Electrical unit converter

Why a unit converter dedicated to electrical engineering

An electrical designer handles a dozen units every day drawn from the International System (SI), plus a few legacy units such as horsepower, the BTU or the kilocalorie. A prefix error — a factor of 1000 between kΩ and Ω, between mA and A, or between µF and nF — derates a protection calculation, skews a voltage-drop note or kills an undersized portable UPS. This converter centralizes the eight unit categories most commonly used on a Swiss schematic NIBT 2020 and automatically applies the context-sensitive conversions that generic tools ignore.

SI prefixes used in electrical engineering

All the prefixes below are decimal and combine with any SI unit (watt, ampere, ohm, farad, etc.). The converter applies them automatically, but a quick read of the table avoids most input errors.

Practical equivalence formulas

Active, apparent and reactive power

The active power P in watts corresponds to the energy actually converted into heat, motion or light per second. The apparent power S in volt-amperes is the product U × I that the network must carry. The reactive power Q in vars circulates between the source and the inductances or capacitances without producing work. The three are related by S² = P² + Q² and P = S × cos φ. In 230 V single-phase, P(W) = U × I × cos φ; in 400 V balanced three-phase, P(W) = √3 × U × I × cos φ. To go from watts to kVA you therefore need to know cos φ: a resistive heater has cos φ = 1, an industrial induction motor cos φ ≈ 0.8, a recent photovoltaic inverter cos φ ≈ 0.98.

Energy and heat

L'energy is the time integral of power. Under constant conditions, E = P × t. 1 watt-hour (Wh) equals 3600 joules; 1 kilowatt-hour (kWh), the commercial unit of the electricity grid, equals 3.6 megajoules. The kilocalorie (kcal), a thermal unit still used for heating balances and nutrition, equals 4184 J or 1,163 Wh. A 2 kW kettle heating 1 litre of water from 20 °C to 100 °C consumes 80 × 1 × 4,184 = 335 kJ or 93 Wh, to be divided by the thermal efficiency (≈ 0,9) to obtain the actual mains consumption.

Ohm's law and voltage-current-resistance conversions

The Ohm's law U = R × I links voltage, resistance and current. In alternating current, the impedance Z replaces pure resistance: Z = √(R² + (Lω − 1/Cω)²) where ω = 2πf. At 50 Hz, ω = 314 rad/s. A 1 mH inductor has a reactance Lω = 0.314 Ω, negligible compared with a cable; at 100 kHz (variable frequency drive), the same inductor rises to 628 Ω and becomes the dominant component. For the designer, the Ohm's law in DC is enough in 95% of cases: calculating the current of a 2000 W heater at 230 V gives I = P/U = 8.7 A, an immediate check of the required 10 A rating.

Electric charge and stored energy (batteries, capacitors)

The load Q in coulombs measures a quantity of electricity. 1 coulomb = 1 ampere for 1 second. The commercial unit is theampere-hour (Ah) : 1 Ah = 3600 C. Pour une batterie, ce qui compte au final est l'énergie en wattheures : E(Wh) = Q(Ah) × U(V). Une batterie 2 Ah à 3,7 V (cellule Li-ion 18650) stocke 7,4 Wh ; une batterie 100 Ah à 12 V (plomb auto) stocke 1,2 kWh. Pour un condensateur, l'énergie stockée vaut E = ½ × C × U² : un condensateur 10 mF chargé à 400 V stocke 800 J, suffisant pour souder une pince à la borne. Pour une self, E = ½ × L × I² : une bobine d'inductance 100 mH parcourue par 10 A stocke 5 J.

Five concrete application cases

Case 1 — 22 kW EV charging station: kW, kVA and breaker rating

A charging station 22 kW three-phase at cos φ close to 1 (power-electronic active load) draws S = 22 / 1 = 22 kVA, i.e. I = S / (√3 × U) = 22000 / (1,732 × 400) = 31,75 A. The cable is sized at 6 mm² three-phase under a 32 A curve C circuit breaker, type B RCD mandatory. The utility bills the increase in subscribed power (installation notice > 3,7 kW single-phase or > 11 kW three-phase according to Swiss DSOs).

Case 2 — 20 000 mAh power bank: real energy and smartphone runtime

A power bank sold as “20 000 mAh” is labelled in mAh on its internal 3.7 V cell. L'énergie réelle vaut 20 × 3,7 = 74 Wh. Un smartphone consomme une batterie de 4000 mAh à 3,85 V, soit 15,4 Wh par charge complète. Le power bank fournit donc théoriquement 74/15,4 = 4,8 charges, ramené à 3-4 charges en pratique avec les pertes du convertisseur 3,7 V → 5 V USB (≈ 85 % de rendement). Convertir directement 20 000 mAh par 4000 mAh = 5 charges est une erreur : on compare alors des charges à 3,7 V avec des charges à 3,85 V, ce qui ignore le rendement et fausse la promesse marketing.

Case 3 — Industrial workshop cos φ 0.75: billing and compensation

A workshop consuming 50 kW active at cos φ = 0,75 draws 50 / 0,75 = 66,7 kVA from the network. The utility bills a reactive-power penalty for tan φ > 0,4 (equivalent to cos φ < 0,93). Installer une batterie de condensateurs de 25 kVAR ramène cos φ à 0,96, kVA appelés à 52 kVA, et supprime la pénalité. Le calcul Q = P × (tan φ₁ − tan φ₂) = 50 × (0,882 − 0,292) = 29,5 kVAR à compenser, ramené à 25 kVAR pour rester sous-compensé et éviter une surcompensation capacitive.

Case 4 — Minimum insulation NIBT 6.1: megohm and milliohm

The final NIBT 2020 verification (chapter 6) requires a insulation resistance ≥ 1 MΩ sous 500 V DC pour les circuits 230/400 V. Le mégohmmètre affiche par exemple 2,3 MΩ : conforme. À l'opposé, la résistance de boucle de terre se mesure en milliohms : un PE de 16 mm² sur 30 m présente R = ρ × L / S = 0,0224 × 30 / 16 = 42 mΩ, valeur à reporter au protocole de mesure. Passer du milli au méga représente un facteur 10⁹ ; mélanger les deux unités au PV de contrôle est l'erreur classique du contrôleur OIBT débutant.

Case 5 — 12 000 BTU/h air conditioner: conversion to electrical kW

A split air conditioner rated 12 000 BTU/h a une puissance frigorifique de 12 000 × 0,29307 = 3517 W = 3,52 kW. Avec un coefficient de performance COP = 3,5 typique, la puissance électrique absorbée est de 3,52 / 3,5 = 1 kW. Sur 230 V monophasé à cos φ = 0,9 (PFC actif), le courant est I = 1000 / (230 × 0,9) = 4,8 A. Le départ se dimensionne en 2,5 mm² sous 10 A courbe C, différentiel 30 mA type F (compresseur Inverter à variation de fréquence).

Frequent mistakes to avoid

L'error by a factor of 1000 between kΩ and Ω, mA and A, µF and nF is responsible for about 30 % of design incidents in electrical engineering offices. Always check the prefix displayed by the measuring instrument (multimeter, megohmmeter, oscilloscope) before recording the value. The W/VA confusion on generator sets leads to undersizing: a 5 kVA set delivers only 4 kW at cos φ 0.8, not 5 kW. The mAh/Wh confusion on drone batteries or portable inverters leads to comparing non-additive quantities between cells of different voltages; always convert to Wh before comparing.