Electrical & Instrumentation

Electrical Power Explained

Electrical power is the rate of energy transfer in a circuit: P = VI. Learn the three equivalent DC power formulas, common units (W, kW, hp), and limitations.

TypeEngineering guide — concept explainer

Definition

Electrical power is the rate at which electrical energy is transferred in a circuit. For a DC resistive circuit, power equals voltage multiplied by current: P = V x I. Combining this with Ohm’s Law yields two additional forms: P = I²R and P = V²/R. Power is measured in watts (W), where 1 watt = 1 volt x 1 ampere = 1 joule per second.

Why it matters

Knowing the power dissipated in a component is essential for sizing conductors, selecting fuses, specifying heat sinks, and ensuring that resistors and other components operate within their rated capacity. In instrumentation, power calculations determine whether a loop can supply enough energy to drive a transmitter, whether a heater element delivers the required heat, and whether a cable run can handle the load without excessive heating.

Formula

Basic power

P = V x I

Power from current and resistance

P = I² x R

Power from voltage and resistance

P = V² / R

Units involved

•W (watts) — the SI unit of power, equal to one joule per second
•kW (kilowatts) — 1,000 watts
•MW (megawatts) — 1,000,000 watts
•hp (horsepower) — 1 mechanical hp ≈ 745.7 W
•V (volts) — voltage
•I (amperes) — current
•R (ohms) — resistance

Concept diagram

Worked example

A 120 V supply feeds a 60 Ω heater element. What power does the heater dissipate?

01V = 120 V, R = 60 Ω
02P = V² / R
03P = 120² / 60
04P = 14,400 / 60
05P = 240 W

Result

The heater dissipates 240 W (0.24 kW).

Common mistakes

•Applying DC power formulas to three-phase AC systems. Three-phase power requires additional factors (√3, power factor) that are not covered here.
•Forgetting to square the variable. P = I²R means current squared times resistance — missing the square gives a result off by a factor of I.
•Ignoring unit prefixes. If current is in milliamps, convert to amps before multiplying: 20 mA = 0.020 A.
•Confusing power (watts) with energy (watt-hours or joules). Power is a rate; energy is power integrated over time.
•Assuming power factor equals 1. For AC loads with motors or capacitors, real power = apparent power x power factor. This guide covers DC/resistive power only.

When to use the calculator

Use the Electrical Power calculator when you know any two of voltage, current, and resistance and need to find power — or when you know power and one other variable and need to find the rest. The calculator shows all three formula forms and handles unit conversions.

Electrical Power Calculator →Ohm's Law Calculator →

FAQ

What is the difference between watts and volt-amps?

In a DC or purely resistive AC circuit, watts and volt-amps are identical. In AC circuits with reactive loads, volt-amps (VA) is the apparent power, while watts is the real (active) power. The ratio is the power factor: W = VA x PF. This calculator works with real power in resistive circuits where PF = 1.

How do I convert watts to horsepower?

One mechanical horsepower equals approximately 745.7 watts. Use the conversion: hp = W / 745.7. ProcessConvert has a dedicated kW to hp conversion page for this.

Can I use these formulas for AC circuits?

For purely resistive AC loads (heaters, incandescent lamps), yes — use RMS voltage and RMS current. For loads with motors, capacitors, or inductors, you need to account for power factor and reactive power, which this guide and calculator do not cover.

What happens when I connect Ohm’s Law and the power formula?

Substituting V = IR into P = VI gives P = I²R. Substituting I = V/R into P = VI gives P = V²/R. These are the three equivalent forms of DC power. The Ohm’s Law guide covers the V-I-R relationship in detail.

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