Earth Bondhon
Creators
Md Jony Islam Author
Md Jony Islam
CalculatorToolsProjectExpert
Reviewers
Małgorzata Koperska, MD Steven Wooding
Last updated: September 23, 2025

3-Phase Power Calculator: kW, kVA & kVAr from V, I, PF

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V
A
Pf
KW
KVA
KVAr

3 phase power calculator

Compute 3-phase real power (kW), apparent (kVA), and reactive (kVAr) using √3·V·I and power factor. Supports line voltage/current and balanced loads.

industrial load kW

For three phase balanced Load use P(kw) = √3 Vl(V) Il(A)pf / 1000 & S(kva) = √3 Vl Il / 1000. Reactive power is Q(kVAr) = P/tan – model(arccos(PF)).

Formula & Table Summary:

  • S (VA): √3 x VL x IL
  • P (W): √3 x VL x IL x PF
  • Q (VAr): √3 x VL x IL x sinφ    where φ = arccos(PF)
  • k-units: divide by 1000
  • Alt: Q (kVAr) = P (kW) x tan(arccos(PF))

400V 3 phase kW; 415V 3 phase kW

The 3 Phase Power Calculator finds the real power (kW), apparent power (kVA), and reactive power (kVAr) of three-phased, balanced systems. To immediately obtain results, enter line-to-line voltage (V L ), line current (I L ),, and the power factor (PF). By definition, the apparent power is S = 1/2 3 VL IL. Real power gets power factor: P = 1/2 3 VL IL PF. The reactive power is obtained as a consequence of the phase angle 4: Q = 3-vector-root-of-3-times-V_L-times-I_L-times-sin4 (replacing the factor of sin4 by PF, the result is Q = P times tan (arccos (PF)). The results can be indicated in kW/ kVA/ kVAr after division by 1000. These formulae are used in motors, HVAC equipment, switchboards, and distribution feeders on a 3-phase network (e.g,. 208V, 400/415V, 480V). Use them to size conductors, breakers, transformers, or check nameplate ratings and energy demand. The calculator uses balanced loads, single-phase calculations may be used with single-phase or unbalanced systems, and adds the answers.

three-phase power calculator

V_L (V)I_L (A)PFS (kVA)P (kW)Q (kVAr)
400500.8534.6429.4518.56
415800.9057.4951.7424.92
4801000.8083.1466.5149.89

Frequently Asked Questions - 3 phase power calculator:

What is the 3-phase power formula for kW?

P(kW)=√3·V_L(V)·I_L(A)·PF/1000.

How do I get kVA from voltage and current?

S(kVA)=√3·V_L·I_L/1000 for balanced loads.

How is reactive power calculated?

Q(kVAr)=P·tan(arccos(PF)) or √3·V_L·I_L·sinφ/1000.

What voltage should I use?

Use line-to-line voltage (e.g., 400/415/480 V) for the √3 formulas.

Does frequency affect the formula?

No, not directly. Frequency affects equipment behavior but not the algebra here.

Can I use these for unbalanced loads?

Compute per phase and sum P, Q, and S. These closed forms assume balance.

How do I improve PF?

Add capacitors/VFDs to reduce reactive power and current draw.

What’s the relation between kW, kVA, and PF?

PF=P/S, with P in kW and S in kVA.

How do I find current from kW?

I_L= P(kW)·1000 /(√3·V_L·PF).

Is motor efficiency part of PF?

No. Efficiency links mechanical kW to electrical kW; PF links kW to kVA.

Md Jony Islam

Md Jony Islam

CalculatorToolsProject

Founder of Earthbondhon.com

a free online tools website designed to make everyday and engineering-related calculations easier for students, professionals, and hobbyists. The site offers a wide range of basic calculators across key categories, including Electrical Calculators, Electronic Calculators, and Time & Date Calculators.