What’s the Actual Uncertainty?#

Understanding measurement uncertainty beyond just “accuracy.” Every reading has an uncertainty band — a range within which the true value lies. Resolution, accuracy, repeatability, environmental effects, and measurement method all contribute. Knowing how many digits of a reading are real prevents false confidence and unnecessary worry.

Resolution vs. Accuracy vs. Precision#

Example: A 3½-digit DMM on the 4V range:

• Resolution: 1 mV (the last digit)
• Accuracy: ±(0.5% + 3 counts) = ±23 mV on a 4V reading
• Precision: Might repeat within ±2 mV

The display shows 4.000V but true voltage could be 3.977V to 4.023V. Three decimal places look precise, but only first two are reliable.

Calculating Measurement Uncertainty#

DMM voltage measurement:

1. Reading accuracy from spec sheet: ±(% of reading + counts)
2. Temperature coefficient if outside 23°C ±5°C
3. Lead resistance for low-resistance measurements
4. Loading effect from DMM input impedance

Total uncertainty = sqrt(error1² + error2² + …) (for independent random errors)

Or conservative: Total = |error1| + |error2| + …

Oscilloscope amplitude:

1. Vertical accuracy: typically ±3–5%
2. Probe attenuation accuracy: ±1–3%
3. DC offset accuracy

For derived quantities (like power = V × I): %uncertainty_result = sqrt(%uncertainty_V² + %uncertainty_I²)

How Many Digits Are Real?#

Only report digits within instrument uncertainty. If reading is 3.456V and uncertainty is ±0.023V, true value is between 3.433V and 3.479V. Meaningful report: 3.46V ±0.02V.

Digital displays create false precision. A DMM showing “3.3021V” on a 3½-digit meter doesn’t mean voltage is known to 0.1 mV.

Repeatability and Environmental Effects#

Checking repeatability: Measure the same quantity 10 times without changing anything. Calculate standard deviation. This is the random component of uncertainty.

Practical Rules of Thumb#

For bench work, formal uncertainty analysis is usually overkill:

1. DMM DC voltage: Trust to ±1% on name-brand meter
2. DMM resistance: Trust to ±1% above 10 Ohm; below 10 Ohm lead resistance matters
3. Scope amplitude: Trust to ±5%; use scope for shape, DMM for voltage
4. Scope timing: Trust to ±0.01% (50 ppm timebase)
5. Component values: A 5% resistor measuring 4.8% off is within spec
6. Frequency: Scope and counter agreeing within 0.1% probably agree — difference is timebase accuracy

Tips#

• Averaging increases precision (reduces random variation) but not accuracy (doesn’t fix systematic errors)
• Temperature is the biggest environmental factor for most measurements
• Systematic errors (miscalibrated meter) don’t reduce with averaging
• The error budget is the fundamental system-level design tool — allocating allowable error across each stage of the chain, then verifying each stage meets its allocation, is more reliable than testing only the end-to-end result

Caveats#

• A meter consistently 1% high is still 1% high after averaging a thousand readings
• Thermoelectric voltages at dissimilar metal junctions create microvolt offsets — matters for precision DC, not everyday bench work
• Standard deviation larger than instrument resolution indicates external factors (temperature drift, noise, contact resistance)

In Practice#

• Two readings differing by less than combined uncertainty are effectively the same
• Reading fluctuating in last digit is normal — that’s the uncertainty
• Component measuring slightly off from marked value is expected — check against tolerance spec, not exact value
• Measurements that seem “too precise” probably are — more digits than accuracy supports
• Disagreement between instruments within their combined uncertainty specs is not meaningful — both may be correct
• A system that works reliably in the lab but fails during field deployment in a specific geographic region often indicates an environmental factor unique to that region — humidity, temperature, altitude (affecting cooling and dielectric strength), or power quality differences between the lab’s clean power and the field installation’s shared circuit.
• A measurement that’s different every time it’s taken is frequently showing a real variation that the bench environment doesn’t normally expose — supply noise, ground bounce, thermal drift, or electromagnetic coupling that varies with system activity. Averaging the measurements hides the variation; capturing and characterizing it reveals the mechanism.
• A datasheet specification that doesn’t match bench measurements commonly appears when the test conditions in the datasheet don’t match the application conditions. Subsystem-level ICs specify performance under specific external component values, load conditions, and input ranges — measurements taken outside those conditions aren’t datasheet violations; they’re operation outside the specification’s scope.