The formulas
| What you want | Formula | Worked example |
|---|---|---|
| Full load current, three phase | I = kVA x 1000 / (1.732 x V) | 500 kVA at 480 volts is 500 x 1000 / (1.732 x 480) = 601 amps. |
| kVA from current, three phase | kVA = 1.732 x V x I / 1000 | A 400 amp service at 208 volts is 1.732 x 208 x 400 / 1000 = 144.1 kVA, so the next standard rating is 150 kVA. |
| Full load current, single phase | I = kVA x 1000 / V | A 50 kVA unit at 240 volts is 50 x 1000 / 240 = 208.3 amps. |
| Real power | kW = kVA x power factor | 300 kVA at a power factor of 0.9 delivers 270 kW. |
| Apparent power from real power | kVA = kW / power factor | 400 kW of load at 0.85 needs 400 / 0.85 = 470.6 kVA, so a 500 kVA unit. |
| Phase voltage in a wye winding | V phase = V line / 1.732 | 480 / 1.732 = 277 volts, which is why the service is written 480Y/277. |
| Turns ratio | a = V primary / V secondary | 12470 / 480 = 26, so primary current is about one twenty sixth of secondary current. |
| Primary current from secondary | I primary = I secondary x V secondary / V primary | 601 amps x 480 / 12470 = 23.1 amps on the primary of a 500 kVA unit. |
| Available fault current at the secondary | I fault = I full load / (%Z / 100) | A 500 kVA unit at 5.5 percent impedance gives 601 / 0.055 = 10,935 amps, before any utility source impedance. |
| Load in percent of rating | Load % = measured kVA / nameplate kVA x 100 | A 300 kVA unit carrying 1.732 x 480 x 290 / 1000 = 241 kVA is at 80 percent. |
V is line to line voltage, I is current per phase, %Z is the nameplate impedance. 1.732 is the square root of three. Free to cite with a link to this page.
Three phase kVA to amps chart
Full load current per phase at the four common secondary voltages.
| kVA | 208 V | 240 V | 480 V | 600 V |
|---|---|---|---|---|
| 15 | 41.6 A | 36.1 A | 18.0 A | 14.4 A |
| 30 | 83.3 A | 72.2 A | 36.1 A | 28.9 A |
| 45 | 125 A | 108 A | 54.1 A | 43.3 A |
| 75 | 208 A | 180 A | 90.2 A | 72.2 A |
| 112.5 | 312 A | 271 A | 135 A | 108 A |
| 150 | 416 A | 361 A | 180 A | 144 A |
| 225 | 625 A | 541 A | 271 A | 217 A |
| 300 | 833 A | 722 A | 361 A | 289 A |
| 500 | 1,388 A | 1,203 A | 601 A | 481 A |
| 750 | 2,082 A | 1,804 A | 902 A | 722 A |
| 1000 | 2,776 A | 2,406 A | 1,203 A | 962 A |
| 1500 | 4,164 A | 3,608 A | 1,804 A | 1,443 A |
| 2000 | 5,551 A | 4,811 A | 2,406 A | 1,925 A |
| 2500 | 6,939 A | 6,014 A | 3,007 A | 2,406 A |
Fault current by rating at 480Y/277
Full load current divided by typical nameplate impedance, with an infinite utility source. Use the actual nameplate impedance for a coordination study.
| kVA | Full load amps | Typical %Z | Available fault current |
|---|---|---|---|
| 45 | 54.1 A | 3.5 | 1,546 A |
| 75 | 90.2 A | 4.0 | 2,255 A |
| 112.5 | 135 A | 4.2 | 3,222 A |
| 150 | 180 A | 4.5 | 4,009 A |
| 225 | 271 A | 5.0 | 5,413 A |
| 300 | 361 A | 5.0 | 7,217 A |
| 500 | 601 A | 5.5 | 10,935 A |
| 750 | 902 A | 5.75 | 15,689 A |
| 1000 | 1,203 A | 5.75 | 20,918 A |
| 1500 | 1,804 A | 6.0 | 30,070 A |
| 2000 | 2,406 A | 6.0 | 40,094 A |
| 2500 | 3,007 A | 6.0 | 50,117 A |
Where these numbers come from
The connection decides which voltage goes into the formula. Delta and wye windings, and what 480Y/277 or 12470 GY/7200 means, are drawn out in the delta wye diagram and the three phase wiring diagram. Impedance, rating and voltages are all read off the nameplate, see the nameplate explained, and tap positions shift the turns ratio by 2.5 percent a step, see taps explained.
Common questions
What is the formula for a three phase transformer?
Full load current is kVA times 1000 divided by the line voltage times 1.732, the square root of three. Going the other way, kVA is 1.732 times voltage times current divided by 1000. Every other three phase transformer calculation starts from those two.
Why does the three phase formula use 1.732?
Because the three phases are 120 degrees apart, and the line voltage of a balanced three phase system is the phase voltage times the square root of three, about 1.732. Total power is spread across three phases, so the current per phase is the total divided by the line voltage times 1.732.
How do you calculate the fault current of a transformer?
Divide the full load secondary current by the percent impedance written as a decimal. A 1000 kVA unit at 480 volts and 5.75 percent impedance has about 1,203 amps full load and about 20,900 amps of available fault current at its terminals. That is the worst case with a stiff utility source, the real figure is lower.
How do you size a three phase transformer?
Add up the load in kVA, or convert the service rating with kVA equals 1.732 times volts times amps divided by 1000, then pick the next standard rating up. The sizing calculator does this from a service rating in one step.
Run the numbers for a specific unit with the kVA to amps calculator, the sizing calculator or the kVA to kW calculator. Need the transformer itself, ask for a quote.