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.

By EnginStack Editorial Team | Reviewed against NIST, BIPM and primary-source documentation About →

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

Exact conversion factors

Electrical units are linked by laws rather than by single factors, so half of this category is not a conversion at all. The table gives the genuine conversions and the definitional constants that the formulas depend on.

From	To	Exact factor	Basis
1 kilowatt-hour	joules	3,600,000	Exact, 1,000 W for 3,600 s
1 watt-hour	joules	3,600	Exact, 3,600 J
1 amp-hour	coulombs	3,600	Exact, one ampere for 3,600 seconds
1 mechanical horsepower	watts	745.699871582	Exact, 550 ft·lbf per second
1 metric horsepower	watts	735.49875	Exact, 75 kgf·m per second
1 kilowatt	mechanical horsepower	1.3410220896	Derived, 1.3410220896
1 kilowatt-hour	watt-hours	1,000	Exact, SI prefix
1 kilowatt	volt-amperes at power factor 1	1,000	Only equal when the load is purely resistive
1 kilowatt-hour at 12 V	amp-hours	0.0833333333333	Split by voltage: amp-hours equals watt-hours divided by volts
1 kilowatt-hour at 48 V	amp-hours	0.0208333333333	The same energy at a higher voltage

Defining values and exact constants

Voltage, current, resistance and power are linked by three equations rather than one factor: V = I × R, P = V × I and P = I² × R. Any conversion between them needs the third quantity as an input.
Apparent power in volt-amperes exceeds real power in watts whenever the load has reactance. The ratio is the power factor, typically 0.8 to 0.95 for motors.
One kilovolt-ampere at a power factor of 0.8 delivers 0.8 kW. Sizing a generator by kilowatts alone under-sizes it, which is why standby sets are rated in kVA.
A kilowatt-hour is 3.6 MJ exactly. Dividing it by the pack voltage gives amp-hours, so a 500 Wh battery is 41.67 Ah at 12 V and 20.83 Ah at 24 V.
The dBm scale is a power ratio referred to one milliwatt. Adding decibels multiplies power, so 0 dBm is 1 mW and 30 dBm is 1 W, a factor of a thousand.

Frequently asked questions

Why is a kilowatt not the same as a kilovolt-ampere?

Because one measures real power and the other apparent power. A load with reactance draws more current than its watts alone suggest, and the ratio between the two is the power factor.

How do you convert watt-hours to amp-hours?

Divide by the voltage. A 500 Wh battery at 12 V holds 41.67 Ah, and the same pack at 24 V holds 20.83 Ah. Watt-hours compare batteries across voltages, amp-hours do not.

How many watts is one horsepower?

About 745.7 for mechanical horsepower, which is 550 foot-pounds per second, and about 735.5 for metric horsepower, which is 75 kilogram-force meters per second. The two differ by about 1.4 percent.

What does dBm actually measure?

Power relative to one milliwatt on a logarithmic scale. Zero dBm is exactly 1 mW, 10 dBm is 10 mW and 30 dBm is 1 W. Because it is logarithmic, adding decibels multiplies the underlying powers.

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).