Example 1
A heater on a 120 V supply, the usual mains voltage in the United States, draws 12.5 A. This is the product, not a product certification.
P = 1500 W (1.5 kW) · R = 9.6 Ω
Power Calculator
Enter voltage U in volts and current I in amperes. The calculator finds electric power from P = U·I. At 120 V and 12.5 A the result is 1500 W, or 1.5 kW. The model does not apply cos φ, three-phase √3, or wire and breaker sizing.
Result
Enter voltage U in volts and current I in amperes. Power, equivalent resistance, and the chart will appear here.
Voltage from power: U = P/I. Current from power: I = P/U. Mechanical rate: P = W/t.
How it works
U120 V
I12.5 A
P1500 W
Electric power in a DC circuit is the product of voltage and current: P = U·I. One watt is one volt times one ampere: 1 W = 1 V·A = 1 J/s. At 120 V and 12.5 A the product is 1500 W, or 1.5 kW. This is the textbook definition of electric power (Halliday, Resnick, and Walker; Young and Freedman). On a resistive element the same number is the Joule heating power.
The calculator uses the two numbers you enter: voltage U in volts (field moc-prad-napiecie-a) and current I in amperes (field moc-prad-napiecie-b). The result is their product. The same 12.5 A at 230 V would be a different power, because the voltage is different. A European kettle at 230 V and 10 A is 2300 W. A 5 V supply at 0.02 A is 0.1 W. A 1.5 V cell at 0.1 A is 0.15 W.
What the result panel shows. Besides power in watts, the calculator repeats the voltage and current you entered, and from 1000 W it also shows kilowatts. When current is not zero, it reports equivalent resistance R = U/I and checks that P = I²·R and P = U²/R give the same watts when resistance is not zero either. It adds the energy of one hour if that power stays constant: 1500 W is then 1.5 kWh. The chart draws power against current at the voltage you entered.
Limits of the model. The calculator does not solve U = P/I or I = P/U. Those unknowns have their own pages. It does not compute efficiency, does not size a wire or a breaker, and does not know the power factor. On alternating current, real power is P = U·I·cos φ. The product alone is real power only when cos φ = 1, for example on direct current or on a resistive load described by RMS values.
A comma and a period in the fields are the same decimal separator. Enter 20 mA as 0.02 A. There is no kilowatt field: 1.5 kW appears beside the result when the product is at least 1000 W. Zero volts or zero amperes gives 0 W. At zero current, R = U/I is undefined. Negative values are allowed and mark the direction of the arrows.
Examples on this page include a 120 V heater at 12.5 A → 1500 W, a 12 V circuit at 5 A → 60 W, and a USB port at 5 V and 0.5 A → 2.5 W. The button “Fill this example” enters those same numbers and refreshes the panel and the chart. The fields start empty. A 230 V, 10 A pair is 2300 W and is included as a European comparison, not as a US branch-circuit model.
Formula
P = U · I
P = I²R and P = U² / R, when R = U/I and the denominator is not zero.
W = P · t at constant power. Time is not a field on this page.
Named model: DC electric power, and Joule heating in a resistive element. The calculator multiplies the voltage and current you enter. It does not compute impedance or power factor.
Theory, derivation, and domain
Definition of electric power and the SI watt
Electric power is the rate of energy transfer. For a two-terminal element on direct current, the power absorbed is P = U·I. U denotes the voltage across the terminals, and I denotes the current through the element. Under the passive sign convention, a positive product means energy absorbed.
The watt is an SI derived unit: 1 W = 1 J/s = 1 V·A. The definition this calculator uses is elementary. It multiplies the two numbers you enter. It does not realize the laboratory standard of the watt.
Watt, Joule, and where the product U·I comes from
The watt is named for James Watt (1736–1819), the mechanical engineer associated with the improved steam engine. James Watt did not write the electrical formula P = U·I. The name of the mechanical power unit later moved into electrical engineering.
In 1841 James Prescott Joule described the heat released in a metallic conductor as proportional to the square of the current. The paper appeared in the Philosophical Magazine, on heat in conductors and in battery cells during electrolysis. For an element that obeys Ohm’s law, that heating power is P = I²R. From U = I·R it follows that I²R = U·I = U²/R.
Relation to Ohm’s law: P = I²R and P = U²/R
This calculator has no resistance field. When current is not zero, it computes equivalent resistance R = U/I from the same pair and checks two textbook forms: P = I²R and, when resistance is not zero either, P = U²/R. At 120 V and 12.5 A the equivalent resistance is 9.6 Ω, and each of the three forms gives 1500 W.
That is not a second resistance measurement. Resistance is the quotient of the voltage and current you entered. A separate Ohm’s-law page fills the missing one of U, I, and R. Here the unknown is watts.
Energy W = P·t and the kilowatt-hour
When power is constant, energy is W = P·t. 1500 W for 3600 s is 1.5 kWh, or 5.4 MJ. The panel shows one hour of energy as an illustration, because time is not a form field. From 1000 W it reports kilowatt-hours, from 1 W kilojoules, and below 1 W joules.
Electrical work with a time you choose, W = U·I·t, is a separate page. Power from work and time, P = W/t, is also a separate page. Here the result stays the product of voltage and current.
Assumptions: direct current and average power
The model assumes that the voltage and current you enter describe the same instant or the same value convention: both steady, or both RMS. On direct current the product is the power. For a sine wave and a resistive load, when the power factor is 1, the product of the RMS values is the average power.
A cold heater has a different resistance than a hot one. A nameplate states power in operation, not the product of a casual measurement on a cold element. The calculator does not ask for temperature or for a temperature coefficient.
Limits: power factor, efficiency, and protection
The calculator has no phase-angle field. It does not separate real, reactive, and apparent power. When cos φ is below 1, real power is smaller than the product of RMS voltage and RMS current. The result is not real power in that case.
The calculator does not compute efficiency η = P_out/P_in, does not choose a wire cross-section, and does not check a breaker. Zero amperes gives zero watts, but equivalent resistance does not exist then. A negative product means energy delivered under the arrow convention you adopted.
Sources
J. P. Joule, on heat evolved in metallic conductors, Philosophical Magazine, 1841. D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, the chapter on current and power. H. D. Young, R. A. Freedman, University Physics, the chapter on current and power. BIPM, The International System of Units (SI), 9th edition: the watt as a derived unit. NIST Special Publication 330. The page is educational.
How to use
- Enter voltage U in volts. For example 120 on a US outlet or 12 on an automotive rail.
- Enter current I in amperes. Enter 20 mA as 0.02.
- Click Calculate or wait for the live result. At 120 V and 12.5 A the calculator shows 1500 W, or 1.5 kW, and an equivalent resistance of 9.6 Ω.
- Check the panel: power, the echoed U and I, the form P = I²R, one hour of energy, and the chart of P(I) at fixed U.
- Need voltage from power? Open U = P/I. Need current? Open I = P/U. This page stays at P = U·I.
Symbol glossary
P denotes power, U denotes voltage, and I denotes current. At 120 V and 12.5 A the result is 1500 W, and the equivalent resistance is 9.6 Ω.
- P
- Power [W]: P = U·I. From 1000 W the calculator also shows kilowatts. At 120 V and 12.5 A the power is 1500 W.
- U
- Voltage [V], field moc-prad-napiecie-a. The same 10 A at 12 V is 120 W, not 2300 W.
- I
- Current [A], field moc-prad-napiecie-b. Enter 20 mA as 0.02 A. Zero amperes gives 0 W.
- R
- Equivalent resistance [Ω], R = U/I, only when current is not zero. At 120 V and 12.5 A the resistance is 9.6 Ω.
- W
- Energy [J] at constant power, W = P·t. One hour at 1500 W is 1.5 kWh. Time is not a field.
Worked examples
Example 2
A European kettle nameplate: 230 V and 10 A. The product is 2300 W. This is not a model of a US branch circuit.
P = 2300 W (2.3 kW) · R = 23 Ω
Example 3
A 12 V automotive circuit at 5 A. That is the order of a cabin lamp or fan, not starter current.
P = 60 W · R = 2.4 Ω
Example 4
A USB port: 5 V and 0.5 A. That is the order of a USB 2.0 load, not a judgment of the cable or the charger.
P = 2.5 W · R = 10 Ω
Example 5
An indicator LED supply: 5 V and 0.02 A. The result is the product at the supply terminals, not the drop on the diode alone.
P = 0.1 W · R = 250 Ω
Example 6
A desk lamp: 120 V and 0.5 A. The classic 60 W order, computed from volts and amperes.
P = 60 W · R = 240 Ω
Example 7
A lithium-ion cell under load: 3.7 V and 2 A. That is terminal power, not capacity in watt-hours.
P = 7.4 W · R = 1.85 Ω
Example 8
A telecom bus: 48 V at 20 A. The product is the bus power in this pair of numbers.
P = 960 W · R = 2.4 Ω
Example 9
A truck circuit: 24 V at 8 A. That is a load on a 24 V rail, not cranking current.
P = 192 W · R = 3 Ω
Example 10
An AA cell: 1.5 V and 0.1 A. A small terminal product, not how long a flashlight runs.
P = 0.15 W · R = 15 Ω
Common questions
What does this calculator compute, and from which formula?
The calculator computes electric power as the product of voltage and current: P = U·I. You enter voltage in volts and current in amperes. At 120 V and 12.5 A the result is 1500 W, or 1.5 kW. When current is not zero, the panel also reports equivalent resistance R = U/I and checks P = I²R and P = U²/R.
Which units should I enter for voltage and current?
Enter voltage in volts and current in amperes. The result is in watts. The field does not read a prefix: enter 20 mA as 0.02 A. A figure such as 1.5 kW is a result from 1000 W upward, not an input. A comma and a period are the same decimal separator. The units switch in the header does not convert volts or amperes.
What happens when voltage or current is zero?
The product is then 0 W. No voltage or no current means no power in this model. At zero current, resistance R = U/I is undefined, so I²R and U²/R have no value. Both fields need a number before the panel appears.
How is this page different from the voltage and current calculators?
Here the unknown is watts, and the inputs are voltage and current. The voltage page solves U = P/I, and the current page solves I = P/U. It is the same trio P, U, and I and the same equation, with a different unknown. A 230 V European kettle at 10 A is 2300 W. This page does not solve for that current from a power target.
Does the formula apply to alternating current?
For direct current, the product U·I is the power. For a sine wave and a resistive load, the same product of RMS values is the average power, because the power factor is 1. When cos φ is below 1, real power is U·I·cos φ, and the product alone is apparent power. The calculator has no phase-angle field.
Where do P = I²R and P = U²/R come from?
James Prescott Joule related heat in a conductor to I²R. When the element obeys Ohm’s law, U = I·R, so I²R = U·I = U²/R. This calculator does not measure resistance separately. It computes R = U/I from the pair you enter and shows that the three forms match when the denominator is not zero.
How is energy different from power on this page?
Power P is the rate of energy transfer, in watts. At constant power, energy is W = P·t. Time is not a form field. The panel adds the energy of one hour only as an illustration: 1500 W for one hour is 1.5 kWh. Work over an arbitrary time is a separate page, W = U·I·t.
Does the calculator compute efficiency, wire size, or a breaker?
No. Efficiency η = P_out/P_in is a separate page and needs two powers. This result is one product. It does not account for conductor length, insulation, temperature, or a breaker trip curve. It does not replace an installation design.
What do a negative voltage or a negative current mean?
The calculator keeps the sign of the product. Two negative signs give positive power, and exactly one negative sign gives negative power. The sign follows the arrow convention: negative power means energy delivered by the element, not a unit mix-up. Nameplate values are usually entered as absolute numbers.
What does the chart under the result show?
The chart holds the voltage you entered and places current at 0, 1/4, 1/2, 3/4, 1, 3/2, and 2 times the absolute value of I. The vertical axis is P = U·I. The button “Fill this example” enters that example’s numbers and refreshes the panel and the chart. The fields start empty.
How do I calculate power with P = U·I?
Multiply voltage in volts by current in amperes. For 120 V and 12.5 A: 120·12.5 = 1500 W.
What is P at 120 V and 12.5 A?
1500 W, or 1.5 kW. That is a typical pair for a resistive load on a 120 V supply.
Must I multiply by cos φ for alternating current?
Not on this page. The result is the product U·I. For a motor or other reactive load, real power is U·I·cos φ; cos φ is not a field here.
Does the calculator find three-phase power √3·U·I?
No. The form has only U and I for one value pair. The √3·U·I·cos φ formula is not a mode on this page.
How is this calculator different from I = P/U and U = P/I?
Here you enter U and I and get P. Separate calculators divide power by voltage or by current when you need I or U.
Sources
The definition, the history, and the derivation come from standard physics and metrology sources, with no invented DOIs.
- Wikipedia — electric power
- Wikipedia — Joule heating
- Wikipedia — James Prescott Joule
- Wikipedia — watt (unit)
- BIPM — The International System of Units (SI), 9th edition
- NIST SP 330 — The International System of Units
- Halliday, D.; Resnick, R.; Walker, J., Fundamentals of Physics — current and power.
- Young, H. D.; Freedman, R. A., University Physics — current and power.
Page updated November 3, 2026.