Three Phase Power Calculator
Free Three phase power Calculator for electrical projects. Enter dimensions to get material lists and cost estimates. Get results you can export or share.
Formula
P = โ3 ร VL ร IL ร PF | S = โ3 ร VL ร IL | Q = โ3 ร VL ร IL ร sin(ฯ)
Three-phase power calculations use the square root of 3 (โ1.732) multiplied by line voltage and line current. Real power (P) includes the power factor, apparent power (S) is the total VA, and reactive power (Q) accounts for the phase angle. These formulas apply to both star (Y) and delta (ฮ) connections when using line values.
Worked Examples
Example 1: Industrial Motor Load
Problem: A 480V three-phase motor draws 52A at a power factor of 0.87 in star connection. Calculate all power values.
Solution: VL = 480V, IL = 52A, PF = 0.87\nReal Power: P = โ3 ร 480 ร 52 ร 0.87 = 37,598W = 37.6kW\nApparent Power: S = โ3 ร 480 ร 52 = 43,217VA = 43.2kVA\nReactive Power: Q = โ3 ร 480 ร 52 ร sin(29.5ยฐ) = 21,297VAR = 21.3kVAR\nPhase Voltage: 480/โ3 = 277.1V\nEquivalent HP: 37,598 / 745.7 = 50.4HP
Result: P = 37.6kW | S = 43.2kVA | Q = 21.3kVAR | 50.4HP
Example 2: Commercial Building Supply
Problem: A building has a 400V three-phase supply (star) drawing 200A with PF = 0.92. What is the total power consumption?
Solution: VL = 400V, IL = 200A, PF = 0.92\nReal Power: P = โ3 ร 400 ร 200 ร 0.92 = 127,435W = 127.4kW\nApparent Power: S = โ3 ร 400 ร 200 = 138,564VA = 138.6kVA\nReactive Power: Q = โ3 ร 400 ร 200 ร sin(23.1ยฐ) = 54,316VAR = 54.3kVAR\nPhase Voltage: 400/โ3 = 230.9V
Result: P = 127.4kW | S = 138.6kVA | Q = 54.3kVAR
Frequently Asked Questions
What is three-phase power?
Three-phase power is an electrical power distribution method that uses three alternating currents, each offset by 120 degrees from each other. It is the standard for industrial and commercial power distribution worldwide because it delivers more power than single-phase with the same amount of wire, provides constant power delivery (no zero-crossing dips), is more efficient for motors and large loads, and enables smaller, lighter electrical equipment. Three-phase power is used in factories, data centers, commercial buildings, and for powering motors above about 5 HP.
What is power factor and why does it matter?
Power factor (PF) is the ratio of real power (kW) to apparent power (kVA), ranging from 0 to 1. It indicates how effectively electrical power is being used. A power factor of 1.0 (unity) means all power is doing useful work. Low power factor (below 0.85) means more current is needed for the same real power, leading to larger cables, higher losses, utility penalties, and reduced transformer capacity. Common causes of low PF include induction motors (0.7-0.85), fluorescent lighting, and welding equipment. Power factor correction capacitors can improve PF.
How do you calculate three-phase power?
Three-phase power formulas: Real Power (P) = sqrt(3) x VL x IL x PF (in watts). Apparent Power (S) = sqrt(3) x VL x IL (in volt-amps). Reactive Power (Q) = sqrt(3) x VL x IL x sin(phi) (in VAR). Where VL = line-to-line voltage, IL = line current, PF = power factor, and phi = phase angle (arccos of PF). These formulas work for both star and delta connections when using line values. The sqrt(3) factor (approximately 1.732) accounts for the 120-degree phase relationship.
What are common three-phase voltages?
Common three-phase voltages vary by region: In North America: 208V (120V phase), 480V (277V phase), and 600V are standard. In Europe/Asia: 400V (230V phase) is most common, with 690V for larger industrial systems. Medium voltage systems use 4.16kV, 13.8kV, or 34.5kV. The relationship between line and phase voltage depends on the connection type. For star (Y) connections, VL = Vphase x sqrt(3). For delta connections, VL = Vphase.
How accurate are the results from Three Phase Power Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Can I use Three Phase Power Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.