Measurement Uncertainty Calculator

Based on ISO/IEC Guide 98-3 (GUM) principles

Understanding Measurement Uncertainty

Every measurement we make in the laboratory has some degree of uncertainty. Think of it like taking a photo - even with the best camera, there's always some blur or imperfection. Measurement uncertainty helps us understand and quantify these imperfections.

Type A Uncertainty: Random Variations

This comes from repeated measurements of the same thing. Like weighing the same sample multiple times - you'll notice small differences each time. The calculator uses statistical methods to determine how much these variations affect your final result.

Type B Uncertainty: Known System Effects

These are uncertainties we know about from other sources, such as:

  • Calibration certificates
  • Equipment specifications
  • Temperature effects
  • Reference material uncertainties
How to Use This Calculator:
  1. Type A Section: Enter your repeated measurements, one per line. The calculator will determine the uncertainty from these variations.
  2. Type B Section: Add each known source of uncertainty. For each source:
    • Normal distribution: Use for calibration certificates where ± is given (divide the ± value by 2)
    • Rectangular distribution: Use when only a range is known (like temperature effects: ±2°C)
    • Triangular distribution: Use when values near the center are more likely than the extremes
  3. Combined Uncertainty: The calculator combines both types and applies your chosen confidence level (k-factor):
    • k=1: 68% confidence
    • k=2: 95% confidence (most common for reporting)
    • k=3: 99.7% confidence
Quick Tips:
  • Always use at least 10 repeated measurements for Type A if possible
  • Don't forget environmental factors in Type B (temperature, humidity, etc.)
  • Most accreditation bodies expect k=2 (95% confidence) for reporting
  • Document all your uncertainty sources for quality system records
Practice Examples
Example: Metal Content Analysis (mg/L)

A laboratory analyzing the copper content of a water sample.

Type A Data (Repeated Measurements)
5.82
        5.76
        5.85
        5.79
        5.81
        5.78
        5.83
        5.80
        5.77
        5.84
Type B Sources
  • Calibration uncertainty: ±0.15 mg/L (Normal distribution)
  • Reference material purity: ±0.1 mg/L (Rectangular distribution)
  • Temperature effect: ±0.05 mg/L (Rectangular distribution)
Example: Pipette Calibration (µL)

Calibration of a 1000 µL pipette using gravimetric method.

Type A Data (Repeated Measurements)
998.2
        1001.5
        999.8
        1000.3
        997.9
        1001.1
        999.4
        998.7
        1000.6
        999.2
Type B Sources
  • Balance calibration: ±0.2 µL (Normal distribution)
  • Temperature effect: ±0.3 µL (Rectangular distribution)
  • Evaporation: ±0.1 µL (Rectangular distribution)
Example: pH Measurement

pH measurement of an environmental water sample.

Type A Data (Repeated Measurements)
7.41
        7.39
        7.42
        7.40
        7.38
        7.41
        7.40
        7.39
        7.42
        7.40
Type B Sources
  • pH meter calibration: ±0.02 pH (Normal distribution)
  • Buffer uncertainty: ±0.01 pH (Normal distribution)
  • Temperature effect: ±0.015 pH (Rectangular distribution)
Expected Outcomes:

When using these examples with k=2 (95% confidence level), you should expect:

  • Chemical Analysis: Approximately ±0.18 mg/L expanded uncertainty
  • Volume Measurement: Approximately ±2.1 µL expanded uncertainty
  • pH Measurement: Approximately ±0.03 pH expanded uncertainty
Type A Uncertainties (Statistical Analysis)
Type B Uncertainties (Systematic Effects)
Combined and Expanded Uncertainty