Electrical Power Formulas: The Complete Reference Sheet
This page collects every core electrical-power formula used across this site's calculators, in one scannable sheet: Ohm's Law, Watt's Law, single- and three-phase AC power, the standard unit conversions, and the power triangle. It's built for looking something up mid-calculation, not for reading start to finish. Skip the prose and jump straight to the formula block you need; every constant on this page matches the calculators exactly, so a number worked out here will match one worked out there.
Ohm's Law
Ohm's Law relates voltage, current and resistance in any DC circuit or any purely resistive AC load, and it's the base every other formula on this page builds from. It says nothing about power or power factor on its own. That's what Watt's Law adds below. Any one of the three rearrangements works once the other two values are known, and none of them requires knowing the circuit's power rating first. Because it has no power-factor term, it's most useful for troubleshooting fixed resistive loads such as heating elements, incandescent lamps, and simple DC circuits like batteries and LEDs.
I = V / R
R = V / I
| Known | Solve for | Formula |
|---|---|---|
| Current, resistance | Voltage | V = I × R |
| Voltage, resistance | Current | I = V / R |
| Voltage, current | Resistance | R = V / I |
Watt's Law
Watt's Law defines power itself: voltage times current. Combining it with Ohm's Law gives two more ways to reach the same power figure without measuring every quantity directly, useful when only current and a resistance value, or only voltage and a resistance value, are on hand. None of these three forms include a power-factor term, which is why they only apply directly to DC or purely resistive AC loads. The two combined forms are handy shortcuts: they skip a step when only two of the three base quantities are already known, rather than solving Ohm's Law first and Watt's Law second.
P = I² × R
P = V² / R
| Known | Solve for | Formula |
|---|---|---|
| Voltage, current | Power | P = V × I |
| Current, resistance | Power | P = I² × R |
| Voltage, resistance | Power | P = V² / R |
| Power, current | Voltage | V = P / I |
| Power, voltage | Current | I = P / V |
Single-phase AC power
For single-phase AC, kilowatts equal apparent power scaled down by the power factor, the fraction of the circuit's current that's actually doing work rather than just circulating. A purely resistive load such as a heater or incandescent lamp runs at PF = 1, which collapses this formula back to Watt's Law. Anything with a motor, transformer or switching supply runs below 1 and needs its real power factor for an accurate result. The formula also runs in reverse to solve for voltage or power factor, shown in the table below.
A = (kW × 1000) / (V × PF)
| Known | Solve for | Formula |
|---|---|---|
| Volts, amps, PF | kW | kW = (V × A × PF) / 1000 |
| kW, volts, PF | Amps | A = (kW × 1000) / (V × PF) |
| kW, amps, PF | Volts | V = (kW × 1000) / (A × PF) |
| kW, volts, amps | PF | PF = (kW × 1000) / (V × A) |
Three-phase power formulas
Three-phase circuits use one of two multipliers depending on which voltage was measured: √3 for line-to-line, or 3 for line-to-neutral. Mixing the two up is the single most common three-phase sizing error, because both numbers look like a plausible answer even when the wrong formula was used. A wye system publishes both voltages together; a delta system has no neutral, so only the line-to-line form applies there. Because the three phases peak 120° apart rather than in unison, a line-to-line voltage reading already reflects a vector sum, which is where the √3 factor comes from instead of a plain 3.
Line-to-line: A = (kW × 1000) / (√3 × VLL × PF)
Line-to-neutral: kW = (3 × VLN × A × PF) / 1000
Line-to-neutral: A = (kW × 1000) / (3 × VLN × PF)
| Voltage measured | kW formula | Amps formula |
|---|---|---|
| Line-to-line (VLL) | kW = (√3 × VLL × A × PF) / 1000 | A = (kW × 1000) / (√3 × VLL × PF) |
| Line-to-neutral (VLN) | kW = (3 × VLN × A × PF) / 1000 | A = (kW × 1000) / (3 × VLN × PF) |
Unit conversions
These are the constants behind every unit-conversion calculator on this site, so a figure computed here matches the calculators exactly. Most rows are a single multiplication or division; the kW-to-kVA rows also need the power factor, and the kW-to-kWh rows also need a number of hours, since kWh measures energy rather than power. The BTU and tons rows exist mainly for sizing HVAC and refrigeration equipment, where cooling capacity is usually rated in one of those two units rather than in kilowatts.
| Convert | Formula |
|---|---|
| kW → HP | HP = kW / 0.7457 |
| HP → kW | kW = HP × 0.7457 |
| kW → kVA | kVA = kW / PF |
| kVA → kW | kW = kVA × PF |
| kW → BTU/hr | BTU/hr = kW × 3412.14 |
| BTU/hr → kW | kW = BTU/hr / 3412.14 |
| kW → kWh | kWh = kW × hours |
| kWh → kW | kW = kWh / hours |
| kW → tons of refrigeration | tons = kW / 3.516853 |
| Tons of refrigeration → kW | kW = tons × 3.516853 |
Horsepower here is mechanical (imperial) horsepower. Some nameplates use metric horsepower, which is a slightly different constant.
The power triangle
Apparent power (kVA), real power (kW) and reactive power (kVAR) form a right triangle, with kVA as the hypotenuse. Real power does the useful work; reactive power is what magnetic fields in motors and transformers draw and return without being consumed. The angle between kVA and kW has a cosine equal to the power factor, so a larger angle means a lower power factor and more reactive power relative to real power. A power factor near 1 means the triangle is nearly flat, with reactive power close to zero; a low power factor means a tall, narrow triangle with a large reactive-power share.
kVAR = √(kVA² − kW²)
θ = cos⁻¹(PF)
| Power factor | Angle θ |
|---|---|
| 1.00 | 0.00° |
| 0.95 | 18.19° |
| 0.90 | 25.84° |
| 0.85 | 31.79° |
| 0.80 | 36.87° |
| 0.70 | 45.57° |
For a full worked breakdown of kVA, kVAR and the correction needed to raise a low power factor, see apparent and reactive power and power factor.
Calculators built on these formulas
Formula lookup
Which formula do I use?
Quick answers for picking the right formula path, not just the theory behind it.
Which three-phase formula do I use if I only have the line-to-neutral voltage?
Use the line-to-neutral formula only when the voltage reading is genuinely phase-to-neutral, not phase-to-phase. Plugging a line-to-neutral reading into the line-to-line formula (or the reverse) is the most common three-phase mistake. A wye ('Y') system publishes both figures together, such as 208Y/120 V or 480Y/277 V. A delta system has no neutral at all, so only the line-to-line formula applies there. When a spec sheet doesn't say which voltage it means, line-to-line is the more common default for equipment ratings, but confirming against the source measurement is safer than assuming.
Which formula applies to a DC circuit that a single-phase AC formula doesn't?
A DC circuit has no phase angle, so power factor is fixed at 1 and drops out of the formula entirely. The single-phase AC formula is what remains once PF stops being assumed. kW = (V × A) / 1000 covers DC; kW = (V × A × PF) / 1000 covers single-phase AC, and setting PF to 1 in the AC version collapses it back to the DC one. Anything with a motor, transformer or switching power supply on an AC circuit needs its real power factor, not an assumed 1.0.
How do I go from horsepower straight to amps in one calculation?
Chain two formulas: Watt's Law's motor form to get kilowatts, then the amps formula for the circuit type. Not one formula, but two run back to back. A 15 HP motor converts to 15 × 0.7457 = 11.1855 kW. On a 480 V three-phase line-to-line circuit at 0.88 power factor, that becomes (11.1855 × 1000) / (1.7321 × 480 × 0.88) ≈ 15.29 A. That figure is electrical-side current only: actual full-load amps also depend on motor efficiency, so check the nameplate or the motor FLA estimate before sizing anything.
Which law do I use when the resistance value is missing?
Use Watt's Law, not Ohm's Law, when resistance isn't known: P = V × I needs only the two quantities that are usually measured directly. A clamp meter reads current and a voltmeter reads voltage on almost any circuit, but resistance under load is rarely measured directly. Ohm's Law becomes useful again once power is found: R = V² / P or R = P / I² recovers it afterward, if it turns out to be needed.
Which law do I use when the current value is missing?
Use Ohm's Law, not Watt's Law, when current isn't known but voltage and resistance are: I = V / R needs neither a power reading nor an assumed power factor. This comes up most on a DC or purely resistive circuit, such as sizing a heating element from its rated resistance and the supply voltage. Once current is found, Watt's Law (P = V × I) gives the power figure the other formulas need.
How do I check a computed answer against a second, independent formula?
Recompute the same load through a different formula path: if a line-to-neutral reading and a line-to-line reading describe the same system, both should land on the same kW within rounding. A 208Y/120 V, 40 A, 0.85 PF three-phase load gives 3 × 120 × 40 × 0.85 / 1000 = 12.24 kW from the line-to-neutral formula, and √3 × 208 × 40 × 0.85 / 1000 ≈ 12.25 kW from the line-to-line formula. The one-hundredth-of-a-kW gap is just the standard 208 V nominal being a rounded stand-in for the exact √3 × 120 V value, not a sign either formula is wrong.
How do I solve for voltage instead of current using these formulas?
Every formula on this page rearranges the same way: isolate V on one side and move kW, A and PF to the other. For single-phase AC: V = (kW × 1000) / (A × PF). For three-phase line-to-line: V = (kW × 1000) / (√3 × A × PF). A dedicated kilowatts-to-volts converter automates this rearrangement for all four circuit types.
Which formula do I use to move between BTU per hour and tons of refrigeration?
Convert through kilowatts rather than jumping straight between BTU/hr and tons. Both conversions share the same kW figure as their middle step. BTU/hr = kW × 3412.14 and tons = kW ÷ 3.516853, so a 5 kW cooling load is 17,060.7 BTU/hr and 1.42 tons. Going from BTU/hr straight to tons (BTU/hr ÷ 12,000) gives the same 1.42 tons, since one ton of refrigeration is defined as exactly 12,000 BTU/hr.