Cross-discipline · Reference

The Engineering Formula Lab

Every formula a controls, electrical or mechanical engineer reaches for, set up as live calculators instead of a dead cheat-sheet. Each card states the formula, explains it in one plain sentence (and what each symbol means), then lets you change the numbers and watch the answer move. Three tabs: the control math you code into a PLC, the electrical math behind the panel, and the mechanical math behind the motion.

🧮 PLC & control⚡ electrical⚙️ mechanical▶ live calculators

📐 Need to size something (a motor, cable, heater), or need a unit converter? That's in Formula Lab Part II →

🧮 Control math is what you actually type into the PLC: turning a raw sensor count into a real-world value, pacing ramps, totalising flow, and filtering noise. Once these are second nature, most "analog" tickets turn into quick fixes.
⚡ Electrical math sizes the panel and reads the bill: Ohm's law, power in DC and three-phase, power factor, motor current, energy cost and timing. The √3 in three-phase trips everyone up once; here it's a slider.
⚙️ Mechanical & motion math connects force, torque, speed and power, and converts between the rotary and linear worlds (gearboxes, belts, leadscrews). This is how you size a motor and predict what a machine will actually do.
∑ · The meta-skill

Units are the cheat code

One habit prevents most engineering mistakes: carry the units through the maths. If the units don't cancel to what you expect, the formula is wrong, and you know it before you ever plug in a number. N·m × (rad/s) = W works; N·m × rpm doesn't, until you convert rpm to rad/s (×2π/60). Every calculator above is built around its units for exactly this reason.

🔢 SI prefixes that bite: k = ×10³, M = ×10⁶, m = ×10⁻³, µ = ×10⁻⁶. A "kW" is 1000 W; a "mA" is 0.001 A. Mixing them is the #1 unit error.

🔄 The conversions you'll redo forever: rpm→rad/s (×2π/60), HP→W (×746), bar→Pa (×10⁵), °C→K (+273.15), inch→mm (×25.4).

⚖️ Sanity-check every answer. A 0.5 kW motor pulling 400 A? Units or a decimal is wrong. A rough order-of-magnitude check catches the errors that the algebra hides.

📋 · Field kit

The pocket formula sheet

The dozen that earn their keep daily, in code-ready form.

  1. EU = (raw−rawMin)/(rawMax−rawMin)×(euMax−euMin)+euMin
  2. % = (mA−4)/16×100
  3. V = I × R  ·  P = V × I = I²R
  4. P₃φ = √3 × VL × IL × PF
  5. PF = kW ÷ kVA  ·  kVAR = √(kVA²−kW²)
  6. Imotor = P ÷ (√3 × V × PF × η)
  7. kWh = kW × hours  ·  τ = R × C
  8. T = F × r  ·  F = m × a
  9. P = T × ω = T × 2π × N ÷ 60
  10. nout = nin ÷ ratio  ·  Tout = Tin × ratio
  11. v = π × D × N ÷ 60  ·  KE = ½ m v²
  12. P = F ÷ A  ·  Jreflected = Jload ÷ ratio²