls form + position relative to a datum axis.
Insufficient angular points per section missing lobing
Use minimum 8 points per section. Increase to 12-16 for high-precision or lobing-prone processes (centerless grinding).

Assumptions

This calculator makes the following assumptions to provide estimates:

Uniform Angular Spacing: Each cross-section is measured at uniform angular intervals around the circumference.
Coaxial Measurement Axis: The measurement axis is assumed aligned with the part axis. Misalignment introduces apparent cylindricity error.
Linear Taper Model: The taper estimate assumes a linear change in average radius along the axis.
Rigid Cylinder: The cylinder is assumed rigid; no deformation from clamping, gravity, or measurement forces.

Limitations

Be aware of these limitations when using this calculator:

Discrete Cross-Sections: Only discrete cross-sections are evaluated. Continuous surface between sections is not measured.
Linear Taper Assumption: Taper is estimated linearly between first and last sections, ignoring non-linear profiles (barreling, hourglass).
No Axis Curvature Analysis: Bowed or curved cylinder axes are not separately identified. Axis curvature is embedded in the cylindricity value.
No Harmonic Decomposition: Lobing and harmonic content at each section is not analyzed. Individual section roundness is reported but not decomposed.

Frequently Asked Questions

Answers to common questions about this calculator.

What is cylindricity in GD&T?
Cylindricity is a 3D form tolerance controlling all surface points of a cylindrical feature. The tolerance zone is two coaxial cylinders separated by the tolerance value.
How is cylindricity measured?
Using CMM with rotary table, or dedicated cylindricity measuring machines. The part is measured at multiple cross-sections and angular positions to capture the complete 3D surface.
Does cylindricity require a datum?
No, cylindricity is a form tolerance and does not require a datum reference. The tolerance zone is self-referencing.
What is the difference between cylindricity and roundness?
Roundness controls a single cross-section (2D). Cylindricity controls the entire cylindrical surface (3D), combining roundness, straightness, and taper.
What is a typical cylindricity tolerance?
Engine cylinders: 0.005-0.020 mm. Hydraulic bores: 0.02-0.08 mm. Precision shafts: 0.005-0.025 mm. General machining: 0.05-0.20 mm.
What is the ISO standard for cylindricity?
ISO 12180 covers cylindricity measurement. ISO 1101 defines cylindricity tolerancing. ASME Y14.5 is the US standard.
How many cross-sections are needed for cylindricity?
Minimum 3 cross-sections. For long cylinders (>300 mm), use one section per 100 mm of length plus extra at each end.
How many points per section?
Minimum 8 points per cross-section. Precision measurements use 16-32 points. The Nyquist criterion requires 2× the highest expected lobe count.
What causes cylindricity errors?
Machine tool geometry errors, spindle runout, thermal distortion, clamping forces, material stress, tool deflection, and inconsistent cutting conditions along the axis.
How do I specify cylindricity on a drawing?
Use the cylindricity GD&T symbol (circle with two slanted lines) followed by the tolerance in a feature control frame. No datum required.
What is the difference between cylindricity and total runout?
Cylindricity controls form only, without a datum. Total runout controls form and position relative to a datum axis, including eccentricity.
Can cylindricity be used with material condition?
No, cylindricity is a form tolerance and cannot have material condition modifiers per ASME Y14.5.
How does taper affect cylindricity?
Taper directly contributes to cylindricity error. A perfectly round but tapered part will have a large cylindricity error equal to the taper amount over the length.
What is the difference between cylindricity and coaxiality?
Cylindricity controls form of a single cylinder. Coaxiality (or concentricity) controls the alignment of two or more cylindrical features relative to a common datum axis.
How do I improve cylindricity?
Use cylindrical grinding, honing, or roller burnishing. Ensure rigid setup, balanced machining, stress-relieved material, and consistent coolant application.
What is the effect of clamping on cylindricity?
Excessive clamping force distorts thin-walled cylinders during machining. Use low-profile chucks, expanding mandrels, or pot fixturing for thin walls.
How does temperature affect cylindricity measurement?
Thermal gradients cause non-uniform expansion, creating apparent cylindricity errors. Measure at 20°C standard temperature after stabilization.
What is barreling in cylindricity?
Barreling is a cylindricity defect where the cylinder is larger in the middle than at the ends, forming a barrel-like shape.
What is hourglass shape in cylindricity?
An hourglass defect is the opposite of barreling - the cylinder is smaller in the middle than at the ends.
How does cylindricity affect piston ring sealing?
Poor cylindricity causes uneven ring contact, blow-by, oil consumption, and reduced engine efficiency. Cylindricity of 0.005-0.010 mm is typical for automotive engines.
What equipment measures cylindricity?
CMM with rotary table, Taylor Hobson roundness/cylindricity systems, Mahr form testers, and laser scanning systems.
How do I interpret a cylindricity polar plot?
Multiple polar plots (one per section) overlaid show how the form changes along the axis. The overall envelope defines the cylindricity error.
What is the relationship between cylindricity and bearing performance?
Poor cylindricity causes edge loading, reduced oil film thickness, and premature bearing failure. Cylindricity of 0.005-0.010 mm is typical for precision bearings.
Can cylindricity be measured on a tapered surface?
No, cylindricity applies only to nominally cylindrical surfaces. Tapered surfaces use profile tolerances.
What is the minimum zone method for cylindricity?
The minimum zone method finds two coaxial cylinders at minimum separation that contain all measured points. This ISO-preferred method gives the smallest error value.
How does surface roughness affect cylindricity?
Roughness adds noise to cylindricity readings. Apply Gaussian filtering (15-50 UPR cutoff) to separate form from roughness.
What is the cost impact of tight cylindricity tolerances?
Tight cylindricity (<0.010 mm) requires grinding or honing, increasing cost 2-5× over turned tolerance (0.050 mm). Specify only as tight as functional requirements dictate.
How do I document cylindricity results?
Record: date, temperature, equipment, section positions, points per section, filter settings, individual section roundness, taper estimate, overall cylindricity, and status.
What is the difference between cylindricity and profile of a surface?
Cylindricity controls form only. Profile of a surface controls form, size, orientation, and location relative to a theoretically exact surface.
How does material hardness affect cylindricity capability?
Harder materials (HRC 45+) maintain cylindricity better after machining but are harder to correct. Soft materials are easier to machine true but distort easily.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

ASME Y14.5
US standard for dimensioning and tolerancing including GD&T.
Barreling
A cylindricity defect where the cylinder diameter is larger in the middle than at the ends.
Coaxial Cylinders
Two or more cylinders sharing the same axis. The cylindricity tolerance zone consists of two coaxial cylinders.
Cylindricity
A 3D form tolerance controlling the complete surface of a nominally cylindrical feature.
Form Tolerance
A GD&T tolerance controlling shape independently of other features (flatness, straightness, roundness, cylindricity).
Harmonic
A sinusoidal component of the roundness/cylindricity profile at a specific frequency per revolution.
Honing
An abrasive finishing process used to improve cylindricity and surface finish of cylinder bores.
Hourglass Shape
A cylindricity defect where the cylinder diameter is smaller in the middle than at the ends.
ISO 1101
International standard for geometrical tolerancing including cylindricity.
ISO 12180
International standard for cylindricity measurement and evaluation.
Lobing
Periodic undulations around the circumference of a cross-section.
Minimum Zone
The ISO-preferred evaluation method using two coaxial cylinders at minimum separation.
Profile of a Surface
A GD&T tolerance controlling form, size, orientation, and location of a surface.
Roundness
Form tolerance for a single cross-section of a cylindrical feature.
Surface Deviation
Average absolute deviation of measured points from the mean cylindrical surface.
Taper
Gradual change in diameter along the axis of a cylindrical feature.
Tolerance Zone
The region within which all surface points must lie. For cylindricity, two coaxial cylinders.
Total Runout
A GD&T tolerance controlling cumulative form and position error relative to a datum axis.
MMC
Maximum Material Condition - condition of maximum material for a feature.
LMC
Least Material Condition - condition of minimum material for a feature.
RFS
Regardless of Feature Size - tolerance applies regardless of actual feature size.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ASME Y14.5-2018ISO 1101:2017ISO 12180-1:2011ISO 2768-1:1989ISO 8015:2011ISO 5459:2011

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

License:

Free to use for educational and professional purposes.