Cross-discipline · Reference

The Engineering Formula Lab

Every formula a controls, electrical or mechanical engineer reaches for — not as a dead cheat-sheet, but as live calculators. 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 a unit converter? That's 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. Master these and most "analog" tickets become trivial.
⚡ 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 up everyone once — here it's a slider.
⚙️ Mechanical & motion math connects force, torque, speed and power — and converts between 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

The single habit that prevents most engineering mistakes: carry the units through the maths. If the units don't cancel to what you expect, the formula is wrong — 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. Order-of-magnitude intuition catches what 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