4–20 mA Scaling Calculator
Signal to value and back, loop resistance, sense resistors and ADC resolution.
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- Free preview: the NE 43 and loop checks and the names of the table’s first rows (up to 3), with the result of the mode you use, the working and every figure hidden.
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Result
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the 4–20 mA Scaling Calculator
Scale an instrument signal to its engineering value or back, for 4–20 mA, 0–20 mA, 0–10 V, 1–5 V, 0–5 V, 2–10 V, ±10 V, raw ADC or PLC counts or any range you type, linear or with square-root extraction for flow from differential pressure. Reverse-acting ranges (20 mA = 0 %) work too, and every 4–20 mA value is checked against the NAMUR NE 43 signal levels for failure information.
Two more modes design the circuit around it. Loop & sense resistor works out the largest loop resistance a supply can drive at the highest current you need, the voltage left for the transmitter, the sense resistor for your input’s range with the nearest E96 and E24 values, its voltages and power, and the longest cable that still works. ADC resolution gives the LSB size, how many codes the signal really uses, the resolution in engineering units and the ideal SNR of 6.02·N + 1.76 dB.
Without a pass, the free preview runs on your own signal: it shows the NE 43 and loop checks and the first rows of the table, with the result of the mode you use, every other figure and the working hidden; the full result, Copy result and the CSV come with a Pro pass.
How to use it
- Choose Scaling, Loop & sense resistor or ADC resolution.
- Scaling: pick the signal type, type the engineering values at the bottom and the top of the range and their unit, choose linear or square root, and type the signal (or the value, after switching the direction).
- Loop: enter the supply, the transmitter’s minimum voltage from its datasheet, the highest current to allow for, the sense resistor (or the voltage your input should see at 20 mA, to size it) and any other devices, and the cable length and conductor size.
- ADC: enter the converter’s bits and input range and the part of it the signal uses. Read the result and the working, then copy it or download the table as CSV — with a pass, or after unlocking this result.
Examples
12 mA on a 4–20 mA, 0–10 bar range
5 bar (50 % of span)
7.2 mA on 0–100 °C
20 °C; and 75 °C is 16 mA
8 mA on a range from 100 % (4 mA) to 0 % (20 mA)
75 %
8 mA, square root, 0–100 m³/h
50 m³/h: 25 % of the Δp span is √0.25 = 50 % of flow
24 V, 10.5 V lift-off, 21 mA, 250 Ω, 300 m of 1 mm² copper
At most 642.9 Ω; the loop has 260.3 Ω, so 382.5 Ω to spare and 18.53 V for the transmitter
5 V at 20 mA
250 Ω; the nearest E96 value, 249 Ω, gives 4.980 V
12 bits, 0–5 V input, 1–5 V signal, 0–10 bar
3,276.8 codes, 0.00305 bar per code, ideal SNR 74.0 dB
The scaling formulas
- Linear: value = EU_low + x·(EU_high − EU_low), where x = (signal − signal_low) ÷ (signal_high − signal_low) is the fraction of the span. The other way round, signal = signal_low + x·(signal_high − signal_low).
- Square root: value = EU_low + √x·(EU_high − EU_low). A differential-pressure flowmeter’s Δp grows with the square of the flow, so 25 % of the Δp signal is 50 % of the flow; below zero the flow reads zero, as a low-flow cut-off does.
- Standard ranges: currents of 4–20 mA and 0–20 mA and voltages such as 0–10 V, 1–5 V and 2–10 V are the standard analogue signals of IEC 60381. A 250 Ω resistor turns 4–20 mA into 1–5 V.
NAMUR NE 43 signal levels
NE 43 (NAMUR recommendations) gives digital transmitters with a 4–20 mA output a way to report failures through the current itself:
- 3.8 mA to 20.5 mA: measurement information, including slightly below and above the range;
- 3.6 mA or less, or 21 mA or more: failure information, so the receiving system should treat the measurement as failed;
- between 3.6 and 3.8 mA and between 20.5 and 21 mA the levels are not defined.
A loop that must carry an upscale failure signal has to be sized for 21 mA, or for the transmitter’s own high-alarm current.
Sizing the loop
A two-wire transmitter needs a minimum voltage at its terminals to work. Everything else in the loop (the sense resistor, indicators, barriers and the cable, both conductors) takes I·R from the supply, so the largest loop resistance is R_max = (V_supply − V_min) ÷ I_max. The calculator adds the cable from its length and conductor size (copper at 20 °C, 1/58 Ω·mm²/m; AWG sizes from their standard diameters) and shows the voltage left for the transmitter at every current from the failure levels to 22 mA.
ADC resolution and SNR
- LSB = full-scale range ÷ 2ᴺ for an N-bit converter.
- Codes over the signal = signal span ÷ LSB: a 1–5 V signal on a 0–5 V input uses 80 % of the codes, which costs log₂(1/0.8) = 0.32 bits.
- Resolution = engineering span ÷ codes over the signal.
- Ideal SNR: quantisation noise of q²/12 against a full-scale sine of power (2ᴺ·q)²/8 gives 10·log₁₀(1.5·2²ᴺ) = 6.02·N + 1.76 dB. Real converters fall short of it; ENOB = (SINAD − 1.76) ÷ 6.02 turns a measured SINAD back into bits.
Limitations
- Scaling is exact; the accuracy of the measurement depends on the transmitter, the sense resistor’s tolerance and the input card.
- The loop check uses the resistances you enter at 20 °C; warm cable has more resistance, and some receivers add their own burden.
- NE 43 levels are shown for 4–20 mA signals only, and only as the recommendation defines them; your transmitter’s alarm currents are in its manual.
- The ideal SNR counts quantisation noise only; noise, distortion and the reference lower the real figure.
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Frequently asked questions
What do I get without a pass?
Without a pass, 4–20 mA Scaling Calculator shows the NE 43 and loop checks and the names of the table’s first rows (up to 3), with the result of the mode you use, the working and every figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I convert 4–20 mA to engineering units?
Work out the fraction of the span, (I − 4) ÷ 16, and multiply it by the range: on a 0–10 bar transmitter, 12 mA is (12 − 4) ÷ 16 = 0.5 of the span, so 5 bar. For a range that does not start at zero, add the bottom value: 7.2 mA on 0–100 °C is 20 °C.
Why does the signal start at 4 mA and not 0?
The “live zero” lets the receiver tell a reading of zero (4 mA) from a broken wire or a dead transmitter (0 mA), and leaves current to power a two-wire transmitter. NAMUR NE 43 uses the room below 3.8 mA and above 20.5 mA to signal failures.
What resistor turns 4–20 mA into a voltage?
R = V ÷ I: 250 Ω gives 1–5 V and 500 Ω gives 2–10 V. At 20 mA a 250 Ω resistor dissipates 0.1 W; choose a precision resistor, because its tolerance goes straight into the measurement.
How much loop resistance can my transmitter drive?
Subtract the transmitter’s minimum voltage from the supply and divide by the highest current: (24 V − 10.5 V) ÷ 21 mA = 643 Ω. The sense resistor, indicators, barriers and both cable conductors must add up to less than that.
What does square-root extraction do?
A differential-pressure flowmeter’s pressure drop rises with the square of the flow. Taking the square root of the signal’s fraction of span turns it back into flow: 8 mA is 25 % of the span, and √0.25 = 50 % of full flow.