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101 Fundamentals

What Is a Tolerance? Linear vs. Angular

Every CNC drawing carries two categories of tolerance: linear (controls distances) and angular (controls angles). Before looking at any numbers, understand what these terms mean and why they exist at all.

The core problem: all manufacturing processes have variation

No CNC machine cuts to an exact number. A spindle cutting a 1.000 in. slot produces 0.9997 in. on one part and 1.0003 in. on the next — due to tool wear, thermal expansion, vibration, and fixture repeatability. A nominal dimension of exactly 1.000 in. is physically unachievable. It would require infinite precision.

A tolerance solves this by defining the acceptable range around the nominal. ±0.005 in. on a 1.000 in. dimension means any part measuring between 0.995 in. and 1.005 in. passes inspection. The question you answer when setting a tolerance is not “how precise is the machine?” — it's “how much variation can my design functionally absorb?” These are very different questions. Confusing them is the #1 source of over-toleranced drawings and unnecessary cost.

Linear Tolerances

Controls: distances measured in a straight line

Linear tolerances apply to any dimension you would measure with a caliper, micrometer, or CMM probe moving in a straight line: width, depth, hole diameter, wall thickness, step height, thread pitch diameter. If a feature has a length, it needs a linear tolerance.

How to read it on a drawing

2.500 ±0.005

→ Accepts 2.495–2.505 in. Rejects everything outside.

Bilateral vs. unilateral

Bilateral (±0.005 in.): zone is symmetric around nominal. Preferred — equal error budget in both directions.
Unilateral (+0.010/−0.000 in.): zone is one-sided. Use for interference fits or press-fit bores where only one direction of error is acceptable.

Angular Tolerances

Controls: the orientation of one surface relative to another

Angular tolerances control angles: chamfers, tapers, mating inclined faces, draft angles. Expressed in degrees (°), arc-minutes (′ = 1/60 of a degree), and arc-seconds (″ = 1/3600 of a degree). Standard CNC holds ±0°30′ reliably; precision work reaches ±0°10′.

How to read it on a drawing

45° ±0°30′

→ Accepts 44°30′–45°30′. That is a 1° total band.

The key notation

= 1 degree  |  1′ = 1 arc-minute (0.0167°)  |  1″ = 1 arc-second (0.000278°)
Most title blocks default to ±1° for angular dimensions unless a tighter callout is specified.

Why angular errors compound with distance (the lever arm effect)

Angular tolerances are not scale-independent. The same 0.5° angular error produces very different linear deviations depending on how far you measure from the origin. Formula: linear deviation = L × tan(angular error), where L is the distance from the angular datum.

Distance from datum0.5° error →1° error →Significance
1 in.0.0087 in.0.0175 in.1.7× standard tolerance — evaluate fit function
3 in.0.026 in.0.052 in.Outside ±0.005 in. — starts to matter
6 in.0.052 in.0.105 in.10× standard tolerance — significant
12 in.0.105 in.0.209 in.Major alignment error at assembly

This is why GD&T perpendicularity and angularity callouts express the tolerance in linear units (a zone width between parallel planes) rather than degrees — it directly represents the functional impact at the mating surface.

Block tolerances: the default that covers most dimensions

Every engineering drawing should have a title block with a general tolerance: typically ±0.005 in. for 3-decimal dimensions, ±0.010 in. for 2-decimal, and ±1° for angular dimensions. This block tolerance applies to every dimension without an explicit callout. You only need to add a specific tolerance callout when your design functionally requires something tighter — or more relaxed — than the block default. This keeps drawings clean and gives the machinist freedom on non-critical features.

Tolerance zone diagram with drawing callout 1.000 +/-0.005 in., upper limit 1.005 in., lower limit 0.995 in., reject oversize and undersize bands, and accept zone from 0.995 to 1.005 in.
Reference Table

Linear Tolerance Reference

Achievable linear tolerances for CNC machining, from standard to ultra-precision. Cost impact is relative to the baseline ±0.005″ standard tolerance.

LevelInchesMetricCost ImpactTypical Use
Standard
±0.005″±0.13 mmBaselineDefault for most features
Precision
±0.002″±0.05 mm+15–30%Mating surfaces, bearing fits
High PrecisionPOPULAR
±0.001″±0.025 mm+40–80%Reamed holes, press fits
Ultra Precision
±0.0005″±0.013 mm+100–200%Optical, safety-critical components
Grinding/Lapping
±0.0002″±0.005 mm+200–400%Requires secondary operations

Design Tip: Avoid Over-Tolerancing

Only call out tight tolerances on features that truly require them. Over-tolerancing is the #1 driver of unnecessary CNC cost. Apply ±0.005″ to general features and reserve ±0.001″ or tighter for critical dimensions.

Bilateral tolerance +/-0.005 in. places equal zone each side of nominal; unilateral +0.010/-0.000 places zone only above nominal for press-fit bores
Figure 1. Bilateral tolerances are the default for most features. Use unilateral only when the functional fit requires error in one direction only.
Reference Table

Angular Tolerance Reference

Achievable angular tolerances for CNC machining, standard to ultra-precision. The “Linear Dev. at 6 in.” column shows the actual linear positional error that the angular deviation produces at a 6 in. reference distance — because angular errors are only meaningful in the context of distance.

LevelToleranceArc-MinutesLinear Dev. at 6 in.Typical Use
Standard
±1°±60′±0.105″General chamfers, draft angles, non-mating faces
Precision
±0°30′±30′±0.052″Mating tapers, angled mating faces
High PrecisionCOMMON
±0°10′±10′±0.017″Precision tool holders, conical seats
Ultra Precision
±0°1′±1′±0.0017″Precision spindles, optical mounts

Angular tolerances tighten when features are long

A ±1° block tolerance is completely acceptable on a 0.25 in. chamfer — the linear deviation at that scale is only 0.0044 in. (0.11 mm). But the same ±1° angular error on a 10 in. column face produces 0.175 in. (4.45 mm) of linear deviation at the top — almost certainly incompatible with assembly. Always ask: how far from the angular datum does this surface extend? If the answer is more than 2–3 in., either tighten the angular callout or replace it with a GD&T perpendicularity or parallelism control, which expresses the tolerance as a linear zone width and is more directly inspectable.

Surface Quality

Surface Finish Guide

Surface finish is measured in Ra (roughness average) in microinches (µin) or micrometers (µm). Lower Ra values mean smoother surfaces - but cost scales accordingly.

FinishRa ValueProcessCost ImpactBest For
As-Machined125 Ra (3.2 µm)Standard milling/turningBaselineNon-critical, internal parts
Fine Machined63 Ra (1.6 µm)Reduced feed rate+10–20%External surfaces, housings
Very Fine32 Ra (0.8 µm)Light finishing passes+20–40%Sealing surfaces, bearing seats
Ground16 Ra (0.4 µm)Surface grinding+50–100%Precision fits, sliding surfaces
Lapped/Polished8 Ra (0.2 µm)Lapping or polishing+100–300%Optical, medical, sealing
Most Common
125 Ra
As-Machined
Good enough for 80% of parts
Balanced
32–63 Ra
Fine Machined
External/visible surfaces
Premium
8–16 Ra
Ground/Polished
Sealing, optical, medical
Surface finish Ra roughness scale comparing five levels: 125 Ra as-machined, 63 Ra fine, 32 Ra very fine, 16 Ra ground, 8 Ra lapped with cross-section profiles and cost impact
Figure 2. Ra roughness scale (ISO 4287): specify only the Ra required by function. As-machined 125 Ra covers 80% of parts; lower values require secondary operations.
Material Guide

Material-Specific Tolerances

Material properties directly impact achievable tolerances. Thermal expansion, hardness, machinability, and chip characteristics all play a role.

Aluminum 6061-T6

Excellent machinability, minimal tool wear. One of the most economical metals for tight tolerances.

±0.001″
Achievable

Stainless Steel 304/316

Work-hardens during cutting. Requires slower speeds and rigid setup.

±0.002″
Achievable

Carbon Steel 1018/1045

Good machinability. Leaded variants (12L14) machine even better.

±0.001″
Achievable

Titanium Ti-6Al-4V

Low thermal conductivity causes heat buildup. Requires specialized tooling.

±0.002″
Achievable

Brass C360

Free-machining. Excellent for precision components and threads.

±0.001″
Achievable

Delrin (Acetal)

Excellent dimensional stability and low moisture absorption. One of the easiest plastics to machine to tight tolerances.

±0.002″
Achievable

PEEK

High-performance plastic. Requires sharp tools and careful feeds.

±0.002″
Achievable
Table comparing achievable CNC tolerances by material: aluminum 6061-T6 and brass C360 hold +/-0.001 in., stainless 304/316 and Ti-6Al-4V hold +/-0.002 in., with machinability ratings relative to AISI B1112
Figure 3. Achievable tolerance depends on machinability. Aluminum and brass routinely hold ±0.001 in.; stainless and titanium are limited to ±0.002 in. without secondary ops.
Advanced Tolerancing

GD&T Essentials

Geometric Dimensioning & Tolerancing (ASME Y14.5) goes beyond simple ± dimensions to control form, orientation, and location. Here are the most commonly specified callouts.

Flatness

How flat a surface must be, independent of any reference datum.

Typical: 0.001″–0.005″
//

Parallelism

How parallel a surface or axis is relative to a datum plane.

Typical: 0.001″–0.005″

Perpendicularity

How perpendicular a surface or axis is to a datum.

Typical: 0.001″–0.005″

Cylindricity

Controls form of a cylindrical surface-roundness, straightness, and taper.

Typical: 0.001″–0.003″

Concentricity

Median points of a feature must lie on the axis of a datum feature.

Typical: 0.002″–0.005″

Position

Controls location of a feature relative to datums. Most commonly used GD&T callout.

Typical: 0.005″–0.010″

When to Use GD&T

Use GD&T when parts must assemble with tight functional requirements - bearing bores, mounting faces, pin locations. For standalone parts without mating constraints, simple ± tolerances are usually sufficient and easier for the shop to inspect.

GD&T feature control frame anatomy: seven compartments showing geometric characteristic (true position), zone shape (cylindrical), tolerance value 0.005 in., material condition modifier MMC, and datum references A B C per ASME Y14.5-2018 / ISO 1101
Figure 4. A feature control frame encodes a complete GD&T requirement in one box. Read left to right: what type of control, how large the zone, what shape, which material condition, and which datums it references.
Fundamentals

Why Tighter Tolerances Cost More: The Physics

Before you look at cost multipliers, understand what physically changes on the shop floor when you tighten a tolerance. Every item below adds time, risk, or secondary operations — and all of that converts directly to dollars.

1

Feed rate drops → cycle time increases

To hold ±0.001 in. instead of ±0.005 in., the CNC programmer reduces the finish-pass feed rate and depth of cut. A surface that takes one pass at ±0.005 in. may require 2–3 light passes at ±0.001 in. The tool is removing less material per revolution, so the spindle runs longer. On a 4-sided housing, going from ±0.005 in. to ±0.001 in. on all faces can increase cycle time by 40–80%.

2

Tool deflection becomes the limit

Every cutting tool deflects under load. A standard end mill cutting 6061-T6 aluminum deflects approximately 0.0005–0.002 in. depending on stick-out length, diameter, and cutting force. At ±0.005 in. tolerance, this deflection is within the zone. At ±0.001 in., it is not — the programmer must use shorter, stiffer tools, reduce cut depth, or add a spring-pass (a final pass at zero additional depth that lets the tool "spring back" and clean up the deflection). Each of these strategies adds time.

3

Thermal expansion matters at ±0.001 in.

Aluminum 6061-T6 has a coefficient of thermal expansion (CTE) of 13.1 μin./in./°F (23.6 μm/m/°C). A 10 in. (254 mm) aluminum part that heats up 10°F (5.5°C) during machining grows by 0.0013 in. (0.033 mm) — larger than a ±0.001 in. tolerance. At tight tolerances, the shop must manage coolant temperature, allow parts to thermally stabilize before inspection, and may need to specify inspection temperature (68°F / 20°C per ASME Y14.5).

4

Inspection time multiplies

At ±0.005 in., a machinist can verify most features with a caliper or micrometer in 30–60 seconds. At ±0.001 in., a CMM (coordinate measuring machine) is required — each feature takes 1–3 minutes to probe, align, and report. A part with 20 toleranced features at ±0.001 in. may require 30–60 minutes of CMM time at $75–$150/hr. At ±0.005 in., the same part is inspected in 5 minutes with hand tools.

5

Scrap rate increases non-linearly

When the tolerance zone shrinks, the percentage of parts that fall outside the zone increases — even if the process has not changed. A process with a standard deviation (sigma) of 0.002 in. produces ~99.7% yield at ±0.006 in. (3σ). The same process at ±0.002 in. (1σ) produces only ~68% yield — a 32% scrap rate. To maintain yield at tight tolerances, the shop must reduce process variation through better tooling, fixturing, and environmental control, all of which add cost.

6

Secondary operations become mandatory

Standard CNC milling holds ±0.005 in. reliably. ±0.001 in. is achievable with careful setup. Below ±0.0005 in., the part typically leaves the CNC mill and moves to a secondary process: grinding (±0.0002 in.), honing (±0.0001 in. on bores), or lapping (±0.00005 in. on flat surfaces). Each secondary operation is a separate setup with its own machine, operator, and inspection cycle — doubling or tripling the number of operations on the part.

The 80/20 rule for tolerances

On a well-designed part, roughly 80% of dimensions should use block tolerances (±0.005 in. or ±0.010 in.) and only 10–20% should carry tighter callouts (±0.001–±0.002 in.). If your drawing has tight tolerances on more than 30% of features, review each one and ask: “Does assembly or function actually require this?” The answer is usually no for at least half of them. See the GD&T Guide for how to use position and form controls instead of stacked ± tolerances.

Cost Analysis

Cost Impact Analysis

Tolerance is the single largest cost driver in CNC machining after material choice. Understanding the cost curve helps you spec only what you need.

Slower Feeds & Speeds

Tighter tolerances require slower cutting speeds and lighter depths of cut, increasing cycle time by 2–5×.

Specialized Tooling

Precision work often requires carbide or diamond tooling, rigid tool holders, and more frequent tool changes.

Climate-Controlled Environment

Ultra-precision work (< ±0.001″) may require temperature-controlled rooms to prevent thermal expansion.

In-Process Inspection

CMM probing between operations adds time but ensures dimensions stay in spec. Critical for medical devices and precision robotics.

Higher Scrap Rate

Tighter specs mean more rejected parts. Scrap costs are passed through, especially for expensive materials like titanium.

Secondary Operations

Grinding, lapping, honing, and EDM may be needed for features beyond standard CNC capability.

Relative Cost by Tolerance

Actual pricing depends on material, geometry, quantity

±0.005″ Standard$
±0.002″ Precision$$
±0.001″ High Precision$$$
±0.0005″ Ultra Precision$$$$
±0.0002″ Grinding/Lapping$$$$$
Best Practices

Design Tips for Tolerances

1

Use bilateral tolerances

Specify ±0.005″ rather than +0.010/-0.000. Bilateral tolerances are easier to manufacture and inspect, and they center the nominal dimension.

2

Tolerance critical features only

Apply tight tolerances only to mating surfaces, bearing bores, sealing grooves, and assembly-critical dimensions. Let everything else float at ±0.005″.

3

Avoid tolerance stacking

When multiple features reference different datums, tolerances accumulate. Use a single datum scheme and GD&T position callouts to control critical relationships.

4

Match tolerance to process

Don't specify ±0.0005″ on a feature that can only be held to ±0.002″ with standard tooling. Consult your machinist early in the design phase.

5

Consider thermal effects

Aluminum expands ~13 µin/in/°F. A 12″ aluminum part heated 20°F changes by 0.003″. Specify inspection temperature (typically 68°F / 20°C) for precision work.

6

Provide complete drawings

Include GD&T callouts, surface finish symbols, material spec, and inspection notes. A clear drawing reduces quoting time and prevents misinterpretation.

Common Questions

Frequently Asked Questions

What is the standard tolerance for CNC machining?
The industry-standard tolerance for CNC machining is ±0.005″ (±0.13 mm). This is achievable on most CNC mills and lathes without special tooling or secondary operations, and is suitable for the majority of mechanical parts.
How tight can CNC tolerances get?
With precision 5-axis CNC machining, tolerances of ±0.0005″ (±0.013 mm) are achievable. For ultra-critical features, grinding and lapping can reach ±0.0002″ (±0.005 mm). However, tighter tolerances dramatically increase cost - each order of magnitude roughly doubles the price.
Does material affect achievable tolerances?
Yes, significantly. Free-machining materials like aluminum 6061 and brass C360 can hold ±0.001″ routinely. Harder or gummier materials like stainless steel and titanium are typically limited to ±0.002″ without secondary operations, due to tool deflection, heat buildup, and work hardening.
What is the difference between tolerance and surface finish?
Tolerance controls dimensional accuracy - how close a dimension is to its nominal value (e.g., ±0.005″). Surface finish (measured in Ra) controls the micro-texture of a surface. A part can have tight tolerances but a rough finish, or loose tolerances with a mirror polish. Both are specified independently.
How do tolerances affect manufacturing cost?
Tighter tolerances increase cost through slower cutting speeds, additional finishing passes, specialized tooling, more frequent inspection, and higher scrap rates. Going from ±0.005″ to ±0.001″ typically adds 40–80% to machining cost. Only specify tight tolerances on critical features.
What is GD&T and when should I use it?
GD&T (Geometric Dimensioning & Tolerancing) is a symbolic language defined by ASME Y14.5 that controls form, orientation, and location of features beyond simple ± dimensions. Use GD&T when you need to control flatness, parallelism, perpendicularity, position, or concentricity - especially for mating assemblies and precision fits.
What is a linear tolerance in CNC machining?
A linear tolerance defines the allowable variation for a distance measurement — width, depth, bore diameter, step height, or any dimension measured along a straight line. Expressed as ±0.005 in. (±0.13 mm), it means the finished dimension must fall within a 0.010 in. (0.25 mm) band centered on nominal. Standard CNC machining holds ±0.005 in. without special setup. Tighter requirements — ±0.001 in. (±0.025 mm) for bearing bores, ±0.0005 in. (±0.013 mm) for press fits — require precision setups, slower feeds, and CMM inspection.
What is an angular tolerance in CNC machining?
An angular tolerance controls the orientation of a surface or axis relative to a reference, expressed in degrees (°), arc-minutes (′ = 1/60°), or arc-seconds (″ = 1/3600°). Standard CNC holds ±0.5° (±30′) reliably. High-precision angular work — conical seats, precision taper fits, indexed features — reaches ±0°10′. The critical engineering consideration is the lever-arm effect: a 0.5° angular error causes only 0.0087 in. (0.22 mm) of linear deviation at 1 in. from the datum, but 0.087 in. (2.2 mm) at 10 in. Always consider feature length when setting angular tolerances.
What's the difference between angular tolerance and GD&T angularity?
An angular tolerance (e.g., ±0.5°) defines the acceptable zone in degree units using a simple degree callout on the drawing. GD&T angularity (ASME Y14.5) defines the same constraint in linear units — a tolerance zone of parallel planes a specified distance apart, oriented at the true angle relative to an explicit datum. GD&T angularity is more precise because it references a datum, and is inspected with a CMM rather than a protractor. For non-critical chamfers, a degree callout is sufficient. For precision conical seats, indexed mating faces, or any feature where angular error compounds over distance, use GD&T angularity instead.

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