If you've dealt with crankshafts, spindles, or turbine shafts, you know misalignment will show up as early failure—vibration, odd wear, and sometimes outright binding. To get a handle on this, you measure how far the center points of several cross-sections drift from your reference axis and compare that to your tolerance zone. This Concentricity Calculator handles the math for you, using the ASME Y14.5 approach. It’s most important anywhere axis alignment is tight—automotive, aerospace, medical—basically, wherever "close enough" isn't good enough. Below you'll find the formula, an example, the technical background, and a FAQ.
What is concentricity?
Concentricity is a GD&T term for how far the center points of each circular cross-section of a feature stray from a datum axis. If all those centers land inside a given cylinder (your tolerance zone), you’re within spec.
Simple Explanation
Picture slicing a shaft into discs and marking the center of each. Concentricity tells you how much those centers drift from a straight reference line. The bigger the drift, the higher your deviation—which often turns into more vibration, uneven wear, or mechanical binding when the part is in service.
📐 Browse all 1000+ Interactive Calculators
Concentricity Measurement Diagram
Concentricity Calculator Interactive Visualizer
Visualize how cross-section center point displacements from a datum axis create the concentricity tolerance zone. Adjust individual displacement values to see how the median calculation and tolerance zone diameter change in real-time.
MEDIAN DISPLACEMENT
0.0015"
CONCENTRICITY
0.003"
MAX DISPLACEMENT
0.0022"
FIRGELLI Automations — Interactive Engineering Calculators
How to Use This Calculator
- Measure the displacement of each cross-section center point from the datum axis.
- Enter all displacement values into the input field, separated by commas (e.g., 0.002, 0.001, 0.003).
- Ensure all values use the same units — inches, millimeters, or microns.
- Click Calculate to see your result.
Concentricity Calculator
This calculator is intended for education, concept evaluation, and preliminary design. Results are based on the equations and assumptions described on this page, but cannot account for every real-world load case, tolerance, material property, environmental condition, installation detail, safety factor, code, or regulatory requirement. Verify all inputs, assumptions, units, and results independently before selecting components or using the result in a real application. Safety-critical, structural, medical, lifting, transportation, or regulated applications must be reviewed by a qualified engineer.
📹 Video Walkthrough — How to Use This Calculator
Mathematical Formula
Use the formula below to calculate concentricity deviation.
Concentricity Deviation Formula:
Concentricity = 2 × Median Point Displacement
Where:
- Median Point Displacement = Middle value of all measured center point deviations from datum axis
- Point Displacement = √[(xi - xdatum)² + (yi - ydatum)²]
- xi, yi = Coordinates of derived center point for cross-section i
- xdatum, ydatum = Coordinates of datum axis
The factor of 2 converts the median radius displacement to the diameter of the tolerance zone per ASME Y14.5 standard.
Simple Example
Given 3 cross-section displacements: 0.001, 0.003, 0.002 (all in inches).
Sorted: 0.001, 0.002, 0.003 — median = 0.002"
Concentricity deviation = 2 × 0.002 = 0.004"
The part passes if the drawing specifies a concentricity tolerance of 0.004" or greater.
Complete Guide to Concentricity Measurement
Understanding Concentricity in ASME Y14.5
Concentricity gives you a way to check how true a feature’s axis is relative to a datum. This is not the same as checking runout with a dial indicator; here you need actual coordinate data to find all those "real" center points and measure how much they wander. The math here matches what ASME Y14.5 requires, not a shortcut.
The concentricity tolerance forces all median center points to stay inside a cylinder equal to the specified tolerance. Because you’re measuring true axis deviation, not just outside surface variations, this is about as tight as it gets for axis control in GD&T.
How Concentricity Measurement Works
You need a few critical steps to measure concentricity properly (not just spin it and check with an indicator):
- Datum Establishment: You have to get your datum right first. Usually, that means taking several measurements along the reference (datum) feature and fitting the best axis through the data.
- Cross-Section Measurement: You’ll want to check several cross-sections along your part (perpendicular to the datum axis), with enough individual measurements around each one to define a center reliably.
- Center Point Derivation: Use a least-squares fit or a similar method to get the geometric center (median point) for each cross-section. Shortcuts here will throw off the result.
- Displacement Calculation: Measure the shortest (perpendicular) distance from each center point to the datum axis. Log all those values.
- Statistical Analysis: Find the median (not the mean!) value from your list of displacements, then double it for the concentricity deviation.
Practical Applications and Industry Usage
You'll see concentricity called out when actual axis location matters—crankshafts in engines, turbine rotors, high-speed spindles, or any shaft or bore that needs to be dead in-line through its length. If you’re designing with linear actuators or making custom mounts, proper concentricity on your assemblies prevents jams and keeps wear rates consistent.
Common places you'll find concentricity tolerances:
- Bearing fits and races
- Hydraulic cylinder internals
- Precision shafts and spindles
- Medical mechanical parts where axis error isn't acceptable
- Optical assemblies with tight axis requirements
Worked Example: Shaft Concentricity Analysis
Let's say you’ve measured five cross-sections of a shaft, and the center displacements are: 0.0015", 0.0008", 0.0022", 0.0012", 0.0018".
Step 1: Sort: 0.0008", 0.0012", 0.0015", 0.0018", 0.0022"
Step 2: Median is the middle value (third one if you have five): 0.0015"
Step 3: Concentricity deviation = 2 × 0.0015" = 0.0030"
So this shaft needs a concentricity tolerance of at least 0.003" to pass. If your drawing says 0.002" max, this one is a reject—it might need rework or replacement.
Design Considerations and Best Practices
Tight concentricity tolerances push up machining and inspection costs, sometimes for no gain. Anything under 0.0005" will often require special tooling, capable machines, and careful inspection.
Tips to keep things reasonable:
- Avoid Over-Specification: Only use concentricity where you really need true axis control. Circular runout might be good enough and much easier to achieve.
- Consider Manufacturing Process: If a part is turned between centers, it’ll usually be pretty concentric. Welded or assembled parts often can't hold tight concentricity without post-ops.
- Datum Selection: Pick datum features that are long and straight enough to serve as a credible axis—you want stability, not something you can only measure over a few millimeters.
- Tolerance Relationships: Set concentricity alongside your position, perpendicularity, and size tolerances so they make sense together. Blindly stacking tight tolerances is a recipe for trouble at inspection (or escalating rejections).
Measurement Equipment and Techniques
You can’t measure concentricity with dial indicators—the standard requires coordinate data, so you'll need a CMM, a laser scanning system, or a special concentricity gage. Spin the part all you want, but to truly check concentricity, you must establish actual center points across multiple sections.
CMMs can automate a lot of this, but understanding the math is useful. You need to know how the software is getting its answer if you’re troubleshooting inconsistent results or explaining why a part is out of spec. This calculator lets you run the check yourself if you want to validate or spot-check automated readings.
Relationship to Other GD&T Controls
Concentricity is stricter than runout—surface variations can be present even if the axis is true, but runout won’t catch that if the axis is wobbly in a particular way. Sometimes position tolerance (especially with MMC or LMC modifiers) can do the job for less cost and headache, but when absolute axis location is non-negotiable, concentricity is the go-to callout.
In actuator-driven or automated setups, off-axis alignment can shorten component life and cause nasty surprises like binding or increased noise. Getting this right at the design phase pays off down the line, even if it takes some extra work up front.
Quality Control and Statistical Analysis
If you log concentricity data on every batch, you get an early warning for things like tool wear or machine misalignment before scrap piles up. SPC charts and tracking the median help flag long-term changes without overreacting to occasional measurement hiccups. Because the method uses the median, it’s naturally a little more robust against rogue points in the measurement set.
Frequently Asked Questions
📐 Browse all 1000+ Interactive Calculators →
About the Author
Robbie Dickson
Chief Engineer & Founder, FIRGELLI Automations
Robbie Dickson brings over two decades of engineering expertise to FIRGELLI Automations. With a distinguished career at Rolls-Royce, BMW, and Ford, he has deep expertise in mechanical systems, actuator technology, and precision engineering.
Need to implement these calculations?
Explore the precision-engineered motion control solutions used by top engineers.
