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

In various industrial applications, square root extraction signals are often employed to represent physical quantities such as flow rates or pressure differentials. However, in certain situations, it may be necessary to convert these square root extraction signals back into linear signals for compatibility with standard instrumentation.

**Conversion Formula**

To convert a square root extraction signal to a linear signal within the 4-20mA range, the following formula can be utilized:

**OutputLinear=((***OutputSqRt***−4***mA***)/4)**^{2}**+4***mA*

**Example Calculation**

Let’s assume we have a square root extraction signal reading of 16mA and we aim to convert it into a linear signal using the provided formula:

OutputLinear=((16mA−4mA)/4mA)^{2}+4mA

OutputLinear=(12mA/4mA)^{2}+4mA

OutputLinear=(3mA)^{2}+4mA

OutputLinear=9mA+4mA

OutputLinear=13mA

Therefore, the linear signal equivalent for a square root extraction signal of 16mA is 13mA.

**Conversion Table**

The table below illustrates the conversion values from square root extraction signals to linear signals within the 4-20mA range:

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

4.00 | 4.00 | 0.00 | 3.00 | 1.00 |

5.00 | 4.06 | 0.39 | 3.04 | 1.07 |

6.00 | 4.25 | 1.56 | 3.19 | 1.06 |

7.00 | 4.56 | 3.52 | 3.42 | 1.14 |

8.00 | 5.00 | 6.25 | 3.75 | 1.25 |

9.00 | 5.56 | 9.76 | 4.17 | 1.39 |

10.00 | 6.25 | 14.06 | 4.69 | 1.56 |

11.00 | 7.06 | 19.14 | 5.30 | 1.77 |

12.00 | 8.00 | 25.00 | 6.00 | 2.00 |

13.00 | 9.06 | 31.64 | 6.80 | 2.27 |

14.00 | 10.25 | 39.06 | 7.69 | 2.56 |

15.00 | 11.56 | 47.30 | 8.67 | 2.89 |

16.00 | 13.00 | 56.25 | 9.75 | 3.25 |

17.00 | 14.56 | 66.02 | 10.92 | 3.64 |

18.00 | 16.25 | 76.56 | 12.19 | 4.06 |

19.00 | 18.06 | 87.89 | 13.54 | 4.52 |

20.00 | 20.00 | 100.00 | 15.00 | 5.00 |

**Instrumentation Standard Square Root Extraction Signal to Linear Signal Converter**

The following calculator serves to convert instrumentation standard square root extraction signals to linear signals within the 4-20mA range, pneumatic signals ranging from 3 to 15 Psi, and voltage signals spanning from 1 to 5 volts.

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

Click here for more **Instrumentation Calculators**