Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Circular Ring - Temperature Expansion

Calculate ring (or pipe) diameter expansion or contraction when temperature changes.

Pipe or tube - change in diameter or radius with changed temperature

The circumference of a thin ring, a pipe or tube, can be expressed as

c0 = 2 π r0                                 (1)


c0 = initial circumference (m, inches)

π = 3.14...

r0 = initial radius (m, inches)

The change in circumference due to temperature change can be expressed as

dc = c1 - c

     =  2 π r0 dt α                                 (2)


dc = change in circumference (m, inches)

c1 = final circumference (m, inches)

dt = temperature change (oC, oF)

α = linear expansion coefficient (mm/moC, μin/inoF)

The final circumference can be expressed as 

c1 = 2 π r1                                           (3)


r1 = final radius (m, inches)

Equation 1, 2 and 3 can be expressed as  

dc = 2 π r1 - 2 π r0 

    = 2 π r0 dt α 

or transformed to

r1 = r0 dt α + r0 

    = r0 (dt α + 1)                                    (4)

Equation 4 can be modified with diameters to

d1 = d0 (dt α + 1)                                     (5)

Example - Steel Pipe Diameter Temperature Expansion

A stainless steel pipe with nominal diameter 10 inches (outside diameter 10.750 inches) is heated from 68oF to 98oF. The expansion coefficient for stainless steel S30100 is 9.4 μin/inoF.

The final outside diameter can be calculated

d1 = d0 [dt α + 1]

    = (10.750 in) [((98 oF) - (68 oF)) (0.0000094 in/inoF) + 1]

    = 10.753 inches

Circular Ring - Temperature Expansion Calculator

Calculate the final diameter of a thin circular ring after temperature expansion. The calculator can be used for metric and imperial units as long as the use of units are consistent.

Related Topics

  • Temperature Expansion

    Thermal expansion and expansion coefficients. Expansion pipes and tubes made of stainless steel, carbon steel, copper, plastics and more.

Related Documents


Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .


This page can be cited as

  • The Engineering ToolBox (2010). Circular Ring - Temperature Expansion. [online] Available at: [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter