# Linear to Square Root Extraction Signal Converter: 4-20mA, 3-15 Psi, 1-5 Volt Signals

- In certain applications, pressure measurements are utilized to indirectly determine other variables, such as the rate of flow of a gas or liquid.
- In a closed pipe, the flow rate is directly linked to the square root of the pressure drop, also known as the differential pressure, between two points.
- This relationship is non-linear, meaning that there’s a more significant change in flow at lower pressures compared to higher ones.
- To enhance the resolution of flow measurement, some differential pressure transmitters can be adjusted so that their output is directly proportional to the flow rate rather than the differential pressure.

**Formula for Conversion**

For the conversion of a linear 4-20mA current loop signal to a square root extraction type, the following formula can be applied:

**Output SqRt = 4mA + (4 x √(OutputLinear – 4mA))**

**Example Calculation **

Let’s say we have a linear 4-20mA current loop signal reading of 12mA and we want to convert it to a square root extraction type using the provided formula:

OutputSqRt = 4mA + (4 x √(OutputLinear – 4mA))

Substituting the given value:

OutputSqRt = 4mA + (4 x √(12mA – 4mA))

OutputSqRt = 4mA + (4 x √8mA)

Now, √8mA ≈ 2.83 (approximately)

OutputSqRt = 4mA + (4 x 2.83)

OutputSqRt = 4mA + 11.32mA

OutputSqRt ≈ 15.32mA

So, the square root extraction type output for a linear input of 12mA is approximately 15.32mA.

**Linear Signal to Square Root Extraction Signals Conversion Table**

The conversion table below illustrates the values for linear to square root extraction conversion from 4 to 20 milliamp current loop signals:

Linear (mA) | Square Root (mA) | Square Root (%) | Square Root (psi) | Square Root (V) |

4 | 4.00 | 0.00 | 3.00 | 1.00 |

5 | 8.00 | 25.00 | 6.00 | 2,00 |

6 | 9.66 | 35.36 | 7.24 | 2.41 |

7 | 10.93 | 43.30 | 8.20 | 2.73 |

8 | 12.00 | 50.00 | 9.00 | 3.00 |

9 | 12.94 | 55.90 | 9.71 | 3.24 |

10 | 13.80 | 61.24 | 10.35 | 3.45 |

11 | 14.58 | 66.14 | 10.93 | 3.65 |

12 | 15.31 | 70.71 | 11.49 | 3.83 |

13 | 16.00 | 75.00 | 12.00 | 4.00 |

14 | 16.65 | 79.06 | 12.49 | 4.16 |

15 | 17.27 | 82.91 | 12.95 | 4.31 |

16 | 17.86 | 86.60 | 13.39 | 4.46 |

17 | 18.42 | 90.14 | 13.82 | 4.60 |

18 | 18.97 | 93.54 | 14.23 | 4.74 |

19 | 19.49 | 96.83 | 14.62 | 4.88 |

20 | 20.00 | 100.00 | 15.00 | 5.00 |

**Instrumentation Standard 4 to 20mA Linear Signal to Square Root Extraction Signals**

This below calculator is used for converting instrumentation standard signals from 4 to 20mA Linear Signal to Square Root Extraction 4 to 20 mA, Pneumatic 3 to 15 Psi and voltage 1 to 5 volt Signals

Click here for Square Root Extraction Signal to Linear Signal Converter: 4-20mA, 3-15 Psi, 1-5 Volt Signals

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