Productive ToolboxThree Phase Power Calculator
Calculate power parameters in 3-phase AC systems including real power (kW), apparent power (kVA), reactive power (kVAR), current, and voltage. Free online calculator for electrical engineers.
Three Phase Power Calculator
Calculate power parameters in 3-phase AC systems including real power (kW), apparent power (kVA), reactive power (kVAR), current, and voltage with instant results.
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Calculation Parameters
Typical: 400-415V (50Hz), 480V (60Hz)
Range: 0.7 to 0.95 (typical industrial)
Standard: 50Hz (EU/Asia), 60Hz (US)
Common System Examples
What Is a Three-Phase Power Calculator?
A three-phase power calculator computes real power (kW), apparent power (kVA), and reactive power (kVAR) for balanced three-phase AC systems — the standard supply configuration for industrial motors, commercial buildings, and most equipment above roughly 10kW. It solves in three directions: find power from voltage, current, and power factor; find required current from a known power rating; or find required voltage from a known power and current.
Three-phase calculations introduce a factor most single-phase formulas don't need: √3 (approximately 1.732), which accounts for the 120-degree phase relationship between the three line conductors. Forgetting this factor — using the single-phase P = V × I × PF formula on a three-phase system — is one of the most common electrical calculation errors, understating power by roughly 42%. This tool builds √3 into every formula so it can't be accidentally dropped, and shows the full derivation so the constant's role is visible at each step.
Built for electrical engineers designing industrial power distribution, electricians sizing motor cables and protection devices, and facility managers verifying three-phase supply and generator capacity. Includes six built-in presets covering common industrial voltage systems in both 50Hz and 60Hz regions, full step-by-step derivation, and text and CSV export — free and entirely browser-based.
Three-Phase Power Formulas
Core Formulas
Real Power (kW) = √3 × V × I × PF ÷ 1000
Apparent Power (kVA) = √3 × V × I ÷ 1000
Reactive Power (kVAR) = √(S² - P²)
Required Current = P × 1000 ÷ (√3 × V × PF)
Example: V = 415V, I = 10A, PF = 0.8
P = 1.732 × 415 × 10 × 0.8 ÷ 1000 = 5.75 kW
- √3 ≈ 1.7321 — the three-phase constant accounting for the 120° phase relationship between lines
- V (line voltage) — measured between any two of the three line conductors
- I (line current) — current flowing in each line conductor (assumes a balanced load)
- PF (power factor) — ratio of real to apparent power, typically 0.80-0.95 for motors at full load
How to Use the Three-Phase Power Calculator
Step-by-Step Guide
- 1Select a calculation mode: Choose to calculate Power, Current, or Voltage, depending on which value you don't already know.
- 2Enter your known values: For Power mode, enter line voltage, line current, and power factor. For Current mode, enter power, voltage, and power factor. For Voltage mode, enter power, current, and power factor.
- 3Enter frequency for reference: Input the system frequency (50Hz or 60Hz) — this doesn't affect the power calculation directly but is recorded for documentation.
- 4Read the calculated result: View the requested value, along with real power (kW), apparent power (kVA), and reactive power (kVAR) derived from the same inputs.
- 5Review the step-by-step derivation: See exactly how √3, voltage, current, and power factor combine at each stage of the calculation.
- 6Apply a preset or export results: Use a built-in preset for common industrial voltage systems, or export the full calculation as text or CSV.
What This Calculator Provides
- ✓Real-time calculation as you type
- ✓Three modes: power, current, voltage
- ✓Real power (kW), apparent power (kVA), reactive power (kVAR)
- ✓50Hz and 60Hz system support
- ✓Full step-by-step derivation with √3 shown explicitly
- ✓Six built-in industrial voltage presets
- ✓Calculation history (saved locally)
- ✓Export as text or CSV file
- ✓No signup required
Real-World Use Cases
Small Industrial Motor Power Verification
An electrician measures a three-phase motor at 415V, 10A, with a power factor of 0.8. Using Power mode, the calculator returns P = 5.75kW, S = 7.19kVA, and Q = 4.31kVAR — confirming the motor's actual power draw against its nameplate rating before commissioning.
Motor Cable Sizing from kW Rating
An engineer needs the full-load current for a 15kW motor at 415V with an expected power factor of 0.85 to size cables and overload protection. Using Current mode, the calculator returns I ≈ 24.55A, which they use to select an appropriately rated cable and overload relay.
Generator Sizing for a Large Industrial System
A project engineer sizing a backup generator for a system rated at 415V, 50A, with power factor 0.9 uses Power mode to find P = 32.35kW and S = 35.94kVA. Since generators are rated in kVA, they specify a unit rated well above 35.94kVA to accommodate the load plus starting surge margin.
US Industrial System at 60Hz
An engineer working on a North American installation at 480V, 15A, power factor 0.85, and 60Hz uses Power mode to find P = 10.6kW — confirming the system's real power draw matches design specifications despite the different regional voltage and frequency standard.
Commercial Building Load Verification
A facility manager verifying a commercial building's three-phase supply at 400V, 30A, power factor 0.85 calculates P = 17.66kW and S = 20.78kVA using Power mode — cross-checking this against the building's utility meter readings to confirm accurate billing.
Required Voltage Verification for a Known Load
A technician troubleshooting a system expected to deliver 20kW at 30A with power factor 0.85 uses Voltage mode to calculate the expected line voltage of approximately 452V — comparing this against a measured 415V supply to identify why the system is underperforming its rated output.
Tips & Common Mistakes
Pro Tips
- 💡Always confirm you're using line voltage (between two phases), not phase voltage (between phase and neutral), as the V input — this calculator's formulas expect line voltage throughout.
- 💡For motor cable and protection sizing, use Current mode with the motor's rated kW and rated power factor from the nameplate, then apply the standard 1.25× continuous load factor on top of the calculated current.
- 💡Use kVA (apparent power), not kW (real power), when sizing generators, transformers, or UPS systems — these components must handle the full current draw regardless of the load's power factor.
- 💡When comparing calculated power against a utility meter reading, remember the meter reads real power (kW) for energy billing purposes — apparent power (kVA) is what determines demand charges on many commercial tariffs.
- 💡Keep frequency-appropriate presets in mind when working across regions — 400-415V/50Hz systems are standard in Europe and much of Asia, while 480V/60Hz is standard for North American industrial systems.
Common Mistakes to Avoid
- ✕Forgetting the √3 factor and using the single-phase formula (V × I × PF) for a three-phase system. This underestimates power by roughly 42% — always confirm the √3 term is included for any three-phase calculation.
- ✕Using phase voltage instead of line voltage in the formula. In a star-connected system, line voltage is √3 times phase voltage — mixing these up produces a result off by that same factor.
- ✕Assuming a perfectly balanced three-phase load when the actual system is unbalanced. This calculator's formulas assume equal current in all three lines — an unbalanced load requires per-phase analysis instead.
- ✕Confusing kW and kVA when specifying generator or transformer capacity. Rating equipment in kW when kVA is needed undersizes it by a factor equal to 1 divided by the power factor.
- ✕Using nominal voltage (415V, 480V) when actual supply voltage differs. Real supply voltage can vary by several percent from nominal, which directly affects calculated current and power figures for precision applications.
Common Three-Phase System Reference
| System | Voltage / Freq | Current / PF | Real Power |
|---|---|---|---|
| Small industrial motor | 415V / 50Hz | 10A / 0.8 | 5.75 kW |
| Medium industrial load | 400V / 50Hz | 20A / 0.85 | 11.78 kW |
| Commercial building | 400V / 50Hz | 30A / 0.85 | 17.66 kW |
| Large industrial system | 415V / 50Hz | 50A / 0.9 | 32.35 kW |
| US industrial (60Hz) | 480V / 60Hz | 15A / 0.85 | 10.60 kW |
| Generator sizing example | 415V / 50Hz | 100A / 0.8 | 57.50 kW |
* Calculated using P = √3 × V × I × PF ÷ 1000. Frequency does not affect the power calculation directly but is shown for regional reference.
Frequently Asked Questions
What is a three-phase power calculator?
A three-phase power calculator is a free online tool that computes real power (kW), apparent power (kVA), and reactive power (kVAR) for balanced three-phase AC systems. It supports three modes: calculate power from voltage, current, and power factor; calculate current from power, voltage, and power factor; or calculate voltage from power, current, and power factor.
What is the formula for three-phase power?
Real power: P = √3 × V × I × PF ÷ 1000 (kW). Apparent power: S = √3 × V × I ÷ 1000 (kVA). Reactive power: Q = √(S² - P²) (kVAR). For example, a 415V, 10A system with power factor 0.8: P = 1.732 × 415 × 10 × 0.8 ÷ 1000 = 5.75kW.
Why does three-phase power use a √3 factor instead of the single-phase formula?
In a balanced three-phase system, the three line voltages and currents are 120 degrees apart in phase, and the vector sum of the power delivered across all three phases simplifies to √3 × V_line × I_line, rather than a simple 3× multiplier you might expect from adding three identical single-phase circuits. Using the single-phase formula (V × I) for a three-phase system without this factor underestimates power by about 42%.
What is the difference between line voltage and phase voltage in a three-phase system?
Line voltage is measured between any two of the three line conductors, while phase voltage is measured between one line conductor and neutral. In a star (wye) connection, line voltage equals phase voltage × √3 — a common 230V phase voltage corresponds to 400V line voltage. In a delta connection, line voltage equals phase voltage directly. This calculator uses line voltage and line current throughout.
How do I calculate the current a three-phase motor draws from its kW rating?
I = P × 1000 ÷ (√3 × V × PF), where P is in kW. A 15kW motor at 415V with a power factor of 0.85 draws I = 15,000 ÷ (1.732 × 415 × 0.85) = 15,000 ÷ 613.4 ≈ 24.5A. This is the full-load current used for cable and protection device sizing.
How do I calculate required voltage from a known power, current, and power factor?
V = P × 1000 ÷ (√3 × I × PF). This is useful when verifying a system's expected voltage given a known load and measured current — for example, confirming a 400V supply is delivering the expected voltage under a specific load condition.
Why is power factor needed for three-phase power calculations?
Power factor separates real power (useful work, kW) from apparent power (total supply demand, kVA) in the same way it does for single-phase circuits. Three-phase motors and transformers typically have power factors between 0.80 and 0.95 at full load, so omitting PF and using apparent power as if it were real power overstates useful output significantly.
How does three-phase power calculation change between 50Hz and 60Hz systems?
Frequency itself doesn't appear directly in the P = √3VI×PF formula — power depends on voltage, current, and power factor, not frequency. However, standard system voltages differ by region (400-415V/50Hz in Europe and much of Asia, versus 480V/60Hz in North American industrial systems), which is why this calculator includes frequency as a reference field alongside region-specific presets.
How do I size a generator for a three-phase load?
Calculate the load's apparent power (kVA) using S = √3 × V × I ÷ 1000, since generators are rated in kVA to reflect maximum current delivery capability regardless of the load's power factor. Add margin for motor starting surge current, which can be several times the running current for a brief period during startup.
Is my data private when using this calculator?
Yes. All calculations run entirely in your browser using JavaScript. Your voltage, current, power, and power factor values are never transmitted to any server, stored in any database, or accessible to anyone other than you.
Who Uses This Three-Phase Power Calculator?
Electrical Engineers
Design three-phase power distribution systems and verify motor, transformer, and switchgear ratings.
Electricians
Size cables, breakers, and overload protection for three-phase motors and industrial equipment.
Facility Managers
Verify three-phase supply capacity and cross-check utility meter readings against calculated loads.
Project Engineers
Size backup generators and UPS systems for three-phase industrial and commercial installations.
Electrical Engineering Students
Learn the √3 factor and three-phase power relationships through worked calculation examples.
International Project Teams
Convert between 50Hz/400-415V and 60Hz/480V regional standards during multi-country installations.