Free Engineering Calculators Online: 4-20 mA Scaling, Motor and VFD, PID Tuning

Free engineering calculators online can save you from arithmetic slips, but only if you know the formula behind them. The three that automation engineers use most are 4-20 mA scaling, motor and VFD figures, and PID tuning. EDWartens has all three free at edwartens.com/resources, running in your browser with no sign-up. This guide gives the exact formulas they use, worked examples you can check by hand, and the cases where you should not trust any calculator.

Checked 1 October 2026. The formulas below are the ones in the calculators' own code. The standards and references behind them are listed under Sources.

How does the 4-20 mA scaling calculator work?

A 4-20 mA transmitter maps its range linearly onto 16 mA of current: 4 mA at the bottom of the range (the lower range value) and 20 mA at the top (the upper range value). Everything follows from that straight line.

Current to engineering value:

value = low + (mA − 4) ÷ 16 × (high − low)

Engineering value to current:

mA = 4 + (value − low) ÷ (high − low) × 16

Percent of span:

% = (mA − 4) ÷ 16 × 100

The 4-20 mA scaling calculator works in three directions: mA to value, value to mA, and percent to mA. It also shows the raw count your PLC's analog card reports. It has presets for Siemens S7 cards (0 to 27648) and for a 16-bit signed range (0 to 32767), plus a custom range for anything else.

Worked example 1: pressure

A transmitter is ranged 0 to 10 bar, and the loop reads 12 mA.

• Percent of span: (12 − 4) ÷ 16 × 100 = 50%
• Value: 0 + 0.5 × 10 = 5 bar
• Siemens raw count: 0.5 × 27648 = 13824
• 16-bit raw count: 0.5 × 32767 = 16383.5, which the calculator rounds to 16384

Worked example 2: a range that does not start at zero

A temperature transmitter is ranged −50 to 150 °C, and you want the current at 100 °C.

• mA = 4 + (100 − (−50)) ÷ (150 − (−50)) × 16 = 4 + 150 ÷ 200 × 16 = 16 mA

Negative low ends are where hand calculations usually go wrong. Most mistakes come from subtracting the wrong way round.

When is a reading a fault, not a measurement?

The calculator flags any current below 3.8 mA or above 20.5 mA as a fault, not a reading. Below 3.8 mA suggests an open loop or a failed transmitter. Above 20.5 mA suggests a short circuit or a failed transmitter. This follows NAMUR NE 43, which reserves 3.8 to 20.5 mA for measurement and uses 3.6 mA or less, or 21 mA or more, to signal a failure. Many transmitters can be set to drive their output high or low on an internal fault, so a PLC that checks these limits catches dead instruments instead of reporting a false value.

Try 3.5 mA in the calculator with the 0 to 10 bar range. It shows −0.3125 bar and a raw count of −864, and the fault note tells you not to believe either. That is the right reaction in your PLC code too.

How does the motor and VFD calculator work?

The motor and VFD calculator turns nameplate data into the figures you need when setting up a drive. It works for 50 Hz and 60 Hz supplies, kW or HP (1 HP = 0.7457 kW), and three-phase or single-phase motors.

P is in watts and efficiency is a fraction (90% = 0.9).

Worked example 3: a 50 Hz motor

A 7.5 kW, 400 V, 4-pole motor has a nameplate speed of 1460 rpm, a power factor of 0.85 and 90% efficiency.

• Synchronous speed: 120 × 50 ÷ 4 = 1500 rpm
• Slip: (1500 − 1460) ÷ 1500 = 2.67%
• Full-load current: 7500 ÷ (1.732 × 400 × 0.85 × 0.9) = 7500 ÷ 530.0 = 14.2 A
• Rated torque: 7500 × 60 ÷ (2π × 1460) = 49.1 N·m
• V/Hz: 400 ÷ 50 = 8 V/Hz
• At 40 Hz on a drive: about 1460 × 0.8 = 1168 rpm, with 8 × 40 = 320 V applied

Worked example 4: a 60 Hz motor, and why the code table wins

A 10 HP, 460 V, 4-pole motor runs at 60 Hz with a power factor of 0.86 and 91% efficiency.

• Synchronous speed: 120 × 60 ÷ 4 = 1800 rpm
• Full-load current: 7457 ÷ (1.732 × 460 × 0.86 × 0.91) = about 12.0 A

In the United States, the National Electrical Code does not let you size conductors or short-circuit protection from either figure. Section 430.6(A)(1) requires the full-load current from its tables, and the table value for a 10 hp, 460 V three-phase motor is 14 A. The nameplate current is used for overload protection. Other countries' codes have their own rules. Whatever the calculator says, protection and cable sizing follow your local electrical code.

What the V/Hz figures mean

A basic drive in V/Hz mode keeps the voltage-to-frequency ratio constant below base frequency, so the motor's magnetic flux, and roughly its available torque, stays constant. Above base frequency the drive cannot raise the voltage past rated, so the motor runs in field weakening and its available torque falls. The calculator says so. Its speed estimate scales the nameplate speed with frequency, which ignores the way slip changes with load. Treat it as a guide to within a few rpm, not a measurement. Our VFD training guide covers the control modes in more depth.

How does the PID tuning calculator work?

The PID tuning calculator gives Ziegler-Nichols starting gains by either of the two classic methods. It shows them in standard form (Kp, Ti, Td) and parallel form (Ki = Kp ÷ Ti, Kd = Kp × Td).

Closed-loop (ultimate gain) method. With the controller on proportional only, raise the gain until the loop oscillates steadily. That gain is Ku, and the period of the oscillation is Pu.

Open-loop (step test, or reaction curve) method. With the controller in manual, step the output and record the response. The process gain K is the change in PV divided by the change in output. L is the dead time and T is the time constant.

Worked example 5: both methods

Closed loop: Ku = 4 and Pu = 20 s. For PID: Kp = 0.6 × 4 = 2.4, Ti = 20 ÷ 2 = 10 s, Td = 20 ÷ 8 = 2.5 s. In parallel form, Ki = 2.4 ÷ 10 = 0.24 per second and Kd = 2.4 × 2.5 = 6 s.

Open loop: K = 2, L = 3 s and T = 30 s. For PID: Kp = 1.2 × 30 ÷ (2 × 3) = 6, Ti = 2 × 3 = 6 s, Td = 0.5 × 3 = 1.5 s. For PI: Kp = 4.5 and Ti = 3 ÷ 0.3 = 10 s.

Three PID traps

1. The gains are aggressive by design. Ziegler-Nichols aims for roughly quarter-amplitude decay: each overshoot is about a quarter of the one before. That means real overshoot. The calculator advises starting at about half of Kp and tuning from there.
2. Units and form. Some controllers take Ti in minutes, some in seconds. Some take integral gain in repeats per minute, and some use the parallel form. Copying a number into the wrong field can make a loop up to 60 times too aggressive or too slow. Check your controller's manual.
3. Consistent gain units. In a step test, express K in the units your controller uses, usually percent of PV span per percent of output, not bar per mA.

The step itself should be modest. A control engineering text used at McMaster University suggests a step of 10 to 20% of full scale. Try the method safely first in the PID tuning simulator walkthrough.

When should you not trust an engineering calculator?

• When the inputs are guesses. A calculator is only as good as the range set in the transmitter or the data on the nameplate. Read them; do not assume them.
• When a code or standard decides the answer. Cable sizes, protective devices and safety functions follow your electrical code and safety standards. A formula gives an estimate, not compliance.
• When the process is non-linear. Flow from a differential-pressure transmitter follows a square root, and level in a horizontal tank is not linear in volume. Linear scaling gives the wrong answer unless the transmitter or the PLC applies the right characterisation.
• When the loop is dangerous to disturb. Never run an ultimate-gain test on a process where sustained oscillation could cause harm. Use a step test, a model or a simulator instead.

Learn the theory behind the tools

The calculators are quicker with the theory behind them:

• Industrial Instrumentation and Process Control covers 4-20 mA loops, calibration, HART and P&IDs.
• Siemens TIA Portal PID Compact and Analog Processing uses NORM_X and SCALE_X with the 0 to 27648 range and PID_Compact.
• Variable Frequency Drives covers wiring, parameters, V/Hz and PLC control.
• PID Control for PLC Engineers covers manual and rule-based tuning, anti-windup and filtering.

All are free. The instrumentation and process control courses list more. The other free tools on the resources page include a PLC code explainer and a structured text generator.

Take the free course

Instrumentation · Beginner · Free

Industrial Instrumentation and Process Control

Drives · Beginner · Free

Variable Frequency Drives: Wiring, Programming, PLC and Network Control

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PID Control for PLC Engineers

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Siemens TIA Portal PID Compact and Analog Processing