AC/DC Power Calculator

Calculate real, apparent, and reactive power plus phase angle for DC, single-phase, and three-phase AC circuits with power factor.

AC/DC Calculator

Calculate real, apparent, and reactive power for DC, AC single-phase, and AC three-phase circuits with power-factor and phase-angle output.

Circuit Type

Voltage

Current

Power Factorcos φ — 0.01 to 1.0

P = V × I × PF · S = V × I · Q = √(S² − P²)
Single-phase AC needs power factor to distinguish real power (watts) from apparent power (VA).

What Is AC/DC Power?

AC and DC describe the two ways electrical power flows. Direct current (DC) flows in one direction at a steady level — the output of a battery, solar panel, or power supply. Alternating current (AC) reverses direction many times a second — 50 Hz across most of the world, 60 Hz in the Americas — and is what every wall outlet delivers because it can be transformed up and down for efficient transmission.

This AC/DC calculator computes real power (watts), apparent power (volt-amps), reactive power (vars), and the phase angle for DC, single-phase AC, and three-phase AC circuits. Enter voltage, current, and — for AC — the power factor, and it applies the correct formula, including the √3 factor for balanced three-phase systems, then shows the live phase relationship between voltage and current on a waveform.

This is one mode of the full Ohm's Law Calculator — you can also jump to the voltage drop calculator or the all-in-one unit converter for related electrical work.

How AC and DC Power Differ

DC power is simply V × I

In a DC circuit there is no phase difference, so all the supplied power is real power: P = V × I. A 12 V battery delivering 5 A provides exactly 60 watts.

AC adds power factor

On AC, current and voltage can fall out of step on reactive loads (motors, transformers, fluorescent ballasts). Real power becomes P = V × I × cos φ, where cos φ is the power factor.

Three-phase uses √3

Balanced three-phase systems carry power on three legs offset by 120°. Line-to-line power is P = √3 × V × I × cos φ, letting smaller conductors carry the same total power as single-phase.

Apparent vs real power

Apparent power (S = V × I, in VA) is what the source must supply; real power (P, in watts) is what does useful work. The gap is reactive power (Q, in vars), which sloshes back and forth without doing work.

AC/DC Power Formulas

Pick the formula for your circuit type. cos φ is the power factor; sin φ = √(1 − PF²). DC has no reactive component, so PF = 1.

P = V × I

All supplied power is real. No phase, no power factor.

Single Phase AC

P = V × I × cos φ

Real power; apparent power S = V × I; reactive Q = √(S² − P²).

Three Phase AC

P = √3 × V × I × cos φ

Line-to-line three-phase; the √3 reflects the three balanced legs.

How to Use the AC/DC Calculator

1
Choose the circuit type
Select DC, AC single-phase, or AC three-phase. The calculator applies the matching formula and shows or hides the power-factor field.
2
Enter voltage and current
Type the source voltage and the line current. For three-phase, use the line-to-line voltage and the line current.
3
Set the power factor for AC
Resistive loads run at PF = 1.0; motors and electronics typically 0.7–0.95. The calculator derives the phase angle from it automatically.
4
Read real, apparent, and reactive power
The result card shows watts, volt-amps, vars, and the phase angle, with an animated waveform illustrating how far current lags voltage.

Key AC/DC Concepts

Power factor (cos φ)

The ratio of real power to apparent power, between 0 and 1. A PF of 1 means voltage and current are in phase; lower PF means the source must supply more current for the same useful power.

Apparent power (VA)

The product of RMS voltage and current, in volt-amps. It sizes your wiring, transformers, and generators — they must carry the full current regardless of power factor.

Reactive power (var)

Power that flows back and forth between source and reactive components without doing net work, measured in volt-amps reactive. Utilities penalise large reactive loads.

Phase angle (φ)

The angle by which current leads or lags voltage on an AC circuit. It equals the inverse cosine of the power factor; 0° is purely resistive, 90° is purely reactive.

AC/DC Power in the Real World

🏠

Home appliance

A 1,500 W resistive heater on 120 V single-phase draws 12.5 A at PF 1.0 — real and apparent power are equal because it's purely resistive.

⚙️

Three-phase motor

A 480 V three-phase motor pulling 60 A at 0.85 PF delivers √3 × 480 × 60 × 0.85 ≈ 42 kW of real power.

🔋

DC battery system

A 48 V battery bank supplying 100 A to an inverter delivers 4,800 W — pure DC, so apparent and real power are identical.

💡

Fluorescent / LED ballast

Lighting ballasts often run at 0.5–0.9 PF, so a fixture drawing 1 A at 120 V supplies 120 VA but only 60–108 W of real power.

🏭

Industrial plant

Factories monitor power factor closely because utilities bill on apparent power; capacitor banks correct PF back toward 1.0 to cut demand charges.

🔌

UPS and generator sizing

UPS and generators are rated in kVA, not kW, because they must supply the full apparent current — power factor decides how many watts you actually get.

Best Practices for AC Power

✓Always include power factor on AC. Ignoring PF overstates the useful power. A 0.8 PF load delivers only 80% of its apparent power as real watts.
✓Size wiring and breakers on apparent power. Conductors carry the full current regardless of phase, so use VA (or the line current) — not watts — to size cables, breakers, and transformers.
✓Use line-to-line voltage for three-phase. The √3 formula expects the line-to-line voltage and the line current. Mixing in phase voltage is a frequent source of error.
✓Correct poor power factor. Capacitor banks bring inductive loads back toward unity PF, reducing current, losses, and utility demand charges above roughly 5 kW.
✓Don't apply DC formulas to reactive AC loads. P = V × I only equals the real power when PF = 1. For motors and electronics, use P = V × I × cos φ.

Common AC/DC Mistakes

Confusing watts and volt-amps

Watts are real power; volt-amps are apparent power. They're equal only at unity power factor — assuming so on motors undersizes equipment.

Forgetting the √3 in three-phase

Omitting the √3 factor understates three-phase power by about 42%. Always use P = √3 × V × I × cos φ for balanced systems.

Ignoring power factor on motors

Motors and ballasts run well below unity PF. Treating them as resistive overstates real power and can trip an undersized supply.

Using phase voltage with the line formula

The three-phase line-to-line formula needs the line-to-line voltage. Plugging in phase voltage gives an answer off by √3.

Why AC/DC Power Analysis Matters

Almost all power is generated, transmitted, and billed as AC, yet the watts that actually do work depend on power factor, phase, and circuit type. Confusing apparent and real power leads to undersized generators, tripped breakers, surprise utility demand charges, and motors that won't start under load — mistakes that scale with the size of the installation.

Three-phase distribution underpins virtually all industrial and commercial power because it moves more energy through less copper. Understanding the √3 relationship, power factor, and the split between real, apparent, and reactive power is fundamental to sizing services, correcting power factor, and keeping an electrical system efficient and code-compliant.

Built for electricians, electrical engineers, facilities and maintenance staff, and students working with single-phase and three-phase power.

Formulas cross-checked against standard electrical engineering references — see our methodology and editorial policy. Educational only — always confirm critical designs with a licensed electrician and your local electrical code.

AC/DC Calculator FAQs

DC (direct current) flows steadily in one direction, like a battery or solar panel. AC (alternating current) reverses direction at a fixed frequency — 50 Hz in most of the world, 60 Hz in the Americas. AC dominates the grid because transformers can step it up to high voltage for efficient long-distance transmission and back down for use; DC dominates electronics and battery systems.

For a balanced three-phase load, real power is P = √3 × V × I × cos φ, where V is the line-to-line voltage, I is the line current, and cos φ is the power factor. For example, 480 V at 60 A and 0.85 PF gives √3 × 480 × 60 × 0.85 ≈ 42,400 W, or about 42 kW.

Power factor is the ratio of real power (watts) to apparent power (volt-amps), a number between 0 and 1. It equals the cosine of the phase angle between voltage and current. A power factor of 1 means they are perfectly in phase (a purely resistive load); motors and electronics typically run at 0.7–0.95.

Real power (watts) does useful work. Apparent power (volt-amps) is the product of RMS voltage and current — what the source must actually supply. Reactive power (vars) is the part that flows back and forth with reactive components without doing work. They relate as S² = P² + Q², where S is apparent, P is real, and Q is reactive power.

Multiply kVA by the power factor: kW = kVA × PF. So 10 kVA at a power factor of 0.8 delivers 8 kW of real power. To go the other way, divide: kVA = kW ÷ PF. This is why generators and UPS units are rated in kVA — the watts you get depend on the load's power factor.

Three-phase distributes the load across three conductors offset by 120°, so the same total power moves through smaller wires than single-phase would need, and the power delivery is smoother (it never drops to zero). This is why nearly all industrial motors and commercial services use three-phase power.

No. Power factor only applies to AC, where voltage and current can be out of phase. In a DC circuit there is no phase difference, so all the supplied power is real power and the calculation is simply P = V × I. This calculator sets the power factor to 1 automatically when you choose DC.

The calculator uses exact trigonometric and algebraic formulas, so its precision exceeds any practical requirement. Real-world accuracy depends on your inputs — particularly the power factor, which varies with load — and on assuming a balanced three-phase system. For critical work, measure power factor with a true-RMS meter or power analyzer.