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Calibration and Uncertainty Cheat Sheet

Calibration and metrology formulas on one page: errors, hysteresis, combined and expanded uncertainty, distribution divisors, TUR, guard bands and common sensor tolerances.

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Errors

Error % of span	(reading − true) ÷ span × 100
mA error % span	(I − I_expected) ÷ 16 × 100
Error % of reading	(reading − true) ÷ true × 100
Hysteresis	\|R_up − R_down\| ÷ span × 100
Correction	true − reading = −error

5 point test (4 to 20 mA)

%	mA
0	4.000
25	8.000
50	12.000
75	16.000
100	20.000

Test rising then falling; never overshoot a point.

Uncertainty (GUM)

Combined	u_c = √(Σ u_i²)
Expanded	U = k × u_c, k = 2 ≈ 95 %
Type A (mean)	u = s ÷ √n
Std deviation	s = √[Σ(x − x̄)² ÷ (n − 1)]
TPE	√(e₁² + e₂² + …)

Type B divisors

Distribution	u =
Normal (certificate, k given)	U ÷ k
Rectangular (spec, resolution)	a ÷ √3
Triangular	a ÷ √6
U shaped	a ÷ √2
Display resolution r	(r ÷ 2) ÷ √3

Decisions

TUR	tolerance ÷ U₉₅ (aim ≥ 4:1)
Guard band	acceptance = tolerance − U
Pass	\|error\| ≤ acceptance limit

Sensor tolerances

Sensor	Tolerance
Pt100 class AA	± (0.1 + 0.0017 \|t\|) °C
Pt100 class A	± (0.15 + 0.002 \|t\|) °C
Pt100 class B	± (0.3 + 0.005 \|t\|) °C
Type K/N class 1	± 1.5 °C or 0.4 % \|t\|
Type K/N class 2	± 2.5 °C or 0.75 % \|t\|
Gauge class 1.0 (EN 837)	± 1 % of span

Deadweight tester

Pressure	p = m × g_local ÷ A
Local gravity	g ≈ 9.780327 (1 + 0.0053024 sin²φ − 0.0000058 sin²2φ) − 3.086 × 10⁻⁶ h

Good practice

Record as found before adjusting.
Use traceable standards within due date.
Let readings settle; note ambient temperature.
Trend as found errors to set intervals (ILAC G24).

Related Calculators and Tools

Measurement Uncertainty CalculatorFree on instrumentationblog.in Uncertainty Budget ExcelFree on instrumentationblog.in Calibration GlossaryFree on instrumentationblog.in

Frequently Asked Questions

Why divide by √3?

For a rectangular distribution of half width a, the standard deviation is a ÷ √3.

What TUR is enough?

4:1 is a common minimum; below it use guard bands or a better standard.

Is TPE the same as uncertainty?

Both combine errors by root sum of squares; uncertainty follows the GUM method with standard uncertainties.

Learn more on the blog

Calibration traceability: 6 proven links for trusted results

A practical guide on instrumentationblog.in that explains the theory behind this cheat sheet.

Read Full Article

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