Electrical Power Formulas Guide | Calculator Workflow

Quick Answer: Use this guide to choose the formula path first: DC, single-phase AC, balanced three-phase AC, power factor, kW/kVA, HP conversion, current, voltage, or conductor loss. Then enter the actual values in the Power Calculator, Power Factor Calculator, Motor Power Calculator, or Voltage Drop Calculator before using the result for equipment decisions.

Electrical power formulas are useful only after the input path is clear. A watts calculation, a three-phase motor check, a kVA transformer review, and a conductor-loss check can all contain voltage and current, but they answer different questions. This page keeps the formulas visible while making the specific answer come from the calculator workflow.

Reviewed 2026-07-07. Use English content as the technical source for U.S. electrical work and verify project-specific results with equipment markings, adopted code requirements, and the appropriate calculator.

Power formula calculator workflow before examples

Choose the calculation path before you enter numbers:

Identify the circuit type: DC, single-phase AC, balanced three-phase AC, motor, transformer, utility billing, or conductor loss.
Choose the unknown: watts, current, voltage, resistance, power factor, kW, kVA, HP, kVAR, or loss.
Record the units exactly: volts, amps, ohms, watts, kW, kVA, HP, PF, phase count, and whether voltage is line-to-line or line-to-neutral.
Use the calculator that matches the task instead of forcing one formula to cover every case.
Use the formula reference below to understand the result and to check whether a missing input, such as PF or efficiency, changes the answer.

Task	Inputs to collect first	Calculator handoff
Basic watts, amps, or voltage	circuit type, voltage, current, resistance, power factor when applicable	Power Calculator
Balanced three-phase power	line voltage, line current, PF, kW or kVA target, line/phase basis	3-Phase Power Calculator
Motor HP or kW comparison	HP or kW, voltage, phase, current, efficiency, PF, service condition	Motor Power Calculator
Power factor correction	kW, kVA, current PF, target PF, utility or owner criteria	Power Factor Calculator
Conductor loss or long run	current, conductor resistance or size, distance, voltage, phase	Voltage Drop Calculator
Operating energy or cost	power, runtime, duty cycle, utility rate, billing period	Electricity Cost Calculator

For a visual record after the calculation, use the Power Factor Triangle Chart when the result needs kW, kVAR, kVA, phase angle, and correction notes. Use the kVA to Amps Chart when apparent power needs line-current review before transformer, feeder, or equipment checks.

Formula reference after choosing the input path

DC power formulas

Use these when voltage, current, and resistance are DC or purely resistive values.

Find	Formula	Notes
Power	P = V x I	Use measured voltage and current.
Power	P = I^2 x R	Use when current and resistance are known.
Power	P = V^2 / R	Use when voltage and resistance are known.
Voltage	V = P / I	Keep watts and amps in consistent units.
Current	I = P / V	Use the actual voltage at the load.
Resistance	R = V / I	Match the same circuit segment.

Single-phase AC power formulas

Use these for single-phase AC loads. Include power factor for non-resistive loads.

Find	Formula	Notes
Real power	P = V x I x PF	PF matters for motors, transformers, and many electronic loads.
Apparent power	S = V x I	Use VA or kVA for apparent-power equipment checks.
Power factor	PF = P / S	Use real and apparent power from the same operating point.
Current	I = P / (V x PF)	Do not omit PF unless the load basis supports it.
Reactive power	Q = sqrt(S^2 - P^2)	Use with consistent VA and W units.

Balanced three-phase formulas

Use line voltage and line current unless your calculation explicitly uses phase values.

Basis	Real power	Apparent power
Line values	P = sqrt(3) x V_L x I_L x PF	S = sqrt(3) x V_L x I_L
Phase values	P = 3 x V_ph x I_ph x PF	S = 3 x V_ph x I_ph

Key inputs:

V_L = line-to-line voltage.
I_L = line current.
V_ph = phase voltage.
I_ph = phase current.
PF = power factor.

Power factor formulas

Find	Formula
Power factor	PF = P / S
Power factor	PF = cos(theta)
Real power	P = S x PF
Apparent power	S = P / PF
Reactive power	Q = S x sqrt(1 - PF^2)
Correction kVAR	kVAR = kW x (tan(theta1) - tan(theta2))

Use the Power Factor Calculator for correction sizing because utility targets, step sizes, harmonic conditions, and owner requirements affect the final capacitor-bank decision.

Conversion formulas

Conversion	Formula	Use carefully
W to kW	kW = W / 1000	Unit conversion only.
kW to W	W = kW x 1000	Unit conversion only.
HP to W	W = HP x 746	Mechanical-output basis.
HP to kW	kW = HP x 0.746	Mechanical-output basis.
kW to HP	HP = kW / 0.746	Mechanical-output basis.
kW to kVA	kVA = kW / PF	Requires power factor.
kVA to kW	kW = kVA x PF	Requires power factor.

For motors, the mechanical conversion is not the same as electrical input. Use the Motor Power Calculator when efficiency, PF, voltage, and current matter.

Common U.S. voltage inputs

These values are common inputs, not automatic answers. Confirm the equipment nameplate and system configuration before calculating.

System	Common voltage input	Typical use
Single-phase	120 V	Receptacles, lighting, small loads
Single-phase	240 V	Residential appliances and equipment
Three-phase wye	208 V line-to-line	Commercial systems derived from 120/208 V
Three-phase delta	240 V line-to-line	Light commercial and some motor loads
Three-phase wye	480 V line-to-line	Industrial equipment and larger motors

When a calculator asks for line-to-line voltage, do not enter line-to-neutral voltage unless the calculator field specifically asks for phase voltage.

Calculator checks instead of worked answers

Use these scenarios as calculator inputs, not as standalone conclusions:

Basic DC load check

Choose DC in the power calculator.
Enter the measured voltage and current, or voltage and resistance.
Use the result only for the circuit segment represented by those measurements.
If conductor loss matters, move the current and conductor data to the voltage drop workflow.

Single-phase AC load check

Choose single-phase AC.
Enter voltage, current, and PF when the load is not purely resistive.
Compare real power and apparent power before sizing equipment that is marked in VA or kVA.
Move operating-hours questions to the electricity cost calculator.

Balanced three-phase load check

Choose the three-phase path.
Enter line-to-line voltage, line current, and PF from the same operating condition.
Confirm whether the result should be kW, kVA, current, or voltage.
Route motor nameplate comparisons to the motor power or motor current tools.

Power factor correction check

Enter existing kW, existing PF, target PF, and voltage or current context.
Review the calculated kVAR requirement.
Check utility tariff, harmonic environment, step switching, and equipment rating before selecting correction hardware.

Transformer or feeder apparent-power check

Enter kW and PF only when both values describe the same load condition.
Review kVA as an apparent-power input, not as a final transformer order by itself.
Apply service margin, temperature, duty cycle, and code or equipment constraints in the transformer or feeder workflow.

Common mistakes to avoid

Mistake	Why it causes errors	Better path
Using DC P = V x I for every AC load	It ignores PF and can understate apparent power.	Choose DC, single-phase AC, or three-phase first.
Mixing line and phase values	Three-phase formulas depend on which voltage and current basis you use.	Keep line-to-line, line-to-neutral, line current, and phase current labeled.
Treating HP conversion as motor input power	HP is usually mechanical output, while electrical input also depends on efficiency and PF.	Use the motor power workflow.
Sizing transformers from kW alone	Apparent power and PF affect kVA.	Use kW, PF, and margin together.
Treating conductor loss as a formula-only task	Distance, conductor material, size, and temperature affect resistance.	Use the voltage drop workflow.

Summary

Use this page as the formula map:

DC: choose voltage, current, or resistance relationships.
Single-phase AC: include PF when the load requires it.
Balanced three-phase AC: use the correct line or phase basis.
kW/kVA/HP: confirm whether the value is real power, apparent power, or mechanical output.
Loss and long runs: move to voltage drop and conductor workflows.

When the inputs are known, calculate the answer in the matching tool and then use the formulas here to understand why the result changed.

Related Calculators

Power Calculator

Power Factor Calculator

Frequently Asked Questions

What is the electrical power formula?

Start by choosing the circuit type. DC uses voltage and current directly; single-phase AC adds power factor when the load is not purely resistive; balanced three-phase AC uses line voltage, line current, and power factor. Enter the actual values in the power calculator before using the result for equipment sizing.

What is the difference between kW and kVA?

kW is real power and kVA is apparent power. The link between them is power factor, so transformer, generator, feeder, and motor checks should use the calculator path that includes PF instead of converting from one label alone.

Why does three-phase power use sqrt(3)?

The sqrt(3) factor connects line values to phase relationships in a balanced three-phase system. Use it with the correct line-to-line voltage and line current inputs, then verify the result with the three-phase or power calculator.

How do I calculate motor running power?

Use measured voltage, running current, phase count, power factor, and efficiency when estimating motor input or shaft output. For nameplate HP or kW comparisons, use the motor power calculator so the mechanical-output and electrical-input sides do not get mixed.

How do I convert between HP and kW?

Use the HP and kW conversion factors only after deciding whether you are comparing mechanical shaft output or electrical input. Motor efficiency and power factor can make the electrical input higher than a simple mechanical conversion.