Spherical Radius in GD&T Explained
By Lucas Lo | Updated: June 17, 2025
Table of Contents
As a specific form of arc feature in 3D space, Spherical Radius is a key parameter in defining spherical geometry in engineering manufacturing. This feature’s accurate representation and control directly affect the assembly accuracy, performance, and quality of components.
In this article, the definition of Spherical Radius, engineering specification, application scenarios and machining guidelines will be introduced in detail, and the difference between it and related concepts will be clarified.
1. What is Spherical Radius?
Spherical Radius (SR) is defined as the radial distance extending from a sphere’s geometric center to any point on its circumferential surface.
As a fundamental parameter, it serves to characterize three-dimensional spherical features. It defines the size and curvature of a sphere, denoted by the symbol “SR”—an abbreviation derived from “Spherical Radius”.
Unlike the 2D arc, the Spherical Radius is a 3D radial measurement and is mainly used to characterize ball bearings, spherical joints, dome structures, etc.
Differences from Cylindrical / Radial Features
Characteristic | Spherical Radius | Cylindrical Radius | Plane |
Geometric Domain | Three-dimensional Volume Curvature | Two-dimensional Linear Curvature | Zero-dimensional Flatness |
Degree of Freedom | Radial Symmetry on All Axes | Radial Symmetry on One Axis | No Curvature |
Detection Complexity | Requiring 3D Scanning (Coordinate Measuring Machine) | Measurable by 2D Profilometer | Inspectable via Flatness Gauge |
Failure Mode | Misalignment in Multi-sphere Components | Axial Runout of Rotating Shaft | Wear Caused by Uneven Loading |
2. How to Callout Spherical Radius in Engineering Drawings
Drawing labeling is the key language for communicating Spherical Radius requirements, but ambiguous labeling can lead to costly errors in machining and inspection.
This section delves into the meticulous rules for labeling spherical radii, including dimensioning protocols, tolerance strategies, and conflict resolution in complex geometries.
The labeling of spherical radii in engineering drawings follows strict criteria to differentiate them from 2D arcs and ensure clarity during manufacturing. The specific rules are listed below:
2.1. Core Labeling Elements
2.1.1. Dimensional Labeling Protocol
It must be prefixed: always use “SR”, e.g., SR25.00±0.03mm, to avoid confusion with cylindrical “R” dimensions.
Guide line direction: It should be directed toward the sphere’s surface (not the center) and perpendicular to the tangent at the contact point.
Datum Integration: Associated with the assembly datum, e.g. “SR40mm constrained by datum B plane”.
2.1.2. Tolerance Accumulation Strategy
Combined tolerance: Pairing of spherical radii with geometrical tolerances:
Roundness, e.g. aerospace components ≤ 0.003mm.
Total Indicated Runout (TIR), e.g. rotating spheres ≤ 0.01mm.
Statistical tolerance analysis: Use of Root Sum of Squares (RSS) methodology for assemblies characterized by multiple spherical radii, e.g. ball and socket joints.
2.2. Specific Labeling Rules
The labeling of Spherical Radius (SR) adheres to a hierarchical framework that consolidates feature classification, dimensional precision, and datum correlation.
First line: feature type, quantity and dimension
Symbol: the label “SR” denotes a three-dimensional sphere (e.g. SR25mm).
Quantity: when multiple identical spherical features, use “×” to connect the quantity with the symbol (e.g. 4×SR18mm).
Basic size: indicate the radius value and unit (e.g. SR30mm).
Tolerance labeling: add the tolerance range after the value (e.g. SR15mm ±0.02mm or SR22mm +0.03/-0.01).
Second line: Datum association and geometric tolerance
Datum association: Define the positioning reference with datum symbols, e.g. Ⓐ, Ⓑ, e.g. SR40mm Ⓐ for a sphere centered on datum A.
Geometric Tolerance: Apply a tolerance framework to a spherical feature, e.g. use roundness to control surface uniformity, e.g. SR50mm has a roundness tolerance of 0.01mm.
2.3. Comparison Table of Labeling Examples
Scenario | Annotation Structure | Paraphrase |
Single Spherical Feature | SR20mm | Sphere, SR20mm; no tolerance or datum specified. |
Multiple Spherical Features | 5×SR12mm±0.05mm | Five spheres each with 12mm radius, tolerance ±0.05mm. |
Spherical Surface with Datum Positioning | SR35mm Ⓑ | Sphere with 35mm radius, positioned centered on datum B. |
Spherical Surface with Roundness Control | SR60mm | Sphere with 60mm radius, roundness tolerance 0.03mm. |
2.4. Conflict Resolution in Hybrid Features
When a Spherical Radius coexists with non-spherical elements ,e.g., planes, grooves:
Partition labeling:
Use a chain line to define the Spherical Radius region and label the non-Spherical Radius feature in a separate tolerance block.
Hierarchical datums:
Use primary datums (e.g., center of sphere) and secondary datums (e.g., adjacent planes) to resolve positional ambiguities.
Example:
A valve body with an SR50mm and a tangential plane uses datum A (center of sphere) as the primary reference for positional tolerance and datum B (plane) as the directional reference.
3. Application of Spherical Radius
Industries requiring 3D surfaces widely employ the Spherical Radius (SR) feature to meet critical needs in assembly, performance, and design.This section describes the main features and application scenarios.
3.1. Main Functions of Spherical Radius Feature
Function 1: Precision Assembly and Load Distribution
Spherical surfaces, such as ball bearings and spherical hinges, support multi-directional rotation and self-centering to reduce stress concentration and ensure smooth movement, such as the flexible rotation of the SR10mm ball in a universal joint.
Function 2: Surface Optimization and Wear Resistance
Spherical Radius eliminates sharp edges, improves surface finish and reduces friction, such as the SR5mm design of medical probe tips to avoid tissue damage.
Function 3: Aerodynamic and Structural Design
In aerospace and automotive applications, spherical features optimize airflow or structural strength, such as the SR200mm dome of an aircraft porthole to withstand differential pressure.
3.2. Application Scenarios
Mechanical Components: Spherical bearings in automotive suspensions, e.g. SR25mm, allow for angular misalignment and enhance ride comfort.
Medical equipment: Spherical tips for surgical instruments, e.g. SR3mm, ensure precise handling and minimize trauma.
Electronics and consumer goods: Spherical buttons for electronic devices, e.g. SR8mm, improve tactile feedback and durability.
New energy field: electric vehicle motor rotor spherical bearings, such as SR18mm, use ceramic coatings combined with high-precision control of the Spherical Radius, with roundness ≤ 0.005mm, which reduces friction loss at high speeds and improves range.
Micro-Nano Manufacturing: miniature spherical structures in MEMS (Micro-Electro-Mechanical Systems), such as SR50μm sensor probes, need to be processed by Focused Ion Beam (FIB) to achieve nanoscale curvature control.
4. Methods for Measuring Spherical Radius
There are 4 equipments to check SR. We will use the following table to show them and explain their advantages and disadvantages.
| Method | Description | Recommended For |
| CMM (Coordinate Measuring Machine) | Measures multiple points on the spherical surface using a probe. The software fits a sphere and calculates center, radius, and sphericity. Highly accurate and widely used in aerospace, medical, and precision tooling industries. | High-precision parts, full 3D analysis |
| Radius Master Gauge / Ball Gauge | A physical gauge with a known spherical radius is placed against the part to visually check conformity. Quick and easy to use, ideal for workshop floor or incoming inspection, but does not provide actual numerical data. | Quick pass/fail inspection |
| Optical Comparator (Profile Projector) | Projects and magnifies the spherical profile for visual comparison or software-assisted curve fitting. Non-contact method, good for small or transparent parts, but limited to partial profile measurement. | Small or delicate parts with visible curves |
| Contour Measuring Machine (Profilometer) | Uses a stylus to scan the curved surface and generates a profile. The software fits the curve to determine radius and curvature continuity. Suitable for analyzing transitions and complex surface blends. | Mold surfaces, decorative curved parts |
5. Spherical Radius VS Sphere Diameter
Spherical Radius and diameter characterize a sphere, but there are differences in definition, labeling, and application. The subsequent content elaborates on the distinctions in detail:
5.1. Definitions
The spherical radius (SR) denotes the distance from a sphere’s center to its surface, exemplified by SR30mm for a sphere with a 30mm radius.
Spherical Diameter (S⌀): the bi-directional distance through the center of the sphere, equal to 2 x SR (e.g. S⌀60mm = 2 x SR30mm).
5.2. Callout
Spherical radius: prefix “SR” (e.g. SR40mm).
Spherical diameter: Prefix “S⌀” (e.g. S⌀80mm).
5.3. Application
Spherical radius: more suitable for defining curvature and surface geometry, e.g. ball bearing SR15mm.
Spherical diameter:It is used to specify overall dimensions and guide tool selection. For example, machining an S⌀20mm hole requires a drill with a matching diameter.
6. Conclusion
The spherical radius plays a key role in 3D geometric design and is essential to precision manufacturing across a wide range of industries.
Understanding how to identify, apply, and measure spherical radii, enables engineers and machinists to ensure accuracy, performance, and consistency in spherical components.
Lucas is a technical writer at ECOREPRAP. He has eight years of CNC programming and operating experience, including five-axis programming. He also spent three years in CNC engineering, quoting, design, and project management. Lucas holds an associate degree in mold design and has self-taught knowledge in materials science. He’s a lifelong learner who loves sharing his expertise.
