AmpSizerThree phase power calculator
Three phase power
22.45 kilowatts
from 30 amps at 480 V, power factor 0.90
| Also equal to | Value |
|---|---|
| Current | 30 A |
| Real power | 22,447 W = 22.45 kW |
| Apparent power | 24,942 VA = 24.94 kVA |
| Mechanical equivalent | 30.10 HP |
| In milliamps | 30,000 mA |
- Breaker for this as a continuous load
- 40 A
- Copper conductor that carries it
- 8 AWG
Use the line-to-line voltage — 208, 480, 600. Putting 120 or 277 into a three-phase formula gives an answer three times too small.
A sizing aid from the published NEC tables, not a design — have it signed off by a licensed electrician against the code your inspector enforces. Calculations follow the US NEC; outside the US, follow your local electrical code.
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MonthlyOne thing a month worth measuring, testing or recalculating on a home electrical system — the part of sizing that happens after the install. No product pitches, and nothing that needs a live panel.
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How do you calculate three phase power?
The AmpSizer three-phase result for 30 amps at 480 volts with a 0.9 power factor is 22.45 kW of real power and 24.94 kVA of apparent power. The formula is 1.732 × volts × amps × power factor.
That 1.732 is the square root of three, and it appears because the three phases peak at different moments. The total power is more than one phase alone but less than three times it, and root three is exactly where it lands.
The practical consequence is copper. The same 22 kW at 240 volts single phase would be 93 amps rather than 30, which is four conductor sizes and a much larger conduit for the identical work.
What a given three-phase current is worth in power, at the two systems that cover most work. Unity power factor; multiply by your own for real loads.
| Current | 208 V, 3-phase | 480 V, 3-phase | 600 V, 3-phase |
|---|---|---|---|
| 10 A | 3.6 kVA | 8.3 kVA | 10.4 kVA |
| 20 A | 7.2 kVA | 16.6 kVA | 20.8 kVA |
| 30 A | 10.8 kVA | 24.9 kVA | 31.2 kVA |
| 50 A | 18.0 kVA | 41.6 kVA | 51.9 kVA |
| 100 A | 36.0 kVA | 83.1 kVA | 103.9 kVA |
| 200 A | 72.1 kVA | 166.3 kVA | 207.8 kVA |
| 400 A | 144.1 kVA | 332.6 kVA | 415.7 kVA |
The two shortcuts worth remembering: at 208 V, kVA ≈ amps ÷ 2.8. At 480 V, kVA ≈ amps ÷ 1.2.
Why three phase exists
A single-phase supply delivers power in pulses — twice per cycle it passes through zero, and a motor running on it has to be tricked into starting with a capacitor or a shaded pole.
Three phases overlap, so the total power delivered is constant rather than pulsing, and a motor connected to them starts by itself in the direction the phases rotate. That is the real reason for three-phase distribution: not the copper saving, which is a bonus, but the fact that it makes a rotating field for free.
The copper saving is substantial anyway. Root three is 1.732, so three-phase moves 1.732 times the power of a single-phase circuit at the same voltage and current — with three conductors instead of two, which works out to about 15% less copper per kilowatt before you even account for the higher voltages three-phase systems usually run at.
Frequently asked questions
Why is there a square root of three in three phase formulas?
Because the three phases are 120 degrees apart, so their peaks do not coincide. The vector sum of three equal currents at that spacing is root three times one of them, not three times. It follows from the geometry rather than from a convention, which is why the same 1.732 turns up in every three-phase expression.
Which voltage do I use, 208 or 120?
The line-to-line voltage — 208 in a 208Y/120 system, 480 in a 480Y/277. The lower figure is line-to-neutral and belongs in single-phase calculations only. Using 120 in a three-phase formula is the single most common three-phase error and it produces an answer exactly root-three-squared out.
Can I take a single phase circuit off a three phase panel?
Yes, and it is normal — a 120 V receptacle circuit in a commercial building comes from one leg of a 208Y/120 panel to neutral. That circuit is single phase and has no root three in it. Two legs without a neutral gives 208 V single phase, which is also not a three-phase circuit.
What is a high leg or wild leg delta?
A 240 V delta transformer with one winding centre-tapped for 120 V, which leaves the third leg at 208 V to neutral. It is common on older commercial services and it means one of the three busbars in the panel cannot be used for 120 V loads at all. Anything landing on that leg has to be 240 V.
Is three phase always cheaper to wire?
For large loads, yes, and by a lot: a third of the current per conductor and a much better voltage-drop profile. Below about 5 kW the saving is smaller than the cost of bringing three phases in, which is why houses are single phase and workshops argue about it.
How we calculate this
1.732 × line-to-line volts × amps × power factor, and apparent power is the
same expression without the power factor, where 1.732 is the square root of three. Current from power is
the inverse: watts ÷ (1.732 × volts × power factor). All figures assume a balanced load; an unbalanced
three-phase load is three single-phase calculations and a neutral current that is the vector sum of them.
Where a device and conductor are shown for the resulting current, the current is taken at 125% as a
continuous load, the device is the next standard rating in NEC 240.6(A), and the conductor satisfies Table
310.16 with the ceiling of 240.4(D) applied — with three current-carrying conductors in the raceway rather
than two.Worked example
With Amount 30, Measured in amps, Convert to kilowatts, Voltage 480 V, Supply Three phase, Power factor 0.90, this page works out 22.45 kilowatts. from 30 amps at 480 V, power factor 0.90
- Breaker for this as a continuous load40 A
- Copper conductor that carries it8 AWG
Sources:
The three systems you will meet
208Y/120. The commercial standard in the US. Line-to-line 208, line-to-neutral 120, so the same panel feeds ordinary receptacle circuits and three-phase equipment.
480Y/277. Industrial and large commercial. 277 V lighting, 480 V motors, and a step-down transformer somewhere for the 120 V loads. Lower current for the same power, which is the whole point.
240 V delta, sometimes with a high leg. Older services and rural supplies. No neutral in the delta itself, which is why a high-leg configuration exists at all.