What the 4-20 mA Scaling Calculator does
This calculator converts between a process signal and the engineering units it represents: give it the signal type, the range low and high, and either a loop current or a value, and it returns the other one, the percentage of span, a scaling table and what a small loop error is worth in real units.
The arithmetic is a straight line, which is why the mistake people make is never the maths. It is the live zero. On a 4-20 mA loop, 4 mA is 0% of the range, not 20%, so a 0-10 bar transmitter reading 4 mA is at zero bar and one reading 12 mA is at 5 bar. Enter a differential-pressure flow transmitter and the transfer function changes to a square root, where 12 mA is 70.7% of full flow instead of 50%.
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How to use it
- Pick the signal type. 4-20 mA is the default; 0-20 mA, 0-10 V, 1-5 V, 2-10 V, 0-5 V and the legacy 10-50 mA are also there.
- Leave the transfer function on linear unless this is a differential-pressure flow transmitter with square-root extraction in the device rather than in the DCS.
- Enter the range low and high as the transmitter is configured, with the engineering unit. A reverse-acting range (high value at 4 mA) is fine: put the higher number in the low box.
- Choose the direction, then type the loop reading or the engineering value. The answer, the percentage of span and the NAMUR NE 43 status update as you type.
- Open the advanced section to change the number of table rows, or to see what a given loop error - your meter's accuracy, for instance - is worth in engineering units at the point you are working.
Reading the results
Percentage of span is the honest way to compare two instruments. A 0.1 mA error is 0.625% of span on any 4-20 mA loop, whatever the range is set to, but it is 0.0625 bar on a 0-10 bar range and 6.25 bar on a 0-1000 bar one.
The NAMUR NE 43 line tells you what the loop current itself is saying. Between 3.8 and 20.5 mA it is measurement; outside 3.6 to 21.0 mA it is a fault signal. NE 43 is a recommendation, not a law, and transmitters are configurable, so check the device manual before acting on a burnout reading.
When the reading sits outside the configured range the calculator extrapolates the same straight line and says so. Real transmitters usually clamp at their own limits instead, so treat the extrapolated figure as arithmetic rather than as what the instrument would show.
On a square-root range the calculator's error figure changes with where you are: the same 0.01 mA is worth far more at 5 mA than at 18 mA. That is the reason low-flow cut-off exists.
Worked example: a 0-10 bar transmitter reading 12 mA, and the same loop at 3.7 mA
A pressure transmitter is configured 0-10 bar on 4-20 mA. The loop reads 12.00 mA. The signal span is 16 mA, so 12.00 mA is (12 - 4) / 16 = 50.0% of span, and 50% of a 0-10 bar range is 5.00 bar.
A 0.01 mA meter error is 0.01 / 16 = 0.0625% of span, which on this range is 0.00625 bar - comfortably below anything the process cares about.
Later the same loop reads 3.70 mA. The straight line says -0.19 bar, which is not a pressure the sensor can see. NAMUR NE 43 puts 3.70 mA in the under-range band: the transmitter is working but the measurement is below its calibrated range. At 3.50 mA it would instead be a downscale failure signal, and at 21.5 mA an upscale burnout alarm.
Change the transfer function to square root, with a 0-1000 m3/h range, and 12.00 mA stops being 500 m3/h. Flow follows the square root of differential pressure, so 50% of signal is sqrt(0.5) = 70.71% of flow: 707.1 m3/h. Half flow is at 8 mA, not 12.
Formulas and scoring rules
- Signal to value (linear)
value = low + (signal - signalLow) / (signalHigh - signalLow) x (high - low)- Value to signal (linear)
signal = signalLow + (value - low) / (high - low) x (signalHigh - signalLow)- Signal to value (square root)
value = low + sqrt((signal - signalLow) / (signalHigh - signalLow)) x (high - low)Used where the transmitter itself does the square-root extraction on a differential-pressure flow element.- Percentage of span
percent = (signal - signalLow) / (signalHigh - signalLow)For 4-20 mA this is (mA - 4) / 16.- Worth of a signal error
valueError = |value(signal + error) - value(signal)|Evaluated at the point you are working, which matters on a square-root range. Nothing is rounded until it is displayed.
Why the live zero exists at all
A 4 mA floor means a healthy loop always draws current. A broken wire drops to 0 mA, which no valid measurement can produce, so the receiver can tell a genuine zero reading from a dead cable - something a 0-10 V or 0-20 mA signal cannot do. The same 4 mA also powers the transmitter in a two-wire loop, which is why the bottom of the range is 4 rather than 1.
The cost of that safety is the arithmetic everyone gets wrong once. Twenty per cent of the signal range carries no measurement, so any calculation that treats 4 mA as 20% of the engineering range will read high by a fifth of span at the bottom and be correct only at the top. If a value looks exactly one-fifth of span too high, this is nearly always why.
Square-root extraction: in the transmitter or in the system?
With an orifice plate or a venturi, differential pressure is proportional to the square of flow. Somebody has to take the square root, and the only real error is having it done twice or not at all. If the transmitter is set to square-root output, the loop already carries flow and the DCS block must be linear. If the transmitter outputs linear differential pressure, the DCS takes the root.
Done twice, a reading at 50% of signal comes out at 84% of range instead of 71%. Done nowhere, it comes out at 50%. Both look plausible on a trend, which is why the check is to compare a known flow against the calculator rather than to eyeball the screen.
Limitations: what the result does not prove
- This is arithmetic on the numbers you type. It does not know how the transmitter is actually configured - if the range in the device does not match the range you entered here, the answer will be confidently wrong.
- It does not model the transmitter's accuracy, its temperature drift, the analogue input card's resolution or the voltage drop around the loop. Those sit underneath every figure here.
- NAMUR NE 43 bands are the common convention, not a requirement. Devices can be set to downscale or upscale burnout, and some use different thresholds; the manual decides.
- Square-root extraction is modelled as the ideal sqrt relationship. Real transmitters apply a low-flow cut-off and often a linearised segment near zero, so readings below about 5% of signal will not match this page exactly.
Privacy: where your data goes
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Standards and sources
- NIST Technical Note 1297 - Evaluating and expressing measurement uncertainty - checked 19 Sep 2026
- NAMUR NE 43 - Standardisation of the signal level for the failure information of digital transmitters
- IEC 60381-1 - Analogue signals for process control systems: direct current signals
Frequently asked questions
What is 12 mA in engineering units?
On a 4-20 mA loop, 12 mA is exactly half of the signal span, so on a linear range it is the midpoint of the engineering range: 5 bar on 0-10 bar, 50 C on 0-100 C, 50 C on a -50 to 150 C range. On a square-root flow range it is 70.7% of full flow instead.
Why is 4 mA zero and not 20% of the range?
Because the 4 mA is the live zero: the bottom of the measurement, not a measurement of 20%. The percentage is worked out over the 16 mA span between 4 and 20 mA, so (4 - 4) / 16 = 0%. Treating 4 mA as 20% is the single most common scaling error in instrumentation.
What does 3.8 mA mean on a 4-20 mA loop?
Under NAMUR NE 43 it is the bottom edge of valid measurement - slightly below the calibrated range but still real information from a working transmitter. Below 3.6 mA the loop is signalling a failure, and a reading pinned near 3.5 mA usually means downscale burnout has been configured.
How do I scale a reverse-acting 4-20 mA signal?
Put the value that corresponds to 4 mA in the range-low box and the value for 20 mA in the range-high box, even though the first number is larger. The calculator handles the negative span and flags the range as reversed.
Should square-root extraction be in the transmitter or the control system?
In exactly one of them. Most modern practice is to leave the transmitter linear on differential pressure and take the square root in the control system, where the low-flow cut-off and the trend are visible. What matters is that it happens once - doing it twice inflates readings by a large and non-obvious amount.
How accurate is a 4-20 mA loop?
The signal itself is rarely the limit. A 0.01 mA reading error is 0.0625% of span, whereas the transmitter is typically 0.1% of span and its temperature drift can be more over a working year. Use the error box on this page to convert your meter's stated accuracy into the units your process cares about.
Can I use this for 0-10 V or 1-5 V signals?
Yes - pick the signal type and the same straight line applies. Note that 1-5 V is simply a 4-20 mA loop measured across a 250 ohm resistor, which is why it has a live zero and 0-10 V does not.
What current corresponds to a given process value?
Switch the direction to value to signal and type the value. For a linear range the calculator returns signalLow plus the fraction of the engineering range times the signal span - for example 90 C on a -50 to 150 C range is 4 + (140/200) x 16 = 15.2 mA.
Last reviewed by the A2Z.Tools team against the sources listed above.
