Relative Error Calculator

Calculate absolute error and relative error to assess measurement accuracy

Calculate Error Analysis

Measured Value

The value obtained from measurement or approximation

Actual (True) Value

The true, real, or accepted reference value

Error Analysis Results

0.700000

Absolute Error

Same units as measurement

0.005776

Relative Error

Unitless ratio

0.578%

Relative Error %

Percentage form

Accuracy Assessment

Good

Good accuracy - Acceptable precision for most applications

Calculation Details

|121.2 - 120.5| = 0.700000

0.700000 / 121.2 = 0.005776

0.005776 × 100% = 0.578%

Formulas Applied

Absolute Error = |Actual Value - Measured Value|

Relative Error = |Absolute Error / Actual Value|

Relative Error % = Relative Error × 100%

Step-by-Step Example

Example Problem

Scenario: Measuring a child's height

Doctor's measurement (actual): 121.2 cm

Home measurement (measured): 120.5 cm

Goal: Determine the accuracy of the home measurement

Solution Steps

Step 1: Calculate absolute error

|121.2 - 120.5| = 0.7 cm

Step 2: Calculate relative error

0.7 / 121.2 = 0.00578

Step 3: Convert to percentage

0.00578 × 100% = 0.578%

Result: The home measurement has a relative error of 0.578%, which indicates very good accuracy.

Accuracy Scale

≤ 0.1%

Exceptional

0.1% - 0.5%

Very Good

0.5% - 1%

Good

1% - 5%

Moderate

5% - 10%

Low

10% - 25%

Poor

> 25%

Very Poor

Types of Error

Absolute Error

• Expressed in measurement units

• Shows magnitude of difference

• Cannot compare across scales

• Formula: |actual - measured|

Relative Error

• Unitless percentage

• Shows proportional accuracy

• Enables cross-scale comparison

• Formula: |absolute error / actual|

Quick Tips

•

Lower relative error indicates higher accuracy

•

Relative error is scale-independent

•

Use relative error to compare measurements

•

Actual value cannot be zero

•

Both errors are always positive

Understanding Relative Error

What is Relative Error?

Relative error, also known as percent error, expresses measurement error as a percentage of the actual value. It provides a standardized way to assess accuracy regardless of the measurement scale or units involved.

Why Use Relative Error?

•Scale-independent comparison
•Universal accuracy assessment
•Easy interpretation (0-100%)
•Quality control standards

Practical Applications

Relative error is widely used across scientific, engineering, and industrial applications to evaluate measurement accuracy, instrument precision, and data quality.

Common Use Cases

•Laboratory measurements
•Manufacturing quality control
•Instrument calibration
•Model validation

Real-world Context

Weighing Apples

Scale: 2 kg ± 1 kg
Relative Error: 50%
Assessment: Unacceptable for retail

Body Weight

Scale: 75 kg ± 1 kg
Relative Error: 1.3%
Assessment: Good for home use

Steel Beam

Scale: 2000 kg ± 1 kg
Relative Error: 0.05%
Assessment: Excellent precision

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