Nothing changes but the voltage across one element
Put three 19.2 ohm elements on a 240 volt three-phase supply. In wye each element sits between a line and the common star point, so it sees 240 divided by 1.732, which is 138.6 volts. It passes 7.22 amps, and because there is only one element in each leg, 7.22 amps is also what the line conductor carries. Three elements at 138.6 volts and 7.22 amps is 3.00 kW.
Move the jumpers to delta and each element now sits directly between two lines, so it sees the whole 240 volts. It passes 12.5 amps. But each line conductor now feeds two elements, and those two currents are 60 degrees apart rather than in step, so the line carries 12.5 times 1.732, which is 21.65 amps. Three elements at 240 volts and 12.5 amps is 9.00 kW.
Three times the power, three times the line current, from the same hardware and the same supply. That is the whole page in two paragraphs, and it is why a machine shipped for one connection and wired for the other either underperforms badly or destroys itself.
Where the 1.732 sits, and where it does not
The factor moves to the opposite side of the ledger between the two connections, and this is where people put it in the wrong place. In wye the voltage is divided by 1.732 and the current is untouched: phase current equals line current. In delta the voltage is untouched and the current is multiplied by 1.732: line current is 1.732 times phase current. Total power comes out as 1.732 times line volts times line amps times power factor either way, which is the one formula that does not care which connection you used.
The factor of three between the two connections is the square of 1.732, and it is exact for any element and any supply voltage. It is not an approximation and it does not drift with the power factor, because both connections carry the same power factor through the same arithmetic.
The single element across two lines
Take one of those 19.2 ohm elements and connect it alone between two of the three lines. It sees 240 volts and draws 12.5 amps, making 3.00 kW — a third of the delta bank, from a third of the elements. Two of the three line conductors carry 12.5 amps and the third carries nothing at all.
That is a perfectly ordinary thing to do and it is also the origin of most panel imbalance. Every 240 volt single-phase load on a three-phase panel loads exactly two of the three lines, and the arithmetic of adding several of those up is not addition, because the currents on any shared line arrive at different angles. The balance calculator handles that properly.
What an open element looks like
The page works both failures because they look different on a meter. In wye with no neutral, losing one element throws the other two into series across the line voltage: 240 volts across 38.4 ohms is 6.25 amps and 1.50 kW, exactly half the original output, on two lines only. In delta, losing one element leaves the other two at full voltage and full current, so output falls to 6.00 kW — two thirds — and the line currents go to 12.5, 12.5 and 21.65 amps.
Neither failure trips anything. Both show up as a process that has quietly slowed down, and the clamp meter reading that identifies which one you have is the lopsided line current rather than the total.
What this does not tell you
It does not tell you whether the wiring, the contactor or the overcurrent device can carry the delta current. Tripling the line current on an existing installation is an installation question with an ampacity table and an inspector attached to it, and no arithmetic on this page has an opinion about it. It also assumes three identical elements, which is what a bank is supposed to be and is not always what it still is after a few years.
Questions people ask
Why does delta give three times the power of wye?
Because each element sees 1.732 times more voltage in delta, and power in a fixed resistance goes as the square of the voltage. 1.732 squared is 3. It is exact rather than approximate, and it holds for any element value, any supply voltage and any power factor, because both connections run through the same arithmetic with the same power factor in it.
Is line current the same as phase current in a delta?
No, and this is the one people get backwards. In delta the phase current is what flows through one element and the line current is 1.732 times larger, because two elements feed every line conductor. In wye it is the other way round: line current equals phase current, and it is the voltage that gets divided by 1.732 instead.
Can I rewire a three-phase heater bank from wye to delta to get more heat?
The elements would make three times the heat, which is exactly the problem. The line current triples too, and whether the conductors, the contactor, the overcurrent device and the elements themselves can live with that is an installation question for a licensed electrician working from the adopted code and the equipment ratings. This page computes the currents and stops there.
How do I get the element resistance if I only have a wattage?
Divide the square of the voltage the wattage is rated at by the wattage, and multiply by the power factor. A 3,000 W element rated at 240 V is 240 squared over 3,000, which is 19.2 ohms. Measuring a cold element with a meter gives a slightly lower figure than it will show hot, because resistance climbs with temperature.
What happens to the line currents if one element opens?
In a three-wire wye the two survivors go in series across the line voltage, halving the output and leaving one line conductor carrying nothing. In delta the two survivors keep full voltage, output falls to two thirds, and the line currents split unevenly: two lines carry the phase current and the line shared by both survivors carries 1.732 times it. The page prints both.