# Process Perfect: Calibration Error Calculator for Instruments

The Calibration Error Calculator is a tool designed to determine the accuracy of measurement devices with linear input and output characteristics.

This calculator assists in assessing the calibration error by quantifying the difference between the actual measured output and the ideal output for a specific input value.

## Input Section

• Enter the input value measured or recorded using a calibrator or another reference instrument with higher accuracy compared to the device under calibration test.
• Ensure that all input values are in the same engineering units.

### Lowest Input value:

• Input the lowest possible value that the unit under test was designed(ranged) to measure.
• Ensure that all input values are in the same engineering units.

### Highest Input value:

• Input the highest possible value that the unit under test was designed(ranged) to measure.
• Ensure that all input values are in the same engineering units

## Output Section

• Enter the output value measured or recorded with a calibrator or another reference instrument with higher accuracy than the device under test.
• If the device under test provides a visual display, use the displayed measurement. Make sure that all output values are in the same engineering units.

### Lowest Output value:

• Input the lowest possible output value that the device under test was designed(ranged) to produce.
• Ensure that all output values are in the same engineering units.

### Highest Output value:

• Input the highest possible output value that the device under test was designed(ranged) to produce.
• Ensure that all output values are in the same engineering units.

## Error Section

### Ideal Output:

• This indicates the theoretical output reading that would be generated if the device under test were perfectly precise. This value is compared to the actual “Output Reading” to determine the output “Error Value” of the device under test at a specific calibration point.

### Error Value:

• Represents the difference between the actual “Output Reading” and the “Ideal Output.” It is presented in the same engineering units as the output.

### %FS Value:

• Displays the output error as a percentage of the full-scale range, calculated as the “Error Value” divided by the difference between “Lowest Output” and “Highest Output.”

By following this user guide, you can effectively use the Calibration Error Calculator to assess the accuracy of your measurement devices.

## Formula for calculations

Ideal output value = (Measured input Value – Lower input value) / (Upper input Value – Lower input Value ) * (Upper Range output Value – Lower Range output Value) + Lower Range output value.

Calibration Error = Measured Value – Reference Value.

Calibration Error (%FS) = (Calibration Error/ (Upper Range Value – Lower Range Value)) * 100.

## Example calculation

To calculate the calibration error in milliamps (mA) and as a percentage of the full scale (%FS) for the pressure transmitter when it measures 2.5 bar and produces a 12.12 mA output within a range of -0.5 bar to 5.5 bar with a 4-20 mA output, follow these steps:

Given values:

• Measured Value (mA): 12.12 mA
• Input Pressure (bar): 2.5 bar
• Lower Range Value (mA): 4 mA (minimum in a 4-20 mA range)
• Upper Range Value (mA): 20 mA (maximum in a 4-20 mA range)
• Lower Pressure (bar): -0.5 bar (minimum pressure)
• Upper Pressure (bar): 5.5 bar (maximum pressure)

### Step 1: Calculate the Calibration Error in mA:

Calibration Error (mA) = Measured Value – Reference Value

Calibration Error (mA) = 12.12 mA – (Conversion from pressure to mA)

To convert the measured pressure (2.5 bar) to mA within the given range:

Pressure (bar) = (Measured Value – Lower Pressure) / (Upper Pressure – Lower Pressure) * (Upper Range Value – Lower Range Value) + Lower Range Value

Pressure (bar) = (2.5 bar – (-0.5 bar)) / (5.5 bar – (-0.5 bar)) * (20 mA – 4 mA) + 4 mA

Pressure (bar) = 3.0 bar / 6.0 bar * 16 mA + 4 mA

Pressure (bar) = 8.0 mA + 4 mA

Pressure (bar) = 12.0 mA is the ideal output.

Now, calculate the calibration error:

Calibration Error (mA) = Measured Value – Reference Value

Calibration Error (mA) = 12.12 mA – 12.0 mA

Calibration Error (mA) = 0.12 mA

### Step 2: Calculate the Calibration Error as a Percentage of Full Scale (%FS):

Calibration Error (%FS) = (Calibration Error (mA) / (Upper Range Value – Lower Range Value)) * 100

Calibration Error (%FS) = (0.12 mA / (20 mA – 4 mA)) * 100

Calibration Error (%FS) = (0.12 mA / 16 mA) * 100

Calibration Error (%FS) = 0.75%

So, the calibration error for the pressure transmitter, when it measures 2.5 bar and produces a 12.12 mA output within a range of -0.5 bar to 5.5 bar with a 4-20 mA output, is approximately 0.12 mA and approximately 0.75% of the full scale range.

## Calibration Error Calculator

This below calculator is used to assists in assessing the calibration error by quantifying the difference between the actual measured output and the ideal output for a specific input value.