How it works
Three-phase: kVA = √3 × V × I / 1000. kW = kVA × PF. kVAR = √(kVA² − kW²). Reverse: I = kVA × 1000 / (√3 × V). Single-phase drops the √3.
V is the line-to-line (phase-to-phase) voltage — always use line-to-line for three-phase, never the 277 V or 120 V line-to-neutral value, or you overstate the current by about 73%. The √3 (≈ 1.732) factor appears because the three line currents in a balanced system are 120° apart. PF is the power factor, the cosine of the angle between voltage and current: kW = kVA × PF is the real power that does work, while kVAR = kVA × √(1 − PF²) is the reactive power that magnetizes motor windings but does no work. For a motor, NEC 430.6(A)(1) requires you to size conductors from the Table 430.250 full-load current, not the nameplate amps, and NEC 430.22 sets the conductor floor at 125% of that FLC. The readout keeps each secondary value short (a number), so the power factor and the reactive kVAR ride in the kVA metric’s label, and the conductor and breaker basis (125% of FLC, 250% for the breaker) ride in their labels. The breaker line shows the maximum 250% inverse-time rating; under 430.52(C)(1) Exception 1 you may go to the next standard size up if the motor will not start on it. The matching 175% dual-element (time-delay) fuse limit — 47.25 A, a 45 A fuse for the default 27 A FLC — is in the breaker FAQ below. Once you have the line amps, confirm the run length on the voltage-drop calculator.
Code references
- Three-phase motor full-load currents NEC 2023, Table 430.250 — Full-Load Current, Three-Phase AC Motors
- Single-motor conductor sizing (125% of FLC) NEC 2023, 430.22 — Single Motor, continuous-duty conductors
- Branch-circuit short-circuit / ground-fault protection NEC 2023, 430.52 and Table 430.52 — 250% FLC inverse-time breaker, 175% dual-element fuse
- Use of Table FLC for sizing, not nameplate NEC 2023, 430.6(A)(1) — ampere-rating determination
- Continuous non-motor feeder / branch load (125%) NEC 2023, 215.2 and 220.14 — feeder and branch-circuit loads
- Standard overcurrent device ratings NEC 2023, 240.6(A)
FAQ
Why is there a √3 in three-phase power?
In a balanced three-phase system the three line currents are 120° apart, not in step. When you add their instantaneous power contributions vectorially, the line-to-line voltage and line current combine through a factor of √3 (about 1.732), not 2 or 3. So total power is √3 × V(line-to-line) × I(line) × PF. It is a consequence of the 120° geometry, not an arbitrary fudge factor.
Do I enter line-to-line or line-to-neutral voltage for three-phase?
Line-to-line (phase-to-phase) — the value the panel nameplate shows and a voltmeter reads across two hot legs: 480 V, 208 V or 240 V. In a wye system the line-to-neutral voltage is the line-to-line value ÷ √3 (277 V on a 480Y/277 system, 120 V on a 208Y/120 system). Using the line-to-neutral value in the three-phase formula shrinks the denominator and overstates the current by about 73% — the single most common wrong answer.
What is the difference between kW, kVA and kVAR?
kW is real power — the part that does work and shows up on the utility energy bill. kVA is apparent power — the actual volt-amperes the conductors and transformer must carry. kVAR is reactive power — the magnetizing current a motor or transformer pulls that does no useful work but still loads the system. They form the power triangle: kVA² = kW² + kVAR², and PF = kW ÷ kVA. You size transformers and generators in kVA, conductors and breakers from the amps (driven by kW and PF), and capacitor banks in kVAR.
Why does the NEC use Table 430.250 FLC instead of the motor nameplate amps?
NEC 430.6(A)(1) requires the full-load current from Table 430.250 (not the nameplate amps) to size branch-circuit conductors and short-circuit/ground-fault protection. The table values are deliberately conservative and standardized so sizing does not vary motor-to-motor. The nameplate amps are still used for the separate overload (running protection) calculation under 430.32. That is why this calculator cross-checks your entered current against the table FLC for the selected horsepower.
What conductor size does a 20 HP, 480 V motor need?
NEC Table 430.250 lists 27 A full-load current for a 20 HP motor at 460 V (the table column nearest 480 V). NEC 430.22 requires the conductor ampacity to be at least 125% of that: 27 × 1.25 = 33.75 A. Pick a conductor whose 75 °C ampacity meets or exceeds 33.75 A — for copper that is 10 AWG (35 A). Then verify voltage drop and conduit fill, and confirm with the wire ampacity chart and a licensed electrician.
How big a breaker does the motor branch circuit need?
For motor branch-circuit short-circuit and ground-fault protection, NEC 430.52 and Table 430.52 allow an inverse-time breaker rated up to 250% of the table FLC and a dual-element (time-delay) fuse up to 175%. For a 27 A FLC that is 67.5 A (round down to a 60 A breaker, or up to the next standard size if the motor will not start, per 430.52(C)(1) Exception 1) and 47.25 A (a 45 A fuse). This protective device is separate from the overload relay that protects against running overcurrent.
This calculator is provided for estimation purposes. Motor and feeder sizing depends on the motor listing, conductor type and terminations, ambient and grouping derating, and local amendments. Always verify against the current NEC edition with a licensed electrician or electrical engineer before sizing conductors or overcurrent protection.