4–20 mA scaling
Convert a 4–20 mA, 0–10 V or other analog signal to engineering units and back for any range — linear or square-root DP flow, with percent of span, in either direction.
Analog signal scaling · two-way, linear or square-root
% = (mA − 4) / 16 · EU = LRV + % · span
What this gives you
A 4–20 mA transmitter reports its measurement as a current: 4 mA at the bottom of its calibrated range and 20 mA at the top, rising in a straight line in between. This tool does that conversion both ways — turn a signal reading into engineering units (PSI, °F, GPM, level percent, whatever the range is), or turn a process value back into the signal the loop should be carrying. The general form is percent = (signal − Slo) ÷ (Shi − Slo) × 100 and EU = LRV + percent ÷ 100 × span, where span is simply URV − LRV. It rearranges to signal = Slo + frac × (Shi − Slo) in the other direction.
Pick the signal type to match your device — 4–20 mA and 0–20 mA current loops, or 0–10 V, 1–5 V and 2–10 V voltage signals — and the low/high span (Slo, Shi) updates so the same percent-of-span math applies to any of them. The scale bar in the diagram relabels its ends to whichever standard you choose.
Why 4 mA and not 0
The bottom of the range is 4 mA, not zero, on purpose — it is a live zero. A healthy loop sitting at the very bottom of its range still carries 4 mA, so a reading of 0 mA tells you the loop itself is broken (a cut wire, a dead transmitter, a blown fuse) rather than a genuine zero measurement. That 16 mA of usable signal between 4 and 20 is what maps onto your engineering range, which is why every term in the formula divides by 16 and not 20.
Field note — the calculator only knows the range you give it
Scaling is only as honest as the LRV and URV you enter, and those live in the transmitter's configuration, not on a sticker you can trust. If a tech re-ranged the instrument last month and the DCS block still holds the old span, the loop current is correct but every engineering value derived from it is wrong. When a reading looks off, confirm the transmitter's actual LRV and URV before you suspect the sensor — a mismatched range is far more common than a failed cell. And confirm the transfer function: a DP transmitter inferring flow needs the square-root relationship, so a block left on linear (or a smart transmitter already extracting root while the DCS roots it a second time) skews every flow number.
Linear vs. square-root
Most loops are linear — pressure, level, temperature — where a signal at half span means a process value at half span. But a differential-pressure flowmeter measures the DP across an orifice, and flow is proportional to the square root of that DP. Switch the transfer function to square root and the tool applies EU = LRV + √frac × span, where frac is the signal fraction (signal − Slo) ÷ (Shi − Slo). Because √ compresses the top of the scale, the diagram's engineering-unit ticks bunch toward the high end to show it.
Worked example
A pressure transmitter is ranged 0–300 PSI and the loop reads 12 mA. The span is 300 PSI, and 12 mA sits at (12 − 4) ÷ 16 = 50 percent of span, so on a linear loop the pressure is 0 + 0.50 × 300 = 150 PSI. On a square-root DP-flow loop ranged 0–100 GPM, that same 12 mA (frac = 0.50) gives √0.50 × 100 = 70.7 GPM — more than half the range, because the curve is steep near the bottom. Going the other way on the linear range, to find the current for 225 PSI: that is 225 ÷ 300 = 75 percent of span, so the loop should read 4 + 0.75 × 16 = 16 mA.