Electric Converters

Electricity has four fundamental quantities — volts, amps, ohms, and watts — and two laws that tie them together: Ohm's law (V = I·R) and watt's law (P = V·I). This hub collects the four-way conversion family those laws define, plus the two specialty conversions every electrician and RF engineer needs: dBm power (the language of radio) and AWG wire gauge (the language of US wire). All of it is exact — the laws are laws, the dBm scale is a definition, and the AWG scale is a geometric formula from 1857 that has never changed.

Ohm's Law & Watt's Law — V, A, Ω, W

Volts to Amps I = V/R or I = P/V. A 120 V circuit at 8 Ω draws 15 A. Breaker sizing starts here. I = V/R Amps to Volts V = I·R or V = P/I. A 15 A current through 8 Ω needs 120 V. The power supply question. V = I·R Volts to Watts P = V·I. A 120 V bulb at 0.5 A burns 60 W. The appliance power calculation. P = V·I Watts to Volts V = P/I. A 60 W device at 0.5 A runs on 120 V. Chargers and solar. V = P/I Amps to Watts P = V·I. 15 A on 120 V burns 1,800 W. The 120/240 V split in action. P = V·I Watts to Amps I = P/V. 1,800 W at 120 V draws 15 A. The breaker and wire sizing workhorse. I = P/V Volts to Ohms R = V/I. A 5 V LED at 20 mA needs a 250 Ω resistor. Electronics starter kit. R = V/I Ohms to Volts V = I·R. Sensors and voltage dividers: resistance becomes the signal. V = I·R Ohms to Amps I = V/R, load-first. An 8 Ω speaker at 12 V draws 1.5 A. Fixed loads and their current. I = V/R Amps to Ohms R = V/I, design-first. A 20 mA LED at 5 V needs a 250 Ω resistor. Sizing the part. R = V/I

RF Power — dBm, mW, W

dBm to Watts 30 dBm = 1 W exactly. Wi-Fi at 20–23 dBm, radios up to 40 dBm. The RF power anchor. W = 10^((dBm−30)/10) Watts to dBm 1 W = 30 dBm, 10 W = 40 dBm. Every transmitter enters the link budget here. dBm = 10·log10(W×1000) dBm to Milliwatts 0 dBm = 1 mW, 10 dBm = 10 mW, 20 dBm = 100 mW. Test equipment language. mW = 10^(dBm/10) Milliwatts to dBm 1 mW = 0 dBm. Receiver sensitivity and sensor outputs in one step. dBm = 10·log10(mW)

Wire Gauge — AWG & mm²

AWG to mm² 12 AWG = 3.31 mm², 14 AWG = 2.08 mm². The US wire gauge table in metric. d = 0.127·92^((36−AWG)/39) mm² to AWG 2.5 mm² ≈ 13 AWG, 1.5 mm² ≈ 15 AWG. European cable meets US terminals. inverse AWG formula

AC Power, Batteries & Wiring — kVA, PF, Wh, V-drop

kVA to kW kW = kVA × PF. A 10 kVA generator at 0.8 PF delivers 8 kW. The nameplate rating explained. × PF kW to kVA kVA = kW ÷ PF. A 5 kW rack at 0.8 PF needs 6.25 kVA — buy the 8 kVA UPS. Sizing work. ÷ PF Power Factor PF = W ÷ VA = cos φ. Why utilities penalize sites below 0.9 and capacitor banks fix it. PF = W/VA Watt Hours to Amp Hours Ah = Wh ÷ V. A 500 Wh 12 V pack holds 41.7 Ah. The honest battery comparison. Ah = Wh/V Amp Hours to Watt Hours Wh = Ah × V. A 100 Ah 12 V deep-cycle pack holds 1,200 Wh. Total pack energy. Wh = Ah×V Voltage Drop Vdrop = I × R. 15 A on 100 ft of 12 AWG loses 4.76 V — over the NEC 3% rule. Wire sizing. V = I×R

What's on this page

Twenty-two converters covering the four quantities of Ohm's law — volts, amps, ohms, watts — in every useful direction, plus the RF power pair (dBm ↔ watts and milliwatts), the wire gauge pair (AWG ↔ mm²), and the AC power and battery family (kVA ↔ kW with power factor, power factor itself, watt hours ↔ amp hours, and voltage drop). The Ohm's law family is exact by definition: V = I·R and P = V·I are laws, not measurements, so the converters carry zero uncertainty. The dBm pages apply the definition of the scale (dB relative to one milliwatt) exactly. The AWG pages reproduce the 1857 geometric definition of the gauge exactly. The kVA, battery, and voltage-drop pages apply definitions — power factor, the watt-hour, and Ohm's law on a conductor — so they are exact for the numbers you enter. If you're converting electrical energy — kilowatt-hours on the bill, watts to kilowatts, horsepower to watts — that is the energy hub. This hub is about the circuit quantities themselves: what flows (amps), what pushes (volts), what resists (ohms), what it costs to run (watts), what the nameplate can deliver (kVA), and what the wire eats on the way (voltage drop).