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

This is an AMP page - Open full page! for all features.

Volumetric (Cubic) Thermal Expansion

Sponsored Links

Specific volume of a unit can be expressed as

v = 1 / ρ = V / m                                                          (1)


v = specific volume (m3/kg, ft3/lb)

ρ = density (kg/m3, lb/ft3)

V = volume of unit (m3, ft3)

m = mass of unit (kg, lb)

The change in the units volume when temperature changes can be expressed as

dV = V0 β (t1 - t0)                                                        (2)


dV = V1 - V0 = change in volume (m3, ft3)

β = volumetric temperature expansion coefficient (m3/m3 oC, ft3/ft3 oF)

t1 = final temperature (oC, oF)

t0 = initial temperature (oC, oF)

The density of a fluid when temperature changes can be expressed as

ρ1 = m / V0 (1 + β (t1 - t0))

    = ρ0 / (1 + β (t1 - t0))                                                (3)


ρ1 = final density (kg/m3, lb/ft3)

ρ0 = initial density (kg/m3, lb/ft3)

Online Thermal Cubic Expansion Calculator - Expansion coefficient and Temperatures

Be aware that the expansion coefficient for some liquids - like water - may vary with temperature. The calculator below is generic and can be used for metric and imperial units as long as the use of units is consistent.

Note that the volumetric expansion coefficient used in the calculator is constant. If you want to calculate volumetric change for a liquid over a temperature range where the volumetric expansion coefficient for the liquid changes a lot - interpolate the coefficient values, or split the calculation in the different temperature ranges. Example - water is a liquid where the volumetric expansion coefficient changes a lot with temperature. Water has its highest density and smallest volume at 4oC (39.2 oF). The volumetric coefficient for water is negative below 4oC and indicates that the a volume decreases when temperature moves from 0oC (32 oF) to 4oC.

Online Thermal Cubic Expansion Calculator - Densities

This calculator can be used to calculate expansion volume when initial volume and initial and final densities for the liquid are known

Volumetric Temperature Coefficients - β - for some Fluids

  • water at 0oC: -0.000050 (1/oC)
  • water at 4oC: 0 (1/oC)
  • water at 10oC: 0.000088 (1/oC)
  • water at 20oC: 0.000207 (1/oC)
  • water at 30oC: 0.000303 (1/oC)
  • water at 40oC: 0.000385 (1/oC)
  • water at 50oC: 0.000457 (1/oC)
  • water at 60oC: 0.000522 (1/oC)
  • water at 70oC: 0.000582 (1/oC)
  • water at 80oC: 0.000640 (1/oC)
  • water at 90oC: 0.000695 (1/oC)
  • ethyl alcohol: 0.00109 (1/ oC), 0.00061 (1/oF)
  • oil: 0.00070 (1/oC), 0.00039 (1/oF)

Convert between Metric and Imperial Volumentric Temperature Coefficients

  • 1 (1/oC) =  0.56 (1/oF)
  • 1 (1/oF) =  1.8 (1/oC)

Example - Cubic Expansion of Oil

100 liters - 0.1 m3 - of oil with volumetric expansion coefficient 0.00070 1/oC is heated from 20oC to 40oC. The volumetric expansion can be calculated using equation (2)

dV = (0.1 m3) (0.00070 1/oC) ((40 oC) - (20 oC)) 

  = 0.0014 m3

  = 1.4 liter

The final volume is

100 liters + 1.4 liters = 101.4 liters

Example - Cubic Expansion of Oil

30 US gallons of oil is heated from 70oF to 100oF. The volumetric expansion can be calculated using equation (2)

dV = (30 gallons) (0.00039 1/oF) ((100 oF) - (70 oF)) 

    = 0.351 gallons

The final volume is

30 gallons + 0.351 gallon = 30.351 gallons

Sponsored Links

Related Topics


Densities of solids, liquids and gases. Definitions and convertion calculators.


Heating systems - capacity and design of boilers, pipelines, heat exchangers, expansion systems and more.


Work, heat and energy systems.

Water Systems

Hot and cold water service systems - design properties, capacities, sizing and more.

Related Documents

Air - Thermophysical Properties

Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.

Circular Ring - Temperature Expansion

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

Ethylene Glycol Heat-Transfer Fluid Properties

Properties like freezing point, viscosity, specific gravity and specific heat of ethylene glycol based heat-transfer fluids, or brines.

Gravity Heating System

The density difference between hot and cold water is the circulating force in a self circulating gravity heating system.

Hot Water Expansion Tanks - Sizing

Required hot water expansion volume in open, closed and diaphragm tanks.

Linear Thermal Expansion

Online linear temperature expansion calculator.

Liquids - Densities vs. Pressure and Temperature Change

Densities and specific volume of liquids vs. pressure and temperature change.

Liquids - Volumetric Expansion Coefficients

Volumetric - or cubical - expansion coefficients for common liquids.

Propylene Glycol based Heat-Transfer Fluids

Freezing points of propylene glycol based heat-transfer fluids suitable for the food processing industry.

Shrink-Fits Assembly

Assembly temperatures for shrink-fits.

Solids - Volume Temperature Expansion Coefficients

Cubical expansion coefficients for solids.

Thermal Expansion - Linear Expansion Coefficients

Linear temperature expansion coefficients for common materials like aluminum, copper, glass, iron and many more.

Thermal Expansion - Superficial i.e. Area

Superficial i.e area temperature expansion - online calculator.

Water - Thermophysical Properties

Thermal properties of water at different temperatures like density, freezing temperature, boiling temperature, latent heat of melting, latent heat of evaporation, critical temperature and more.

Sponsored Links

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

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 the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.