Measure bias, spread, confidence, and tolerance against target values. Review trends with an interactive graph. Export results quickly for audits, calibration, and reporting tasks.
| Reference | Readings | Mean | Bias | Std. Dev. | CV |
|---|---|---|---|---|---|
| 50.00 kPa | 49.95, 50.03, 50.01, 49.98, 50.02 | 49.998 kPa | -0.002 kPa | 0.032 kPa | 0.064% |
| 100.00 °C | 99.7, 99.8, 100.2, 100.1, 99.9 | 99.94 °C | -0.06 °C | 0.207 °C | 0.207% |
| 10.00 mm | 10.05, 10.06, 10.04, 10.05, 10.05 | 10.05 mm | 0.05 mm | 0.008 mm | 0.080% |
Use the example values to check how low spread improves precision and how low bias improves accuracy.
Mean reading: x̄ = Σx / n
Bias: Bias = x̄ − Reference
Absolute bias: |Bias|
Percent error: |Bias| / |Reference| × 100
Sample variance: s² = Σ(x − x̄)² / (n − 1)
Sample standard deviation: s = √s²
Coefficient of variation: CV = s / |x̄| × 100
Standard error: SE = s / √n
Resolution uncertainty: ures = Resolution / √12
Combined uncertainty: uc = √(SE² + ures²)
Expanded uncertainty: U = k × uc
Approximate confidence interval: x̄ ± 1.96 × uc
RMSE: √[Σ(x − Reference)² / n]
Accuracy reflects closeness to the reference value. Precision reflects closeness among repeated readings. Both matter during calibration, inspection, and process verification.
Accuracy and precision are different but connected. A sensor may repeat nearly identical readings and still miss the target value. That condition shows good precision but poor accuracy. A different instrument may average close to the target while showing wide scatter, which means acceptable accuracy but weak precision.
In calibration work, both properties support decision making. Accuracy helps confirm closeness to the accepted reference. Precision shows repeatability and stability during repeated measurements. When you evaluate both together, you can identify bias, random variation, and the possible impact of resolution limits.
This calculator turns repeated readings into a practical quality review. It summarizes mean, bias, percent error, standard deviation, coefficient of variation, uncertainty, and confidence limits. The export tools help technicians, engineers, auditors, and quality teams keep traceable records for reports and verification files.
Accuracy shows how close the average reading is to the reference value. Lower bias and lower percent error indicate better accuracy in this calculator.
Precision shows how tightly repeated readings cluster together. Lower standard deviation, lower range, and lower coefficient of variation indicate better precision.
Yes. An instrument can repeat nearly the same reading every time while staying offset from the true value. That means low spread but noticeable bias.
Multiple readings reveal random variation. A single value cannot show repeatability, dispersion, or confidence bounds, so repeated measurements give a more reliable assessment.
Expanded uncertainty is the combined uncertainty multiplied by the coverage factor k. It gives a wider interval often used for reporting practical measurement confidence.
Resolution affects the smallest readable change. Adding it improves the uncertainty estimate because display or scale limits contribute to measurement doubt.
The coefficient of variation compares spread to the average reading. It is useful when you want a normalized precision measure expressed as a percentage.
Set tolerance according to your calibration rule, product requirement, or quality procedure. The calculator converts that percent into an absolute acceptance band around the reference.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.