The consistency of bias across the full operating range of a measurement instrument. An instrument with good linearity has the same amount of error at every point in its range.
Linearity describes whether the bias of a measurement instrument remains constant throughout its measurement range. An instrument with perfect linearity has the same offset (or zero offset) at every point from the bottom to the top of its range. Poor linearity means the error varies — the instrument might read accurately at low values but show increasing bias at higher values, or vice versa.
Linearity is assessed by measuring known reference values distributed across the instrument's full range and plotting the errors against the reference values. If the resulting error plot shows a flat, horizontal line near zero, linearity is good. If the errors form a sloped line, a curve, or show irregular patterns, linearity is poor. Statistical analysis of the regression line through these error points quantifies linearity.
In calibration management, linearity is critical because instruments are often calibrated at only a few discrete points across their range. If linearity is good, calibration at a handful of points gives confidence that the instrument performs well everywhere in between. If linearity is poor, more calibration points are needed, or the usable range of the instrument may need to be restricted. Poor linearity that cannot be corrected by adjustment is often a sign of wear or damage requiring repair or replacement.
In aerospace calibration labs, linearity verification is critical when calibrating pressure transducers used in flight test applications. For a 0-3000 psi transducer, technicians test at 0, 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700, and 3000 psi points. Good linearity means the bias remains consistent—if there's a +2 psi error at 300 psi, it should be approximately +2 psi at 2700 psi. Poor linearity might show +1 psi at low pressures but +5 psi at high pressures. In medical device labs, linearity testing of temperature controllers for sterilization equipment is essential. A controller displaying 121°C must maintain the same accuracy offset whether the actual temperature is 60°C or 134°C. Non-linear behavior could mean acceptable accuracy during qualification but dangerous inaccuracy during actual sterilization cycles. Poor linearity documentation led to a major aerospace supplier's AS9100 finding when their torque wrench calibrations showed acceptable overall accuracy but hidden non-linearity that caused fastener under-torquing at critical load points. The finding required complete recalibration of 200+ tools and review of six months of assembly records.
ISO/IEC 17025:2017 addresses linearity in Section 7.2.2.1(e), requiring labs to validate measurement procedures including linearity checks when applicable. AS9100D references this through its calibration requirements in Section 7.1.5, where aerospace suppliers must demonstrate measurement system linearity for critical applications. ISO 13485:2016 Section 7.6 requires medical device manufacturers to validate measurement equipment linearity when it affects product safety or performance. The GUM (ISO/IEC Guide 98-3) discusses linearity in uncertainty evaluation, particularly in Section 4.2.7 regarding systematic effects. ANSI/NCSL Z540.3-2006 Section 4.3.3 requires linearity assessment during calibration interval studies. IATF 16949:2016 references measurement system analysis including linearity studies per Section 7.1.5.2.1. During audits, assessors look for documented linearity verification procedures, evidence of linearity testing at multiple points across the measurement range, and proper handling of non-linear instruments through curve-fitting or segmented calibration approaches.
CalibrationOS addresses linearity through its Advanced Measurement Analysis module, which automatically calculates linearity metrics during multi-point calibrations. When technicians enter measurement data at multiple reference points, the system computes best-fit lines, residual errors, and linearity coefficients according to ISO/IEC Guide 98-3 requirements. The Certificate Generation engine includes linearity plots and statistical summaries, showing deviation from the best-fit line at each test point. The Uncertainty Calculator incorporates linearity contributions into expanded uncertainty calculations automatically. During audit preparation, the Compliance Dashboard generates linearity trend reports across instrument families, highlighting instruments requiring attention. The system flags instruments exceeding linearity specifications and triggers automatic work orders for investigation. Calibration certificates include graphical linearity plots and tabulated residual data, providing auditors with clear evidence of linearity verification. The module also supports segmented linearity analysis for instruments with inherent non-linear behavior, documenting appropriate calibration approaches for regulatory compliance.
Linearity is the consistency of measurement error across an instrument's full operating range. Good linearity means the instrument's bias is the same at all measurement points; poor linearity means error varies with the measured value.
Linearity is tested by measuring reference standards at multiple points across the instrument's range, calculating the error at each point, and analyzing whether the errors remain consistent or vary systematically.
This article is licensed CC BY-SA 4.0. Share, adapt, and reuse with attribution to calibrationos.com/glossary/linearity.
Industry benchmarks, best practices, and calibration tips — delivered to your inbox.
Free calibration management software with audit-ready tracking, uncertainty budgets, and compliance tools.
Start Free — No Credit Card