# Thermal Expansion Measurement Error Calculator > Source: https://netray.co/tools/thermal-expansion-measurement-error-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Find the measurement error caused by part and gage temperatures that differ from the 20 C reference, using each material's expansion coefficient. ## Category quality ## Industry Precision Manufacturing ## Audience - Metrologist - Inspection technician - Quality engineer ## Tool **Kind:** calculator **Inputs:** #### Nominal length **Key:** len **Type:** number **Default:** 300 **Min:** 0 **Step:** 10 **Unit:** mm #### Part expansion coefficient **Key:** a_part **Type:** select **Default:** 11.5 **Options:** ##### Carbon steel, 11.5 ppm/C **Value:** 11.5 ##### Stainless 304, 17.3 ppm/C **Value:** 17.3 ##### Aluminum, 23 ppm/C **Value:** 23 ##### Titanium, 8.6 ppm/C **Value:** 8.6 #### Gage scale expansion coefficient **Key:** a_gage **Type:** select **Default:** 11.5 **Options:** ##### Steel, 11.5 ppm/C **Value:** 11.5 ##### Granite or ceramic, 5 ppm/C **Value:** 5 ##### Glass scale, 8 ppm/C **Value:** 8 ##### Invar, 1.2 ppm/C **Value:** 1.2 #### Part temperature **Key:** t_part **Type:** slider **Default:** 24 **Min:** 10 **Max:** 40 **Step:** 0.5 **Unit:** C #### Gage temperature **Key:** t_gage **Type:** number **Default:** 21 **Min:** 10 **Max:** 40 **Step:** 0.5 **Unit:** C #### Total tolerance **Key:** tol **Type:** number **Default:** 50 **Min:** 0 **Step:** 1 **Unit:** um **Outputs:** #### Part length change from 20 C **Key:** part_dev **Expr:** len * a_part * (t_part - 20) / 1000 **Format:** decimal **Description:** In micrometers. #### Gage scale change from 20 C **Key:** gage_dev **Expr:** len * a_gage * (t_gage - 20) / 1000 **Format:** decimal **Description:** In micrometers, reads short when the scale has grown. #### Net measurement error **Key:** net **Expr:** part_dev - gage_dev **Format:** decimal **Primary:** true **Description:** Micrometers. Positive means the part reads larger than its 20 C size. #### Error as share of tolerance **Key:** pct **Expr:** abs(net) / tol * 100 **Format:** percent **Primary:** true **Chart:** #### Net error vs part temperature **Type:** line **X:** t_part **From:** 15 **To:** 35 **Steps:** 20 **Series:** - net **Disclaimer:** First-order linear model for temperatures near 20 C. It ignores temperature gradients, fixture expansion and the uncertainty of the coefficients themselves. ## Content **Intro:** Dimensions are defined at 20 C, but shops measure at 22, 25 or 30 C. Metal grows, the gage scale grows too, and the difference becomes error. This calculator shows how large it is for your length and materials. **Sections:** #### How to use it **Body:** Enter the length, then select the part material and the gage scale material from the lists. Set the part temperature and the gage temperature, since they are often different after a part comes from a machine or the gage sits in a case. Enter the tolerance in micrometers to see the error as a share. The chart sweeps part temperature so you can pick a soak time or room limit that keeps thermal error under a target fraction of tolerance. **Bullets:** - Measure the part surface with a contact thermometer, not the room air. - Let parts soak to room temperature before critical measurement. - Use compensation only when the coefficient is known well. #### The formula **Body:** Length change equals length times expansion coefficient times temperature difference from 20 C. The part grows by its own coefficient, and the gage scale grows by its coefficient, so the reading is the part change minus the scale change. When part and gage are the same material and the same temperature, errors cancel, which is why comparison against a same-material master works well. Different materials and temperatures leave a net error that scales with length. #### Worked example **Body:** A 300 mm aluminum part measured at 24 C with a steel scale at 21 C. The part is 4 C above reference, so it grows 300 times 23 times 4 divided by 1000, about 27.6 micrometers. The scale grew 300 times 11.5 times 1 divided by 1000, about 3.5 micrometers. Net error is 24.1 micrometers, nearly half of a 50 micrometer tolerance. Soaking the part to 21 C would reduce it to about 2 micrometers. #### Common mistakes **Body:** Many people assume that only the room temperature matters. The part temperature after machining, handling in warm hands or coolant residue can differ by several degrees from the room. Another mistake is using the wrong coefficient, since alloys vary, and aluminum alloys range from about 21 to 24 ppm per degree C. Finally, do not apply software compensation without a calibrated temperature sensor, or you replace a known error with an unknown one. **Cta:** If inspection results in your ERP lack temperature context, we can help capture environmental readings with the measurement record. **Faq:** #### Why is 20 C the reference temperature? **Answer:** ISO 1 sets 20 C as the standard reference temperature for geometrical product specifications and dimensional measurement, so drawings and gage calibrations refer to that condition. #### When can I ignore thermal error? **Answer:** For short lengths with tight tolerances you usually cannot. A 25 mm steel part 5 C warm grows about 1.4 micrometers. For long parts or low-expansion gages, it quickly becomes significant. #### Does it matter if part and gage are the same material? **Answer:** Yes, when both are at the same temperature the thermal growth cancels in a comparison measurement. Differences in temperature or material break that cancellation. #### Can I include this in an uncertainty budget? **Answer:** Yes. Estimate the temperature range and coefficient uncertainty, then treat the resulting length change as a rectangular or normal contributor in your budget. ## Search terms thermal expansion measurement error, 20 c reference temperature, cmm temperature compensation, dimensional measurement temperature error, coefficient of thermal expansion steel aluminum, inspection room temperature, iso 1 reference temperature, temperature effect on gage --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json