Signal Conversion · 4-20 mA · 1-5V · 3-15 psi · 0.2-1.0 bar · Percentage
4-20 mA to 1-5V, 3-15 psi and 0.2-1.0 bar Signal Conversion: Formula, History, Calculator and NAMUR NE43 Fault Zones
A complete guide to converting between all four standard instrumentation signal ranges: where these ranges came from (pneumatic then electronic), the unified linear interpolation formula derived from first principles, an interactive calculator that converts any one signal to all four simultaneously, NAMUR NE43 fault zones for each range, and a full 11-point reference table.
4 to 20 mA Signal Conversion: Introduction
On any given day in a process plant, an instrumentation technician might measure 11.5 mA on a 4-20 mA transmitter loop, see 2.6 V at a DCS input card, watch a pneumatic I/P converter send 8.6 psi to a control valve positioner, or read 0.59 bar on a pneumatic indicator. All four of those readings describe exactly the same process condition: 46.9% of the measurement range. They are the same signal expressed in four different physical forms.
These four signal ranges did not appear by accident. Each arose from a different era of instrumentation technology, became a standard in its time, and remains in use today for specific applications. The 3-15 psi and 0.2-1.0 bar pneumatic ranges were the global standard before electronics, running from the 1940s through the 1970s. The 4-20 mA electronic range replaced pneumatics in the 1970s and remains the dominant field signal worldwide. The 1-5V range is what you get when you pass 4-20 mA through a 250-ohm resistor at the DCS input card.
Understanding that all four are the same percentage on a linear scale means you can convert any one to any other instantly using a single formula. This guide explains that formula from first principles, shows how to apply it to every combination, gives NAMUR NE43 fault zone values for each signal type, and provides a calculator that takes any one signal and outputs all four simultaneously. For background on the 4-20 mA loop itself, see our guide on the 4-20 mA current loop explained.
The unified linear interpolation formula derived from first principles
Why all four ranges represent the same percentage on a linear scale
Converting 4-20 mA to percentage, 1-5V, 3-15 psi and 0.2-1.0 bar simultaneously
Converting in reverse: from any signal back to 4-20 mA
SVG diagram showing all four signals aligned on the same 0-100% scale
Interactive multi-input calculator: enter any one signal, get all four plus percentage
NAMUR NE43 fault zones: what values below 4 mA and above 20 mA mean for each signal
Complete 11-point reference table with fault zone rows highlighted
Where each signal type is still used in process plants today
Why These Four Signal Ranges Exist: A Brief History
The 3-15 psi pneumatic range was established in the 1940s when the ISA (Instrument Society of America, now ISA) standardised pneumatic signal transmission for process control. The minimum of 3 psi (not 0 psi) was chosen deliberately: a live zero. If the signal went to 0 psi it could mean either "0% of range" or "air supply failed or tube broken." With a 3 psi live zero, any signal below 3 psi immediately indicates a fault in the supply or transmission line. This concept of a live zero to enable fault detection became the most important design principle inherited by all subsequent signal standards.
The 0.2-1.0 bar range is simply the metric equivalent of 3-15 psi. When European process industries adopted metric units, 3 psi became approximately 0.207 bar (rounded to 0.2 bar for a clean number) and 15 psi became approximately 1.034 bar (rounded to 1.0 bar). The range is exactly proportional: 0.2 bar and 3 psi both represent 0%, and 1.0 bar and 15 psi both represent 100%.
The 4-20 mA electronic range was introduced in the late 1950s and early 1960s as transistor-based transmitters made electronic field signals practical. Again, the live zero: 4 mA at 0% of range, so that any reading below 4 mA (open circuit, broken wire, transmitter fault) is immediately recognisable as a fault rather than a valid measurement. The range of 16 mA (from 4 to 20) was chosen to be compatible with the power supply voltages and wire resistance levels typical of field instrument installations.
The 1-5V range is not a separate transmitter output standard but rather what appears across the standard 250-ohm input resistor of a DCS or PLC analog input card when 4-20 mA flows through it. At 4 mA: 0.004 A x 250 ohm = 1 V. At 20 mA: 0.020 A x 250 ohm = 5 V. The 250-ohm resistor is the minimum load required for HART communication, and the 1-5V appearing across it is what the ADC inside the input card measures to determine the 4-20 mA value.
The Unified Linear Interpolation Formula
All four signal ranges share a single underlying formula because they all represent the same physical quantity (a process variable from 0% to 100% of range) using different physical units. The formula is simply linear interpolation: where is a given value within its range, expressed as a fraction, mapped onto another range?
The term in brackets is the percentage expressed as a decimal (0.0 to 1.0):
Percentage (%) = [(Input - In_min) / (In_max - In_min)] x 100
Signal range reference values: Signal In_min In_max At 0% At 100%
4-20 mA: 4 mA 20 mA 4 mA 20 mA
1-5 V: 1 V 5 V 1 V 5 V
3-15 psi: 3 psi 15 psi 3 psi 15 psi
0.2-1.0 bar: 0.2 bar 1.0 bar 0.2 bar 1.0 bar
Because all four ranges start at 0% and end at 100%, you can always: 1. Convert input to percentage first 2. Then convert percentage to any output range This two-step approach works for any combination.
1-5 V: V = 1 + [(I - 4) / 16] x 4
3-15 psi: P = 3 + [(I - 4) / 16] x 12
0.2-1.0 bar: B = 0.2 + [(I - 4) / 16] x 0.8
Reverse: converting any signal back to 4-20 mA: From voltage: I = 4 + [(V - 1) / 4] x 16
From psi: I = 4 + [(P - 3) / 12] x 16
From bar: I = 4 + [(B - 0.2) / 0.8] x 16
From %: I = 4 + (% / 100) x 16
Simplification for 4-20 mA to 1-5V: Because (V-1)/4 = (I-4)/16 and R=250 ohm, the relationship V = I(mA) x 0.25 does NOT hold for the offset. Always use: V = 1 + [(I-4)/16] x 4, NOT V = I x 0.25.
All Four Signals on the Same Scale
Figure 1: All four standard instrumentation signal ranges aligned on the same 0-100% scale. Each vertical position represents the same process condition. At 50% of range: 12 mA, 3 V, 9 psi, 0.6 bar are all equivalent. The dashed line at 50% confirms perfect alignment across all four standards.
Worked Examples
Example 1: Convert 14 mA to All Signal Types
% = 62.5%
Step 2: Voltage (1-5V) V = 1 + [(14 - 4) / 16] x 4 = 1 + (10/16) x 4 = 1 + 2.5
V = 3.5 V
Step 3: Pneumatic psi (3-15 psi) P = 3 + [(14 - 4) / 16] x 12 = 3 + (10/16) x 12 = 3 + 7.5
P = 10.5 psi
Step 4: Pneumatic bar (0.2-1.0 bar) B = 0.2 + [(14 - 4) / 16] x 0.8 = 0.2 + (10/16) x 0.8 = 0.2 + 0.5
B = 0.700 bar
Example 2: Convert 9 psi to 4-20 mA and All Other Signals
% = 50.0%
Step 2: mA from percentage I = 4 + (50/100) x 16 = 4 + 8
I = 12.0 mA
Step 3: Voltage V = 1 + (50/100) x 4 = 1 + 2
V = 3.000 V
Step 4: Bar B = 0.2 + (50/100) x 0.8 = 0.2 + 0.4
B = 0.600 bar
Signal Conversion Calculator: Enter Any Signal, Get All Four
Select the signal type you want to enter from the tabs, enter the value, and the calculator outputs the equivalent in all four signal ranges plus percentage. NAMUR NE43 fault status is shown automatically.
NAMUR NE43 Fault Zones: Signals Beyond the Normal Range
NAMUR Recommendation NE43 defines how field instruments should behave when they detect a fault condition. Instead of failing silently to a value within the normal measurement range (which could be mistaken for a valid reading), the transmitter drives the output beyond the normal range to a defined fault zone. This allows the control system to immediately detect a fault versus a valid measurement at the extreme end of range.
| Condition | 4-20 mA | 1-5 V | 3-15 psi | 0.2-1.0 bar | % |
|---|---|---|---|---|---|
| FAULT LOW (open circuit) | below 3.6 mA | below 0.9 V | below 2.7 psi | below 0.19 bar | below -2.5% |
| ALARM LOW (pre-fault) | 3.6 to 3.8 mA | 0.9 to 0.95 V | 2.7 to 2.85 psi | 0.19 to 0.195 bar | -2.5% to -1.25% |
| NORMAL 0% (4 mA live zero) | 4.0 mA | 1.000 V | 3.000 psi | 0.200 bar | 0.0% |
| 25% of range | 8.0 mA | 2.000 V | 6.000 psi | 0.400 bar | 25.0% |
| 50% of range | 12.0 mA | 3.000 V | 9.000 psi | 0.600 bar | 50.0% |
| 75% of range | 16.0 mA | 4.000 V | 12.000 psi | 0.800 bar | 75.0% |
| NORMAL 100% (20 mA) | 20.0 mA | 5.000 V | 15.000 psi | 1.000 bar | 100.0% |
| ALARM HIGH (pre-fault) | 20.0 to 20.5 mA | 5.000 to 5.125 V | 15.0 to 15.375 psi | 1.00 to 1.025 bar | 100.0% to 103.1% |
| FAULT HIGH (short circuit) | above 20.5 mA | above 5.125 V | above 15.375 psi | above 1.025 bar | above 103.1% |
| SATURATION HIGH (max) | 21.0 to 23.0 mA | 5.25 to 5.75 V | N/A (pneumatic) | N/A (pneumatic) | above 106.25% |
Complete 11-Point Signal Conversion Reference Table
| Percentage | 4-20 mA | 1-5 V | 3-15 psi | 0.2-1.0 bar |
|---|---|---|---|---|
| 0% | 4.000 mA | 1.000 V | 3.000 psi | 0.2000 bar |
| 10% | 5.600 mA | 1.400 V | 4.200 psi | 0.2800 bar |
| 20% | 7.200 mA | 1.800 V | 5.400 psi | 0.3600 bar |
| 25% | 8.000 mA | 2.000 V | 6.000 psi | 0.4000 bar |
| 30% | 8.800 mA | 2.200 V | 6.600 psi | 0.4400 bar |
| 40% | 10.400 mA | 2.600 V | 7.800 psi | 0.5200 bar |
| 50% | 12.000 mA | 3.000 V | 9.000 psi | 0.6000 bar |
| 60% | 13.600 mA | 3.400 V | 10.200 psi | 0.6800 bar |
| 70% | 15.200 mA | 3.800 V | 11.400 psi | 0.7600 bar |
| 75% | 16.000 mA | 4.000 V | 12.000 psi | 0.8000 bar |
| 80% | 16.800 mA | 4.200 V | 12.600 psi | 0.8400 bar |
| 90% | 18.400 mA | 4.600 V | 13.800 psi | 0.9200 bar |
| 100% | 20.000 mA | 5.000 V | 15.000 psi | 1.0000 bar |
Where Each Signal Type Is Used in Process Plants Today
| Signal | Where still actively used | Not used for |
|---|---|---|
| 4-20 mA | All modern field instrument transmitters (pressure, flow, temperature, level, analytical). PLC and DCS field wiring for all new installations. The dominant global standard for all new instrumentation. | Long-distance high-speed data. Replaced by fieldbus (Profibus, Foundation Fieldbus) or wireless (WirelessHART) for very large multi-point networks. |
| 1-5 V | Inside control panels at DCS/PLC analog input cards (across 250-ohm input resistor). Short cable runs inside panels. Some dataloggers and indicators with voltage inputs. Not a field wiring standard. | Long cable runs (voltage drops with distance; 4-20 mA is immune to resistance drop). Never wire 1-5V from a transmitter in the field over cable runs of more than a few metres. |
| 3-15 psi | Legacy pneumatic control valves still in service (still very common in older refineries and chemical plants with no capital budget for upgrades). Some new pneumatic valve actuators and positioners accept 3-15 psi directly. Field instruments in hazardous areas where electronics are not permitted or impractical. | New transmitter output standards. New DCS/SCADA installations. Any application where the pneumatic air supply infrastructure is not already installed. |
| 0.2-1.0 bar | Metric equivalent of 3-15 psi. Same applications in metric countries and European plants. Legacy pneumatic valve positioners with metric connections. Pneumatic indicators and controllers still in use in European chemical plants. | New designs. Predominantly a legacy maintenance and replacement context. |
Quick FAQs
- 4-20 mA Current Loop Explained: How It Works, Wiring and Troubleshooting
- 4-20 mA Signal Conversion: Percentage to mA Calculator and Formula
- HART Protocol: How It Works and How to Use a HART Communicator
- Signal-to-Noise Ratio (SNR) in Instrumentation: Formulas and Calculator
- HART Loop Voltage Budget Calculator: Resistance, Voltage Drop and Communication Verdict
What we learn today
- All four signal ranges (4-20 mA, 1-5V, 3-15 psi, 0.2-1.0 bar) represent the same 0-100% process variable on a linear scale. Convert using: % = (Input - Min) / (Max - Min) x 100, then Output = Out_min + (% / 100) x (Out_max - Out_min).
- At 50%: 12 mA = 3 V = 9 psi = 0.6 bar. At 25%: 8 mA = 2 V = 6 psi = 0.4 bar. At 75%: 16 mA = 4 V = 12 psi = 0.8 bar. These anchor points make mental conversion fast in the field.
- NAMUR NE43 fault zones: below 3.6 mA and above 20.5 mA are fault states (transmitter failed). Between 3.6-3.8 mA and 20.0-20.5 mA are alarm states. These apply to 4-20 mA and 1-5V only, not to pneumatic signals.