Repeat strip and uncertainty contributionsCurrent records, mean, interval, and component widths
Unit Converters
Illuminance Precision Calculator
Preserve repeated lux readings and combine repeatability, display quantization, and calibration standard uncertainty without claiming that repeatability alone proves accuracy.
REPEAT MEASUREMENT PRECISION
Separate scatter of readings from resolution and calibration evidence
This calculator is for technicians and metrology-aware reviewers summarizing repeated lux readings at one stable point. It reports a Type A contribution for the mean and combines only the uncertainty components entered.
Minimum evidence: at least two nonnegative readings under repeat conditions. Calibration input is a standard uncertainty; do not enter an expanded value without first converting it.
Mean illuminance—
Expanded uncertainty—
Expanded interval—
Sample standard deviation—
Relative standard deviation—
Reading count—
READINGS AND BUDGET
See repeat scatter and entered uncertainty sources together
The upper strip preserves every reading against the mean and expanded interval. The lower composition compares standard-uncertainty magnitudes; the exact variance terms remain in the table.
| Record | Reading | Residual | Interval state |
|---|
| Component | Standard uncertainty | Variance |
|---|
HOW TO USE
Preserve the measurement conditions
- Repeat the meter placement, orientation, source state, ambient condition, and settling time.
- Enter readings in acquisition order so drift or alternating resolution patterns remain visible.
- Enter the smallest display increment as resolution, not the number of decimal places.
- Convert certificate uncertainty to a standard uncertainty before entering the calibration component.
- Interpret the mean and expanded interval separately from bias, reproducibility, and method validity.
PRECISION FUNDAMENTALS
Six quantities answer different questions
CALCULATION METHOD
Combine variances only after defining each component
x̄ = Σxi/ns = √[Σ(xi−x̄)²/(n−1)]uA = s/√nures = q/√12uc = √(uA² + ures² + ucal²)U = kuc
REPEATABILITY VERSUS ACCURACY
A tight cluster can still be biased
Repeatability describes variation under specified close conditions. A stable offset, spectral mismatch, cosine-response error, or calibration bias can move every reading together while leaving standard deviation small. Treat the calibration term and other bias evidence independently.
SEQUENCE EVIDENCE
Residual order can reveal what one statistic hides
Alternation may indicate display quantization; a monotonic sequence may indicate warm-up or daylight drift; clusters may identify repositioning or operator states. Never delete a reading merely to improve RSD. Apply any exclusion rule to the original sequence and retain both records.
UNCERTAINTY SCOPE
The root-sum-square is conditional on the component model
The calculation assumes the entered standard components are independent enough for quadrature. It omits positioning, cosine response, spectral mismatch, ambient subtraction, source instability, temperature, and reproducibility unless they are represented in the calibration input—which should be documented, not assumed.
DETAILED CALCULATION PROCESS
Default three-reading substitution
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| xi | Readings | 500, 510, 490 | lx |
| q | Resolution | 1 | lx |
| ucal | Calibration standard uncertainty | 5 | lx |
| k | Coverage factor | 2 | dimensionless |
- Mean = (500 + 510 + 490)/3 = 500 lx.
- Residuals are 0, +10, and −10 lx.
- Sample deviation = √[(0²+10²+10²)/2] = 10 lx.
- Type A of mean = 10/√3 = 5.7735 lx.
- Resolution standard uncertainty = 1/√12 = 0.2887 lx.
- Combined standard uncertainty = √(5.7735²+0.2887²+5²) = 7.6431 lx.
- Expanded uncertainty = 2 × 7.6431 = 15.2862 lx.
- Reconciliation: interval endpoints average back to 500 lx.
RESULT INTERPRETATION
Read scatter, mean uncertainty, and coverage separately
Sample deviation describes individual spread. Type A uncertainty decreases with sample size only when additional readings are genuinely representative. Expanded uncertainty depends on the selected k and included components. A zero mean makes RSD undefined; it does not make the absolute uncertainty disappear.
EVIDENCE AND DATA LINEAGE
Keep the complete measurement record
Retain every reading, sequence, unit, meter and serial number, calibration certificate and date, certificate coverage factor, range, display resolution, source stabilization, geometry, operator, ambient-light method, temperature, and any documented exclusion.
LIMITS AND EXCLUSIONS
What this repeat model does not establish
- No normality test or outlier test is applied.
- No reproducibility or inter-instrument effect is estimated.
- No spectral or cosine-response correction is calculated.
- No bias correction is inferred from repeat scatter.
- The entered components are not a complete uncertainty budget by default.
WORKED DECISION CASES
Different evidence produces different actions
Stable bench source
Scatter is small, calibration dominates, and the expanded interval is adequate for a planning comparison. More repeated readings would barely reduce the governing component.
Daylit workplane
Readings rise monotonically as daylight changes. Treating them as stationary repeats understates temporal variation; redesign the sampling window before quoting precision.
TECHNICAL GLOSSARY
Measurement terms
- Repeatability
- Precision under specified close conditions.
- Residual
- Reading minus the mean.
- Type A evaluation
- Uncertainty evaluated statistically.
- Standard uncertainty
- Uncertainty expressed as a standard deviation.
- Expanded uncertainty
- Combined standard uncertainty multiplied by k.
- Resolution
- Smallest displayed increment.
- Bias
- Systematic difference from a reference.
- RSD
- Sample deviation divided by mean.
IMPORTANT NOTE
Do not use repeated readings to manufacture confidence
Increasing n reduces the Type A term only under a defensible repeat model. It cannot erase bias, changing illumination, poor geometry, or missing uncertainty components.
Frequently asked questions
Why require at least two readings?
Sample standard deviation needs at least two records.
Should calibration uncertainty be divided by k?
Yes, when a certificate reports an expanded uncertainty with coverage factor k.
Why is resolution divided by √12?
A rounding interval of one display step has standard uncertainty step/√12 under a uniform model.
Can I remove an outlier?
Only under a documented rule, while retaining the original record.
Does more data always reduce uncertainty?
Only the Type A mean term, and only under stable representative repeats.
Why can RSD be undefined?
Division by a zero mean has no finite relative interpretation.
Does k=2 mean exactly 95%?
Not without distribution and effective-degrees-of-freedom justification.
Does this certify the meter?
No. It summarizes entered evidence; calibration status is external.
AUTHORITATIVE BASIS
SI unit context
- BIPM SI Brochure — SI quantity and unit framework.
- BIPM realization of the lux.